Sihangli/scibench-rl huggingface dataset:
Problem: Count Rumford observed that using cannon boring machinery a single horse could heat $11.6 \mathrm{~kg}$ of ice water $(T=273 \mathrm{~K})$ to $T=355 \mathrm{~K}$ in 2.5 hours. Assuming the same rate of work, how high could a horse raise a $225 \mathrm{~kg}$ weight in 2.5 minutes? Assume the heat capacity of water is $4.18 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~g}^{-1}$.
Answer:  30 $\mathrm{~m}$
Numeric value: 30
Problem: The vibrational frequency of $I_2$ is $208 \mathrm{~cm}^{-1}$. At what temperature will the population in the first excited state be half that of the ground state?
Answer:  432  $\mathrm{~K}$
Numeric value: 432
Problem: One mole of $\mathrm{H}_2 \mathrm{O}(l)$ is compressed from a state described by $P=1.00$ bar and $T=350$. K to a state described by $P=590$. bar and $T=750$. K. In addition, $\beta=2.07 \times 10^{-4} \mathrm{~K}^{-1}$ and the density can be assumed to be constant at the value $997 \mathrm{~kg} \mathrm{~m}^{-3}$. Calculate $\Delta S$ for this transformation, assuming that $\kappa=0$.

Answer:  57.2  $\mathrm{~K}^{-1}$
Numeric value: 57.2
Problem: A mass of $34.05 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}(s)$ at $273 \mathrm{~K}$ is dropped into $185 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}(l)$ at $310 . \mathrm{K}$ in an insulated container at 1 bar of pressure. Calculate the temperature of the system once equilibrium has been reached. Assume that $C_{P, m}$ for $\mathrm{H}_2 \mathrm{O}(l)$ is constant at its values for $298 \mathrm{~K}$ throughout the temperature range of interest.
Answer:  292 $\mathrm{~K}$
Numeric value: 292
Problem: Calculate $\Delta H_f^{\circ}$ for $N O(g)$ at $975 \mathrm{~K}$, assuming that the heat capacities of reactants and products are constant over the temperature interval at their values at $298.15 \mathrm{~K}$.
Answer:  91.7  $\mathrm{~kJ} \mathrm{~mol}^{-1}$
Numeric value: 91.7
Problem: A two-level system is characterized by an energy separation of $1.30 \times 10^{-18} \mathrm{~J}$. At what temperature will the population of the ground state be 5 times greater than that of the excited state?
Answer:  5.85  $10^4$
Numeric value: 5.85
Problem: At what temperature are there Avogadro's number of translational states available for $\mathrm{O}_2$ confined to a volume of 1000. $\mathrm{cm}^3$ ?
Answer:  0.068  $\mathrm{~K}$
Numeric value: 0.068
Problem: The half-cell potential for the reaction $\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}_2 \mathrm{O}(l)$ is $+1.03 \mathrm{~V}$ at $298.15 \mathrm{~K}$ when $a_{\mathrm{O}_2}=1.00$. Determine $a_{\mathrm{H}^{+}}$
Answer:  4.16  $10^{-4}$
Numeric value: 4.16
Problem: The partial molar volumes of water and ethanol in a solution with $x_{\mathrm{H}_2 \mathrm{O}}=0.45$ at $25^{\circ} \mathrm{C}$ are 17.0 and $57.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$, respectively. Calculate the volume change upon mixing sufficient ethanol with $3.75 \mathrm{~mol}$ of water to give this concentration. The densities of water and ethanol are 0.997 and $0.7893 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively, at this temperature.
Answer:  -8  $\mathrm{~cm}^3$
Numeric value: -8
Problem: Use the $D_0$ value of $\mathrm{H}_2(4.478 \mathrm{eV})$ and the $D_0$ value of $\mathrm{H}_2^{+}(2.651 \mathrm{eV})$ to calculate the first ionization energy of $\mathrm{H}_2$ (that is, the energy needed to remove an electron from $\mathrm{H}_2$ ).
