Question: What is the energy of a photon?

Answer: 6981358000000000000♠3.58×10−19 J

hf = 6981358000000000000♠3.58×10−19 J .

Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = <hl> hf = 6981358000000000000♠3.58×10−19 J . <hl> That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of 7005216000000000000♠216 kJ/mol, a typical energy of everyday life.

Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = hf = <hl> 6981358000000000000♠3.58×10−19 J <hl>. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of 7005216000000000000♠216 kJ/mol, a typical energy of everyday life.

question: What is the energy of a photon?, context: Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = hf = 6981358000000000000♠3.58×10−19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of 7005216000000000000♠216 kJ/mol, a typical energy of everyday life.


Question: How much energy is contained in the light to which human eyes are most sensitive?

Answer: 7005216000000000000♠216 kJ/mol

Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = hf = 6981358000000000000♠3.58×10−19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. <hl> The result is that green light of wavelength 555 nm has an energy of 7005216000000000000♠216 kJ/mol , a typical energy of everyday life. <hl>

Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = hf = 6981358000000000000♠3.58×10−19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of <hl> 7005216000000000000♠216 kJ/mol <hl>, a typical energy of everyday life.

The result is that green light of wavelength 555 nm has an energy of <hl> 7005216000000000000♠216 kJ/mol <hl> , a typical energy of everyday life.

question: How much energy is contained in the light to which human eyes are most sensitive?, context: Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = hf = 6981358000000000000♠3.58×10−19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of 7005216000000000000♠216 kJ/mol, a typical energy of everyday life.


Question: What type of radiation was Planck studying in the late 19th century?

Answer: black-body

<hl> In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of <hl> black-body <hl> radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: What type of radiation was Planck studying in the late 19th century?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: How many years prior to Planck's study had the scientific community first discussed black body radiation?

Answer: forty

<hl> In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some <hl> forty <hl> years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: How many years prior to Planck's study had the scientific community first discussed black body radiation?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What scientist first studied black body radiation?

Answer: Kirchhoff

<hl> In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by <hl> Kirchhoff <hl> some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: What scientist first studied black body radiation?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What is required for the electromagnetic field to come to thermal equilibrium?

Answer: hot atoms

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. <hl> The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms . <hl> The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with <hl> hot atoms <hl>. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with <hl> hot atoms <hl> .

question: What is required for the electromagnetic field to come to thermal equilibrium?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What does a hot object in equilibrium absorb as much as it emits?

Answer: light

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. <hl> The hot object in equilibrium with light absorbs just as much light as it emits. <hl> If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with <hl> light <hl> absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: What does a hot object in equilibrium absorb as much as it emits?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What was Planck studying in the last part of the nineteenth century?

Answer: the problem of black-body radiation

<hl> In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating <hl> the problem of black-body radiation <hl> first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: What was Planck studying in the last part of the nineteenth century?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: Who posed the problem of black-body radiation?

Answer: Kirchhoff

<hl> In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by <hl> Kirchhoff <hl> some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: Who posed the problem of black-body radiation?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: Cooler objects glow less than objects that are what?

Answer: hotter

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. <hl> The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that <hl> hotter <hl> objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: Cooler objects glow less than objects that are what?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What does a black object do to any of the light that hits it?

Answer: it absorbs all the light

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. <hl> If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized. <hl>

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning <hl> it absorbs all the light <hl> that hits it, then its thermal light emission is maximized.

question: What does a black object do to any of the light that hits it?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What is maximized as a result of a black object absorbing all the light that hits it?

Answer: thermal light emission

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. <hl> If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized. <hl>

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its <hl> thermal light emission <hl> is maximized.

question: What is maximized as a result of a black object absorbing all the light that hits it?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: Planck studied what problem posed originally by Kirchhoff?

Answer: black-body radiation

<hl> In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. <hl> It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of <hl> black-body radiation <hl> first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: Planck studied what problem posed originally by Kirchhoff?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: If an object is black, what is known about its thermal light emission?

Answer: its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. <hl> If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized. <hl>

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then <hl> its thermal light emission is maximized. <hl>

question: If an object is black, what is known about its thermal light emission?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What is known about the light absorption of a hot object in equilibrium with light?

Answer: absorbs just as much light as it emits

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. <hl> The hot object in equilibrium with light absorbs just as much light as it emits . <hl> If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light <hl> absorbs just as much light as it emits <hl>. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

The hot object in equilibrium with light <hl> absorbs just as much light as it emits <hl> .

question: What is known about the light absorption of a hot object in equilibrium with light?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: Electromagnetic fields obey what laws?

Answer: laws of motion

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. <hl> The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. <hl> The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys <hl> laws of motion <hl> similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

question: Electromagnetic fields obey what laws?, context: In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.


Question: What do scientists assume black body radiation is?

Answer: thermal

<hl> The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is <hl> thermal <hl> leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What do scientists assume black body radiation is?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What kind of prediction does the assumption that black body radiation is thermal lead to?

Answer: accurate

The assumption that black-body radiation is thermal leads to <hl> an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an <hl> accurate <hl> prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What kind of prediction does the assumption that black body radiation is thermal lead to?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What type of changes in the light a hot object emits as the object's temperature changes?

Answer: colour

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". <hl> Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the <hl> colour <hl> of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What type of changes in the light a hot object emits as the object's temperature changes?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What law describes the changes in light emitted by a hot object?

