Question: What factor of the initial light source does the energy of the photoelectrons depend on?

Answer: frequency

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. <hl> This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency ; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) <hl> Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the <hl> frequency <hl>; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the <hl> frequency <hl> ; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect)


Question: When the photon energy is less than the work function of the material the light is shone upon, how many photoelectrons are emitted?

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

Answer: no photoelectrons are emitted at all

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. <hl> This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all , unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) <hl> Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), <hl> no photoelectrons are emitted at all <hl>, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), <hl> no photoelectrons are emitted at all <hl> , unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect)


Question: If the photoelectric effect is occuring, increasing the intensity of the light source causes what?

Answer: more photoelectrons to be emitted with the same kinetic energy

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) <hl> Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy , rather than the same number of photoelectrons to be emitted with higher kinetic energy. <hl>

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes <hl> more photoelectrons to be emitted with the same kinetic energy <hl>, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes <hl> more photoelectrons to be emitted with the same kinetic energy <hl> , rather than the same number of photoelectrons to be emitted with higher kinetic energy.


Question: Who introduced the first quantized model of the atom?

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Answer: Niels Bohr

<hl> Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. <hl> In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

<hl> Niels Bohr <hl> introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En


Question: When was the first quantized model of the atom introduced?

Answer: 1913

<hl> Niels Bohr introduced the first quantized model of the atom in 1913 , in an attempt to overcome a major shortcoming of Rutherford's classical model. <hl> In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Niels Bohr introduced the first quantized model of the atom in <hl> 1913 <hl>, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Niels Bohr introduced the first quantized model of the atom in <hl> 1913 <hl> , in an attempt to overcome a major shortcoming of Rutherford's classical model.


Question: Why was the first quantized model of the atom introduced?

Answer: to overcome a major shortcoming of Rutherford's classical model

<hl> Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model . <hl> In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt <hl> to overcome a major shortcoming of Rutherford's classical model <hl>. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt <hl> to overcome a major shortcoming of Rutherford's classical model <hl> .


Question: In classical electrodynamics, a charge moving in a circle should do what?

Answer: radiate electromagnetic radiation

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. <hl> In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation . <hl> If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should <hl> radiate electromagnetic radiation <hl>. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

In classical electrodynamics, a charge moving in a circle should <hl> radiate electromagnetic radiation <hl> .


Question: Who modeled the atom in 1913, challenging Rutherford's model?

Answer: Niels Bohr

<hl> Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. <hl> In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

<hl> Niels Bohr <hl> introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En


Question: What was predicted to happen to a nucleus-orbiting electron under Rutherford's model?

Answer: the radiation would cause it to lose energy and spiral down into the nucleus

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. <hl> If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus . <hl> Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, <hl> the radiation would cause it to lose energy and spiral down into the nucleus <hl>. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

If that charge were to be an electron orbiting a nucleus, <hl> the radiation would cause it to lose energy and spiral down into the nucleus <hl> .


Question: What statement did Bohr make about the electron of an atom, citing Planck's work?

Answer: an electron in a Bohr atom could only have certain defined energies

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. <hl> Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En <hl>

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: <hl> an electron in a Bohr atom could only have certain defined energies <hl> En


Question: Who introduced the reduced Planck constant?

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Answer: Bohr

<hl> Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. <hl> At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

<hl> Bohr <hl> also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values


Question: What is the reduced Planck constant also known as?

Answer: the quantity

<hl> Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. <hl> At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced <hl> the quantity <hl> , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values


Question: Who helped to give the correct quantization rules for electrons in 1925?

Answer: Heisenberg

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. <hl> The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg 's <hl> matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by <hl> Heisenberg <hl>'s matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by <hl> Heisenberg <hl> 's


Question: Who helped to give the correct quantization rules for electrons in 1926?

Answer: Schrödinger

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. <hl> The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. <hl> In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the <hl> Schrödinger <hl> wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values


Question: According to Heisenberg and Schrödinger, the reduced Planck constant remains what?

Answer: the fundamental quantum of angular momentum

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. <hl> The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum . <hl> In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains <hl> the fundamental quantum of angular momentum <hl>. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains <hl> the fundamental quantum of angular momentum <hl> .


Question: Bohr introduced what value as the quantum of angular momentum?

Answer: the reduced Planck constant

<hl> Bohr also introduced the quantity , now known as the reduced Planck constant , as the quantum of angular momentum. <hl> At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as <hl> the reduced Planck constant <hl>, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as <hl> the reduced Planck constant <hl> , as the quantum of angular momentum.