Answer:  15.425  $\mathrm{eV}$
Numeric value: 15.425
Problem: Calculate the energy of one mole of UV photons of wavelength $300 \mathrm{~nm}$ and compare it with a typical single-bond energy of $400 \mathrm{~kJ} / \mathrm{mol}$.
Answer:  399  $\mathrm{~kJ} / \mathrm{mol}$
Numeric value: 399
Problem: Calculate the magnitude of the spin angular momentum of a proton. Give a numerical answer. 
Answer:  9.13  $10^{-35} \mathrm{~J} \mathrm{~s}$
Numeric value: 9.13
Problem: The ${ }^7 \mathrm{Li}^1 \mathrm{H}$ ground electronic state has $D_0=2.4287 \mathrm{eV}, \nu_e / c=1405.65 \mathrm{~cm}^{-1}$, and $\nu_e x_e / c=23.20 \mathrm{~cm}^{-1}$, where $c$ is the speed of light. (These last two quantities are usually designated $\omega_e$ and $\omega_e x_e$ in the literature.) Calculate $D_e$ for ${ }^7 \mathrm{Li}^1 \mathrm{H}$.
Answer:  2.5151  $\mathrm{eV}$
Numeric value: 2.5151
Problem: The positron has charge $+e$ and mass equal to the electron mass. Calculate in electronvolts the ground-state energy of positronium-an "atom" that consists of a positron and an electron.
Answer:  -6.8 $\mathrm{eV}$
Numeric value:  -6.8
Problem: What is the value of the angular-momentum quantum number $l$ for a $t$ orbital?
Answer:  14  
Numeric value: 14
Problem: How many states belong to the carbon configurations $1 s^2 2 s^2 2 p^2$?
Answer:  15  
Numeric value: 15
Problem: Calculate the energy needed to compress three carbon-carbon single bonds and stretch three carbon-carbon double bonds to the benzene bond length $1.397 Å$. Assume a harmonicoscillator potential-energy function for bond stretching and compression. Typical carboncarbon single- and double-bond lengths are 1.53 and $1.335 Å$; typical stretching force constants for carbon-carbon single and double bonds are 500 and $950 \mathrm{~N} / \mathrm{m}$.
Answer:  27  $\mathrm{kcal} / \mathrm{mol}$
Numeric value: 27
Problem: When a particle of mass $9.1 \times 10^{-28} \mathrm{~g}$ in a certain one-dimensional box goes from the $n=5$ level to the $n=2$ level, it emits a photon of frequency $6.0 \times 10^{14} \mathrm{~s}^{-1}$. Find the length of the box.
Answer:  1.8 $\mathrm{~nm}$
Numeric value: 1.8
Problem: Use the normalized Numerov-method harmonic-oscillator wave functions found by going from -5 to 5 in steps of 0.1 to estimate the probability of being in the classically forbidden region for the $v=0$ state.
Answer:  0.16  
Numeric value: 0.16
Problem: Calculate the de Broglie wavelength of an electron moving at 1/137th the speed of light. (At this speed, the relativistic correction to the mass is negligible.)
Answer:  0.332 $\mathrm{~nm}$
Numeric value: 0.332
Problem: Calculate the angle that the spin vector $S$ makes with the $z$ axis for an electron with spin function $\alpha$.
Answer:  54.7  $^{\circ}$
Numeric value: 54.7
Problem: The AM1 valence electronic energies of the atoms $\mathrm{H}$ and $\mathrm{O}$ are $-11.396 \mathrm{eV}$ and $-316.100 \mathrm{eV}$, respectively. For $\mathrm{H}_2 \mathrm{O}$ at its AM1-calculated equilibrium geometry, the AM1 valence electronic energy (core-core repulsion omitted) is $-493.358 \mathrm{eV}$ and the AM1 core-core repulsion energy is $144.796 \mathrm{eV}$. For $\mathrm{H}(g)$ and $\mathrm{O}(g), \Delta H_{f, 298}^{\circ}$ values are 52.102 and $59.559 \mathrm{kcal} / \mathrm{mol}$, respectively. Find the AM1 prediction of $\Delta H_{f, 298}^{\circ}$ of $\mathrm{H}_2 \mathrm{O}(g)$.