Answer: Stefan–Boltzmann law

<hl> The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the <hl> Stefan–Boltzmann law <hl> (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What law describes the changes in light emitted by a hot object?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What assumption that black-body radiation is what leads to an accurate prediction?

Answer: thermal

<hl> The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is <hl> thermal <hl> leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What assumption that black-body radiation is what leads to an accurate prediction?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What does the Stefan-Boltzmann law state?

Answer: the total amount of emitted energy goes up with the temperature according to a definite rule

<hl> The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule , the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: <hl> the total amount of emitted energy goes up with the temperature according to a definite rule <hl>, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: <hl> the total amount of emitted energy goes up with the temperature according to a definite rule <hl> , the Stefan–Boltzmann law (1879–84).

question: What does the Stefan-Boltzmann law state?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What about a hot object changes with the temperature?

Answer: the colour of the light

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". <hl> Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that <hl> the colour of the light <hl> given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What about a hot object changes with the temperature?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What color is hotter than "red hot"?

Answer: white hot

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that " white hot " is hotter than "red hot". <hl> Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "<hl> white hot <hl>" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

But it was also known that the colour of the light given off by a hot object changes with the temperature, so that " <hl> white hot <hl> " is hotter than "red hot".

question: What color is hotter than "red hot"?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What did Wilhelm Wien discover?

Answer: the mathematical relationship between the peaks of the curves at different temperatures

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". <hl> Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures , by using the principle of adiabatic invariance. <hl> At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered <hl> the mathematical relationship between the peaks of the curves at different temperatures <hl>, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

Nevertheless, Wilhelm Wien discovered <hl> the mathematical relationship between the peaks of the curves at different temperatures <hl> , by using the principle of adiabatic invariance.

question: What did Wilhelm Wien discover?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What rule predicts that emitted energy increases with temperature?

Answer: the Stefan–Boltzmann law

<hl> The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, <hl> the Stefan–Boltzmann law <hl> (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What rule predicts that emitted energy increases with temperature?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: What characteristic of the light emitted by a hot object changes with temperature?

Answer: the colour of the light given off

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). <hl> But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". <hl> Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that <hl> the colour of the light given off <hl> by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: What characteristic of the light emitted by a hot object changes with temperature?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: Who discovered the mathematical relationship between peaks and curves of light at different temperatures?

Answer: Wilhelm Wien

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". <hl> Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. <hl> At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, <hl> Wilhelm Wien <hl> discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: Who discovered the mathematical relationship between peaks and curves of light at different temperatures?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: The rule that adjust the curve at different temperatures is known as what?

Answer: Wien's displacement law

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. <hl> At each different temperature, the curve is moved over by Wien's displacement law (1893). <hl> Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by <hl> Wien's displacement law <hl> (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

question: The rule that adjust the curve at different temperatures is known as what?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: Wien's spectrum model could not predict accurate at what end of the spectrum?

Answer: at low frequencies (long wavelength)

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). <hl> Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength) . <hl> It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not <hl> at low frequencies (long wavelength) <hl>. It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not <hl> at low frequencies (long wavelength) <hl> .

question: Wien's spectrum model could not predict accurate at what end of the spectrum?, context: The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).


Question: Before Planck, it was assumed that the energy of a body could take on what value?

Answer: any

<hl> Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. <hl> The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it had been assumed that the energy of a body could take on <hl> any <hl> value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

question: Before Planck, it was assumed that the energy of a body could take on what value?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.


Question: The Rayleigh-Jeans law makes close predictions for what amount of values?

Answer: a narrow range

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. <hl> The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. <hl> To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for <hl> a narrow range <hl> of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

question: The Rayleigh-Jeans law makes close predictions for what amount of values?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.


Question: What does Planck's law correctly predict?

Answer: blackbody emissions

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. <hl> To make Planck's law, which correctly predicts blackbody emissions , it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. <hl> The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts <hl> blackbody emissions <hl>, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

To make Planck's law, which correctly predicts <hl> blackbody emissions <hl> , it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator.

question: What does Planck's law correctly predict?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.


Question: In making Planck's law, what was in both the numerator and denominator of the formula that was used?

Answer: h

<hl> Prior to Planck's work, it h ad been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. <hl> The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it <hl> h <hl>ad been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it <hl> h <hl> ad been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable.

question: In making Planck's law, what was in both the numerator and denominator of the formula that was used?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.


Question: Planck's work disproved what assumption?

Answer: that the energy of a body could take on any value whatsoever

<hl> Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. <hl> The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it had been assumed <hl> that the energy of a body could take on any value whatsoever <hl> – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

question: Planck's work disproved what assumption?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.


Question: What rule predicted narrow range of energy values at lower temperatures?

Answer: The Rayleigh–Jeans

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. <hl> The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. <hl> To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. <hl> The Rayleigh–Jeans <hl> law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

question: What rule predicted narrow range of energy values at lower temperatures?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.


Question: Planck's law involved what necessary mathematical step to correctly predict blackbody emission?

Answer: multiply the classical expression by a complex factor that involves h in both the numerator and the denominator

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. <hl> To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator . <hl> The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to <hl> multiply the classical expression by a complex factor that involves h in both the numerator and the denominator <hl>. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

To make Planck's law, which correctly predicts blackbody emissions, it was necessary to <hl> multiply the classical expression by a complex factor that involves h in both the numerator and the denominator <hl> .

question: Planck's law involved what necessary mathematical step to correctly predict blackbody emission?, context: Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.