Question: What incorrect belief did Bohr hold about the reduced Planck constant?

Answer: Bohr thought that this was the angular momentum of each electron in an atom

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. <hl> At first, Bohr thought that this was the angular momentum of each electron in an atom : this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. <hl> The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, <hl> Bohr thought that this was the angular momentum of each electron in an atom <hl>: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

At first, <hl> Bohr thought that this was the angular momentum of each electron in an atom <hl> : this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.


Question: What scientist used matrix mechanics to bring electron behavior in line with the Bohr model?

Answer: Heisenberg

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. <hl> The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg 's <hl> matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by <hl> Heisenberg <hl>'s matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by <hl> Heisenberg <hl> 's


Question: When was the Schrödinger wave equation proposed?

Answer: 1926

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. <hl> The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926 : the reduced Planck constant remains the fundamental quantum of angular momentum. <hl> In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in <hl> 1926 <hl>: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in <hl> 1926 <hl> : the reduced Planck constant remains the fundamental quantum of angular momentum.


Question: What measurable value obeys a similar rule of angular momentum?

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

Answer: time vs. energy

One example is time vs. energy .

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. <hl> One example is time vs. energy . <hl> The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is <hl> time vs. energy <hl>. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

One example is <hl> time vs. energy <hl> .


Question: What forces measurement attempts to choose between trade-offs, in quanta?

Answer: either-or nature of uncertainty

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. <hl> The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis. <hl>

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The <hl> either-or nature of uncertainty <hl> forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.


Question: What form do measurement attempt trade-offs for quanta take the form of?

Answer: either-or (as in Fourier analysis)

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. <hl> The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis) , rather than the compromises and gray areas of time series analysis. <hl>

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of <hl> either-or (as in Fourier analysis) <hl>, rather than the compromises and gray areas of time series analysis.

The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of <hl> either-or (as in Fourier analysis) <hl> , rather than the compromises and gray areas of time series analysis.


Question: How is uncertainly measured in this experience?

Answer: the standard deviation of the measured value from its expected value

<hl> where the uncertainty is given as the standard deviation of the measured value from its expected value . <hl> There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

where the uncertainty is given as <hl> the standard deviation of the measured value from its expected value <hl>. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

where the uncertainty is given as <hl> the standard deviation of the measured value from its expected value <hl> .


Question: What type of analysis fits the either-or nature of the uncertainty?

Answer: Fourier analysis

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. <hl> The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis ), rather than the compromises and gray areas of time series analysis. <hl>

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in <hl> Fourier analysis <hl>), rather than the compromises and gray areas of time series analysis.

The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in <hl> Fourier analysis <hl> ), rather than the compromises and gray areas of time series analysis.


Question: What example is given as another paired relationship of uncertainly related to standard deviation?

Answer: time vs. energy

One example is time vs. energy .

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. <hl> One example is time vs. energy . <hl> The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is <hl> time vs. energy <hl>. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

One example is <hl> time vs. energy <hl> .


Question: What is the unit of magentic properties of the electron?

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

Answer: Bohr magneton

<hl> The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. <hl> The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

The <hl> Bohr magneton <hl> and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.


Question: What is the unit of magentic properties of atomic nuclei?

Answer: nuclear magneton

<hl> The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. <hl> The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

The Bohr magneton and the <hl> nuclear magneton <hl> are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.


Question: The Bohr magneton is the magnetic moment of an electron under what restriction?

Answer: behaved as a spinning charge according to classical electrodynamics

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. <hl> The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics . <hl> It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it <hl> behaved as a spinning charge according to classical electrodynamics <hl>. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

The Bohr magneton is the magnetic moment which would be expected for an electron if it <hl> behaved as a spinning charge according to classical electrodynamics <hl> .


Question: What three terms define the Bohr magneton value?

Answer: the reduced Planck constant, the elementary charge and the electron mass

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. <hl> It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass , all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables. <hl>

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of <hl> the reduced Planck constant, the elementary charge and the electron mass <hl>, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

It is defined in terms of <hl> the reduced Planck constant, the elementary charge and the electron mass <hl> , all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.


Question: How was the Planck constant calculated in the early 20th century?

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

Answer: the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons

<hl> In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons , and this is how its value was first calculated in the early twentieth century. <hl> In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

In principle, <hl> the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons <hl>, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

In principle, <hl> the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons <hl> , and this is how its value was first calculated in the early twentieth century.