Answer:  -59.24  $\mathrm{kcal} / \mathrm{mol}$
Numeric value: -59.24
Problem: Given that $D_e=4.75 \mathrm{eV}$ and $R_e=0.741 Å$ for the ground electronic state of $\mathrm{H}_2$, find $U\left(R_e\right)$ for this state.
Answer:  -31.95  $\mathrm{eV}$
Numeric value:  -31.95
Problem: For $\mathrm{NaCl}, R_e=2.36 Å$. The ionization energy of $\mathrm{Na}$ is $5.14 \mathrm{eV}$, and the electron affinity of $\mathrm{Cl}$ is $3.61 \mathrm{eV}$. Use the simple model of $\mathrm{NaCl}$ as a pair of spherical ions in contact to estimate $D_e$. [One debye (D) is $3.33564 \times 10^{-30} \mathrm{C} \mathrm{m}$.]
Answer:  4.56  $\mathrm{eV}$
Numeric value:  4.56
Problem: Find the number of CSFs in a full CI calculation of $\mathrm{CH}_2 \mathrm{SiHF}$ using a 6-31G** basis set.
Answer:  1.86 $10^{28} $
Numeric value: 1.86
Problem: Calculate the ratio of the electrical and gravitational forces between a proton and an electron.
Answer:  2  $10^{39}$
Numeric value: 2
Problem: A one-particle, one-dimensional system has the state function
$$
\Psi=(\sin a t)\left(2 / \pi c^2\right)^{1 / 4} e^{-x^2 / c^2}+(\cos a t)\left(32 / \pi c^6\right)^{1 / 4} x e^{-x^2 / c^2}
$$
where $a$ is a constant and $c=2.000 Å$. If the particle's position is measured at $t=0$, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$.
Answer:  0.000216  
Numeric value: 0.000216
Problem: The $J=2$ to 3 rotational transition in a certain diatomic molecule occurs at $126.4 \mathrm{GHz}$, where $1 \mathrm{GHz} \equiv 10^9 \mathrm{~Hz}$. Find the frequency of the $J=5$ to 6 absorption in this molecule.
Answer:  252.8  $\mathrm{GHz}$
Numeric value:  252.8
Problem: Assume that the charge of the proton is distributed uniformly throughout the volume of a sphere of radius $10^{-13} \mathrm{~cm}$. Use perturbation theory to estimate the shift in the ground-state hydrogen-atom energy due to the finite proton size. The potential energy experienced by the electron when it has penetrated the nucleus and is at distance $r$ from the nuclear center is $-e Q / 4 \pi \varepsilon_0 r$, where $Q$ is the amount of proton charge within the sphere of radius $r$. The evaluation of the integral is simplified by noting that the exponential factor in $\psi$ is essentially equal to 1 within the nucleus.

Answer:  1.2  $10^{-8} \mathrm{eV}$
Numeric value: 1.2
Problem: An electron in a three-dimensional rectangular box with dimensions of $5.00 Å, 3.00 Å$, and $6.00 Å$ makes a radiative transition from the lowest-lying excited state to the ground state. Calculate the frequency of the photon emitted.
Answer: 7.58  $10^{14} \mathrm{~s}^{-1}$
Numeric value: 7.58
Problem: Do $\mathrm{HF} / 6-31 \mathrm{G}^*$ geometry optimizations on one conformers of $\mathrm{HCOOH}$ with $\mathrm{OCOH}$ dihedral angle of $0^{\circ}$. Calculate the dipole moment.
Answer:  1.41  $\mathrm{D}$
Numeric value: 1.41
Problem: Frozen-core $\mathrm{SCF} / \mathrm{DZP}$ and CI-SD/DZP calculations on $\mathrm{H}_2 \mathrm{O}$ at its equilibrium geometry gave energies of -76.040542 and -76.243772 hartrees. Application of the Davidson correction brought the energy to -76.254549 hartrees. Find the coefficient of $\Phi_0$ in the normalized CI-SD wave function.
Answer:  0.9731  
Numeric value: 0.9731
Problem: Let $w$ be the variable defined as the number of heads that show when two coins are tossed simultaneously. Find $\langle w\rangle$.
Answer:  1  
Numeric value: 1
Problem: Calculate the force on an alpha particle passing a gold atomic nucleus at a distance of $0.00300 Å$.
Answer:  0.405  $\mathrm{~N}$
Numeric value: 0.405
Problem: When an electron in a certain excited energy level in a one-dimensional box of length $2.00  Å$ makes a transition to the ground state, a photon of wavelength $8.79 \mathrm{~nm}$ is emitted. Find the quantum number of the initial state.
Answer: 4 
Numeric value: 4
Problem: For a macroscopic object of mass $1.0 \mathrm{~g}$ moving with speed $1.0 \mathrm{~cm} / \mathrm{s}$ in a one-dimensional box of length $1.0 \mathrm{~cm}$, find the quantum number $n$.
Answer:  3 $10^{26}$
Numeric value: 3
Problem: For the $\mathrm{H}_2$ ground electronic state, $D_0=4.4781 \mathrm{eV}$. Find $\Delta H_0^{\circ}$ for $\mathrm{H}_2(g) \rightarrow 2 \mathrm{H}(g)$ in $\mathrm{kJ} / \mathrm{mol}$
Answer:  432.07  $\mathrm{~kJ} / \mathrm{mol}$
Numeric value: 432.07
Problem: The contribution of molecular vibrations to the molar internal energy $U_{\mathrm{m}}$ of a gas of nonlinear $N$-atom molecules is (zero-point vibrational energy not included) $U_{\mathrm{m}, \mathrm{vib}}=R \sum_{s=1}^{3 N-6} \theta_s /\left(e^{\theta_s / T}-1\right)$, where $\theta_s \equiv h \nu_s / k$ and $\nu_s$ is the vibrational frequency of normal mode $s$. Calculate the contribution to $U_{\mathrm{m}, \text { vib }}$ at $25^{\circ} \mathrm{C}$ of a normal mode with wavenumber $\widetilde{v} \equiv v_s / c$ of $900 \mathrm{~cm}^{-1}$.
Answer:  0.14  $\mathrm{kJ} / \mathrm{mol}$
Numeric value: 0.14
Problem: Calculate the magnitude of the spin magnetic moment of an electron.
Answer:  1.61  $10^{-23} \mathrm{~J} / \mathrm{T}$
Numeric value: 1.61
Problem: A particle is subject to the potential energy $V=a x^4+b y^4+c z^4$. If its ground-state energy is $10 \mathrm{eV}$, calculate $\langle V\rangle$ for the ground state.
Answer:  $3rac{1}{3}$  $\mathrm{eV}$
Numeric value: 3.333333333
Problem: For an electron in a certain rectangular well with a depth of $20.0 \mathrm{eV}$, the lowest energy level lies $3.00 \mathrm{eV}$ above the bottom of the well. Find the width of this well. Hint: Use $\tan \theta=\sin \theta / \cos \theta$
Answer:  0.264 $\mathrm{~nm}$
Numeric value: 0.264
Problem: Calculate the uncertainty $\Delta L_z$ for the hydrogen-atom stationary state: $2 p_z$.
Answer:  0  
Numeric value: 0
Problem: Calculate the de Broglie wavelength for an electron with a kinetic energy of $100 \mathrm{eV}$
Answer:  0.123 nm 
Numeric value: 0.123
Problem: The threshold wavelength for potassium metal is $564 \mathrm{~nm}$. What is its work function? 

Answer:  3.52 $10^{-19} \mathrm{~J}$
Numeric value: 3.52
Problem: Evaluate the series
$$
S=\sum_{n=0}^{\infty} \frac{1}{3^n}
$$
Answer:  3 / 2  
Numeric value: 1.5
Problem: The relationship introduced in Problem $1-48$ has been interpreted to mean that a particle of mass $m\left(E=m c^2\right)$ can materialize from nothing provided that it returns to nothing within a time $\Delta t \leq h / m c^2$. Particles that last for time $\Delta t$ or more are called real particles; particles that last less than time $\Delta t$ are called virtual particles. The mass of the charged pion, a subatomic particle, is $2.5 \times 10^{-28} \mathrm{~kg}$. What is the minimum lifetime if the pion is to be considered a real particle?