Question: The value quoted here for the Planck constant is based on a measurement in what year?

Answer: 2007

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. <hl> The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). <hl> Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a <hl> 2007 <hl> watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.


Question: Where was this measurement made?

Answer: the U.S. National Institute of Standards and Technology (NIST)

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. <hl> The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST) . <hl> Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at <hl> the U.S. National Institute of Standards and Technology (NIST) <hl>. Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at <hl> the U.S. National Institute of Standards and Technology (NIST) <hl> .


Question: What method was was used to obtain the measurement?

Answer: watt-balance measurement

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. <hl> The CODATA value quoted here is based on three watt-balance measurement s of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). <hl> Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three <hl> watt-balance measurement <hl>s of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

The CODATA value quoted here is based on three <hl> watt-balance measurement <hl> s of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST).


Question: One other measure involved the molar volume of what element?

Answer: silicon

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. <hl> The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon , but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). <hl> Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of <hl> silicon <hl>, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of <hl> silicon <hl> , but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST).


Question: What is a main practical difficulty in determining n?

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault.

Answer: the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another

There are both practical and theoretical difficulties in determining h. <hl> The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another . <hl> The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault.

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that <hl> the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another <hl>. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault.

The practical difficulties can be illustrated by the fact that <hl> the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another <hl> .


Question: Why does this difficulty occur?

Answer: it is (or they are) not as precise as is currently believed

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. <hl> The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault. <hl>

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – <hl> it is (or they are) not as precise as is currently believed <hl> – but for the time being there is no indication which method is at fault.


Question: Which method is at fault or the discrepancy?

Answer: there is no indication which method is at fault

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. <hl> The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault . <hl>

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being <hl> there is no indication which method is at fault <hl>.

The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being <hl> there is no indication which method is at fault <hl> .


Question: Other than the X-ray crystal density method, other methods rely on what two effects?

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

Answer: the Josephson effect and the quantum Hall effect

<hl> The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect . <hl> If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of <hl> the Josephson effect and the quantum Hall effect <hl>. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of <hl> the Josephson effect and the quantum Hall effect <hl> .


Question: Why does relying on these effects create concern?

Answer: If these theories are slightly inaccurate

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. <hl> If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. <hl> More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. <hl> If these theories are slightly inaccurate <hl> – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.


Question: Using Planck constant values from these effects would lead to what logical issue?

Answer: a circular argument

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. <hl> More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument . <hl> Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into <hl> a circular argument <hl>. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into <hl> a circular argument <hl> .


Question: What is the saving grace of relying on these theories?

Answer: there are other statistical ways of testing the theories, and the theories have yet to be refuted.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. <hl> Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted. <hl>

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, <hl> there are other statistical ways of testing the theories, and the theories have yet to be refuted. <hl>


Question: What is a watt balance?

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant.

Answer: an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units

<hl> A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units . <hl> From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant.

A watt balance is <hl> an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units <hl>. From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant.

A watt balance is <hl> an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units <hl> .


Question: What value does RK represent?

Answer: the von Klitzing constant which appears in the quantum Hall effect

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. <hl> From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect . <hl> If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant.

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is <hl> the von Klitzing constant which appears in the quantum Hall effect <hl>. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant.

From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is <hl> the von Klitzing constant which appears in the quantum Hall effect <hl> .


Question: If the effects are valid, for RK = n/e2, what is the measurement of KJ2RK equal to?

Answer: the Planck constant

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect. <hl> If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant . <hl>

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of <hl> the Planck constant <hl>.

If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of <hl> the Planck constant <hl> .


Question: The gyromagnetic ratio is the constant proportion between the magentic field and what?

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

Answer: the frequency ν of nuclear magnetic resonance

<hl> The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. <hl> It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

The gyromagnetic ratio γ is the constant of proportionality between <hl> the frequency ν of nuclear magnetic resonance <hl> (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.


Question: How does the water molecule impact the effect of magnetic fields on protons?

Answer: The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. <hl> The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule , the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. <hl> The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. <hl> The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule <hl>, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

<hl> The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule <hl> , the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p.


Question: What three factors impact the gyromagnetic ratio?

Answer: related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. <hl> The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant. <hl>

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is <hl> related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant. <hl>


Question: The gyromagnetic ratio is often difficult to determine due to difficulty accurately determining the value of what?