Answer:  2.9 $10^{-23} \mathrm{~s}$ 
Numeric value: 2.9
Problem: A household lightbulb is a blackbody radiator. Many lightbulbs use tungsten filaments that are heated by an electric current. What temperature is needed so that $\lambda_{\max }=550 \mathrm{~nm}$ ?
Answer:  5300  $\mathrm{~K}$

Numeric value: 5300
Problem: Evaluate the series
$$
S=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots
$$

Answer:  1  
Numeric value: 1
Problem: Through what potential must a proton initially at rest fall so that its de Broglie wavelength is $1.0 \times 10^{-10} \mathrm{~m}$ ?
Answer:  0.082 V 
Numeric value: 0.082
Problem: Example 5-3 shows that a Maclaurin expansion of a Morse potential leads to
$$
V(x)=D \beta^2 x^2+\cdots
$$
Given that $D=7.31 \times 10^{-19} \mathrm{~J} \cdot$ molecule ${ }^{-1}$ and $\beta=1.81 \times 10^{10} \mathrm{~m}^{-1}$ for $\mathrm{HCl}$, calculate the force constant of $\mathrm{HCl}$.
Answer:  479 $\mathrm{~N} \cdot \mathrm{m}^{-1}$ 
Numeric value: 479
Problem: A line in the Lyman series of hydrogen has a wavelength of $1.03 \times 10^{-7} \mathrm{~m}$. Find the original energy level of the electron.
Answer:  3  
Numeric value: 3
Problem: A helium-neon laser (used in supermarket scanners) emits light at $632.8 \mathrm{~nm}$. Calculate the frequency of this light.
Answer:  4.738 $10^{14} \mathrm{~Hz}$ 
Numeric value: 4.738
Problem: What is the uncertainty of the momentum of an electron if we know its position is somewhere in a $10 \mathrm{pm}$ interval?
Answer:  6.6  $10^{-23} \mathrm{~kg} \cdot \mathrm{m} \cdot \mathrm{s}^{-1}$
Numeric value:  6.6
Problem: Using the Bohr theory, calculate the ionization energy (in electron volts and in $\mathrm{kJ} \cdot \mathrm{mol}^{-1}$ ) of singly ionized helium.
Answer:  54.394 $\mathrm{eV}$ 
Numeric value: 54.394
Problem: When an excited nucleus decays, it emits a $\gamma$ ray. The lifetime of an excited state of a nucleus is of the order of $10^{-12} \mathrm{~s}$. What is the uncertainty in the energy of the $\gamma$ ray produced?
Answer:  7 $10^{-22} \mathrm{~J}$ 
Numeric value: 7
Problem: Calculate the wavelength and the energy of a photon associated with the series limit of the Lyman series.
Answer:  91.17 nm 
Numeric value: 91.17
Problem: Given a context information that there is also an uncertainty principle for energy and time:
$$
\Delta E \Delta t \geq h
$$, another application of the relationship has to do with the excitedstate energies and lifetimes of atoms and molecules. If we know that the lifetime of an excited state is $10^{-9} \mathrm{~s}$, then what is the uncertainty in the energy of this state?
Answer:  7  $10^{-25} \mathrm{~J}$
Numeric value: 7
Problem: One of the most powerful modern techniques for studying structure is neutron diffraction. This technique involves generating a collimated beam of neutrons at a particular temperature from a high-energy neutron source and is accomplished at several accelerator facilities around the world. If the speed of a neutron is given by $v_{\mathrm{n}}=\left(3 k_{\mathrm{B}} T / m\right)^{1 / 2}$, where $m$ is the mass of a neutron, then what temperature is needed so that the neutrons have a de Broglie wavelength of $50 \mathrm{pm}$ ?
Answer:  2500 $\mathrm{K}$ 
Numeric value: 2500
Problem: The temperature of the fireball in a thermonuclear explosion can reach temperatures of approximately $10^7 \mathrm{~K}$. What value of $\lambda_{\max }$ does this correspond to? 
Answer:  3  $10^{-10} \mathrm{~m}$

Numeric value: 3
Problem: Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit
$$
\lim _{x \rightarrow 0} \frac{\ln (1+x)-x}{x^2}
$$
both ways and report the final result.
Answer:  -1/2  
Numeric value: -0.5
Problem: Evaluate the series
$$
S=\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2^n}
$$
Answer:  1/3  
Numeric value: 0.3333333
Problem: Calculate the percentage difference between $\ln (1+x)$ and $x$ for $x=0.0050$
Answer:  0.249  %
Numeric value: 0.249
Problem: Calculate the reduced mass of a nitrogen molecule in which both nitrogen atoms have an atomic mass of 14.00.
Answer:  7.00  
Numeric value: 7.00
Problem: Two narrow slits are illuminated with red light of wavelength $694.3 \mathrm{~nm}$ from a laser, producing a set of evenly placed bright bands on a screen located $3.00 \mathrm{~m}$ beyond the slits. If the distance between the bands is $1.50 \mathrm{~cm}$, then what is the distance between the slits?

Answer:  0.139 mm 
Numeric value: 0.139
Problem: Calculate the energy associated with an $\alpha$ particle that has fallen through a potential difference of $4.0 \mathrm{~V}$. Take the mass of an $\alpha$ particle to be $6.64 \times 10^{-27} \mathrm{~kg}$.
Answer:  1.3 $10^{-18} \mathrm{~J} / \alpha \text {-particle}$
Numeric value: 1.3
Problem: Calculate the number of photons in a $2.00 \mathrm{~mJ}$ light pulse at (a) $1.06 \mu \mathrm{m}$

Answer:  1.07  $10^{16}$ photons
Numeric value: 1.07
Problem: The force constant of ${ }^{35} \mathrm{Cl}^{35} \mathrm{Cl}$ is $319 \mathrm{~N} \cdot \mathrm{m}^{-1}$. Calculate the fundamental vibrational frequency
Answer:  556  $\mathrm{~cm}^{-1}$
Numeric value: 556
Problem: $$
\text {Calculate the energy of a photon for a wavelength of } 100 \mathrm{pm} \text { (about one atomic diameter). }
$$

Answer:  2  $10^{-15} \mathrm{~J}$
Numeric value: 2
Problem: A proton and a negatively charged $\mu$ meson (called a muon) can form a short-lived species called a mesonic atom. The charge of a muon is the same as that on an electron and the mass of a muon is $207 m_{\mathrm{e}}$. Assume that the Bohr theory can be applied to such a mesonic atom and calculate the frequency associated with the $n=1$ to $n=2$ transition in a mesonic atom.
Answer:  1.69 $10^{17} \mathrm{~Hz}$
Numeric value: 4.59
Problem: $$
\beta=2 \pi c \tilde{\omega}_{\mathrm{obs}}\left(\frac{\mu}{2 D}\right)^{1 / 2}
$$
Given that $\tilde{\omega}_{\mathrm{obs}}=2886 \mathrm{~cm}^{-1}$ and $D=440.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ for $\mathrm{H}^{35} \mathrm{Cl}$, calculate $\beta$.
Answer:  1.81  $10^{10} \mathrm{~m}^{-1}$
Numeric value: 1.81
Problem: Two narrow slits separated by $0.10 \mathrm{~mm}$ are illuminated by light of wavelength $600 \mathrm{~nm}$. If a detector is located $2.00 \mathrm{~m}$ beyond the slits, what is the distance between the central maximum and the first maximum?
Answer:  12  mm
Numeric value: 12
Problem: $$
\text { If we locate an electron to within } 20 \mathrm{pm} \text {, then what is the uncertainty in its speed? }
$$
Answer:  3.7 $10^7 \mathrm{~m} \cdot \mathrm{s}^{-1}$ 
Numeric value: 3.7
Problem: The mean temperature of the earth's surface is $288 \mathrm{~K}$. What is the maximum wavelength of the earth's blackbody radiation?