Answer: the applied magnetic field B

<hl> The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B : ν = γB. <hl> It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and <hl> the applied magnetic field B <hl>: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 7002298150000000000♠25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′p, the spin number I (I = 1⁄2 for protons) and the reduced Planck constant.

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and <hl> the applied magnetic field B <hl> : ν = γB.


Question: How many methods of measuring the gyromagnetic ratio are there?

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

Answer: there are two methods of measuring the value

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. <hl> In addition, there are two methods of measuring the value , a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. <hl> Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, <hl> there are two methods of measuring the value <hl>, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

In addition, <hl> there are two methods of measuring the value <hl> , a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases.


Question: How do conversion factors compare in "low-field" and "high-field" methods of measuring the gyromagnetic ratio?

Answer: the conversion factors are different in the two cases

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. <hl> In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases . <hl> Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and <hl> the conversion factors are different in the two cases <hl>. Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and <hl> the conversion factors are different in the two cases <hl> .


Question: Which method is of interest in determining the Planck constant?

Answer: Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. <hl> Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant . <hl>

A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. <hl> Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant <hl>.

<hl> Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant <hl> .


Question: Why is the measurement of electric current an issue in the estimate of the gyromagnetic ratio?

Answer: electric current: this is invariably measured in conventional amperes rather than in SI amperes

<hl> A further complication is that the measurement of γ′p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes , so a conversion factor is required. <hl> The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

A further complication is that the measurement of γ′p involves the measurement of an <hl> electric current: this is invariably measured in conventional amperes rather than in SI amperes <hl>, so a conversion factor is required. The symbol Γ′p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value Γ′p-90(hi) is of interest in determining the Planck constant.

A further complication is that the measurement of γ′p involves the measurement of an <hl> electric current: this is invariably measured in conventional amperes rather than in SI amperes <hl> , so a conversion factor is required.


Question: What is the Faraday constant?

The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant NA multiplied by the elementary charge e. It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

Answer: the charge of one mole of electrons

<hl> The Faraday constant F is the charge of one mole of electrons , equal to the Avogadro constant NA multiplied by the elementary charge e. <hl> It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

The Faraday constant F is <hl> the charge of one mole of electrons <hl>, equal to the Avogadro constant NA multiplied by the elementary charge e. It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

The Faraday constant F is <hl> the charge of one mole of electrons <hl> , equal to the Avogadro constant NA multiplied by the elementary charge e.


Question: How is the Faraday constant determined?

Answer: by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.

The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant NA multiplied by the elementary charge e. <hl> It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. <hl> Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant NA multiplied by the elementary charge e. It can be determined <hl> by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. <hl> In practice, it is measured in conventional electrical units, and so given the symbol F90. Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.


Question: How does the Faraday constant relate to the Planck constant?

Answer: Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant NA multiplied by the elementary charge e. It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. <hl> Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant. <hl>


Question: How is the Farday constant value quickly calculated?

Answer: the Avogadro constant NA multiplied by the elementary charge e

<hl> The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant NA multiplied by the elementary charge e . <hl> It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

The Faraday constant F is the charge of one mole of electrons, equal to <hl> the Avogadro constant NA multiplied by the elementary charge e <hl>. It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F90. Substituting the definitions of NA and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

The Faraday constant F is the charge of one mole of electrons, equal to <hl> the Avogadro constant NA multiplied by the elementary charge e <hl> .


Question: What is the primary method for determining the Avogadro constant?

The X-ray crystal density method is primarily a method for determining the Avogadro constant NA but as the Avogadro constant is related to the Planck constant it also determines a value for h. The principle behind the method is to determine NA as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance. Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry. The unit cell volume is calculated from the spacing between two crystal planes referred to as d220. The molar volume Vm(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used. The Planck constant is given by

Answer: The X-ray crystal density method

<hl> The X-ray crystal density method is primarily a method for determining the Avogadro constant NA but as the Avogadro constant is related to the Planck constant it also determines a value for h. <hl> The principle behind the method is to determine NA as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance. Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry. The unit cell volume is calculated from the spacing between two crystal planes referred to as d220. The molar volume Vm(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used. The Planck constant is given by

<hl> The X-ray crystal density method <hl> is primarily a method for determining the Avogadro constant NA but as the Avogadro constant is related to the Planck constant it also determines a value for h. The principle behind the method is to determine NA as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance. Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry. The unit cell volume is calculated from the spacing between two crystal planes referred to as d220. The molar volume Vm(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used. The Planck constant is given by