Answer:  1.01  10^{-5} \mathrm{~m}
Numeric value: 1.01
Problem: The power output of a laser is measured in units of watts (W), where one watt is equal to one joule per second. $\left(1 \mathrm{~W}=1 \mathrm{~J} \cdot \mathrm{s}^{-1}\right.$.) What is the number of photons emitted per second by a $1.00 \mathrm{~mW}$ nitrogen laser? The wavelength emitted by a nitrogen laser is $337 \mathrm{~nm}$.
Answer:  1.70  $
10^{15} \text { photon } \cdot \mathrm{s}^{-1}
$
Numeric value: 1.70
Problem:  Sirius, one of the hottest known stars, has approximately a blackbody spectrum with $\lambda_{\max }=260 \mathrm{~nm}$. Estimate the surface temperature of Sirius.

Answer: 11000  $\mathrm{~K}$

Numeric value: 11000
Problem: A ground-state hydrogen atom absorbs a photon of light that has a wavelength of $97.2 \mathrm{~nm}$. It then gives off a photon that has a wavelength of $486 \mathrm{~nm}$. What is the final state of the hydrogen atom?
Answer:  2  
Numeric value: 2
Problem: It turns out that the solution of the Schrödinger equation for the Morse potential can be expressed as
$$
G(v)=\tilde{\omega}_{\mathrm{e}}\left(v+\frac{1}{2}\right)-\tilde{\omega}_{\mathrm{e}} \tilde{x}_{\mathrm{e}}\left(v+\frac{1}{2}\right)^2
$$
The Harmonic Oscillator and Vibrational Spectroscopy
where
$$
\tilde{x}_{\mathrm{e}}=\frac{h c \tilde{\omega}_{\mathrm{e}}}{4 D}
$$
Given that $\tilde{\omega}_{\mathrm{e}}=2886 \mathrm{~cm}^{-1}$ and $D=440.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ for $\mathrm{H}^{35} \mathrm{Cl}$, calculate $\tilde{x}_{\mathrm{e}}$.
Answer:  0.01961  
Numeric value:  0.01961
Problem:  In the infrared spectrum of $\mathrm{H}^{127} \mathrm{I}$, there is an intense line at $2309 \mathrm{~cm}^{-1}$. Calculate the force constant of $\mathrm{H}^{127} \mathrm{I}$.
Answer: 313  $ \mathrm{~N} \cdot \mathrm{m}^{-1}$
Numeric value: 313
Problem: Calculate the percentage difference between $e^x$ and $1+x$ for $x=0.0050$
Answer:  1.25  $10^{-3} \%$
Numeric value: 1.25
Problem: Calculate the kinetic energy of an electron in a beam of electrons accelerated by a voltage increment of $100 \mathrm{~V}$
Answer:  1.602  $10^{-17} \mathrm{~J} \cdot$ electron ${ }^{-1}$
Numeric value: 1.602
Problem: Suppose that $10.0 \mathrm{~mol} \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})$ is confined to $4.860 \mathrm{dm}^3$ at $27^{\circ} \mathrm{C}$. Predict the pressure exerted by the ethane from the perfect gas.
Answer:  50.7 $\mathrm{atm}$ 
Numeric value: 50.7
Problem: Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the standard enthalpy of solution of $\mathrm{AgCl}(\mathrm{s})$ in water from the enthalpies of formation of the solid and the aqueous ions.
Answer:  +65.49 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: +65.49
Problem: Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from $1.8 \mathrm{~atm}$ to $29.5 \mathrm{~atm}$ at $40^{\circ} \mathrm{C}$.
Answer:  +7.3 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: +7.3
Problem: Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in entropy when $25 \mathrm{~kJ}$ of energy is transferred reversibly and isothermally as heat to a large block of iron at $100^{\circ} \mathrm{C}$.
Answer:  67 $\mathrm{J} \mathrm{K}^{-1}$ 
Numeric value: 67
Problem: Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \mathrm{~mol}$ of diatomic perfect gas molecules at $200 \mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \mathrm{~K}$. Given that $C_{V, \mathrm{~m}}=27.5 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, calculate $q$.
Answer: 0   
Numeric value: 0