For the H₂ molecule the equilibrium spacing of the two protons is $0.074$ nm. The mass of a hydrogen atom is $1.67\times {10}^{-27}$ kg. Calculate the wavelength of the photon emitted in the rotational transition $l=2$ to $l=1$.

During each of these processes, a photon of light is given up. In each process, what wavelength of light is given up, and in what part of the electromagnetic spectrum is that wavelength? A molecule decreases its vibrational energy by $0.198$ eV.

The H₂ molecule has a moment of inertia of $4.6\times {10}^{-48}$ kg-m². What is the wavelength $l$ of the photon absorbed when H₂ makes a transition from the $l=3$ to the $l=4$ rotational level?

Two atoms of cesium (Cs) can form a $C{s}_2$ molecule. The equilibrium distance between the nuclei in a $C{s}_2$ molecule is $0.447$ nm. Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is $2.21\times {10}^{-25}$ kg.

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=(\frac12)I\omega^2$, for the $l = 1$ level, what is the angular speed of the rotating molecule?

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=\left(\frac{1}{2}\right)I{\omega }^2$, for the $l=1$ level, what is the linear speed of each atom?

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=(\frac12)I\omega^2$, for the $l = 1$ level, what is the rotational period (the time for one rotation)?

The average kinetic energy of an ideal-gas atom or molecule is $\left(\frac{3}{2}\right)kT$, where $T$ is the Kelvin temperature (Chapter $18$). The rotational inertia of the H₂ molecule is $4.6\times {10}^{-48}$ kg-m². What is the value of $T$ for which $\left(\frac{3}{2}\right)kT$ equals the energy separation between the $l=0$ and $l=1$ energy levels of H₂? What does this tell you about the number of H₂ molecules in the $l=1$ level at room temperature?

Potassium bromide (KBr) has a density of $2.75\times {10}^3$ kg/m³ and the same crystal structure as NaCl. The mass of a potassium atom is $6.49\times {10}^{-26}$ kg, and the mass of a bromine atom is $1.33\times {10}^{-25}$ kg. Calculate the average spacing between adjacent atoms in a KBr crystal.

The maximum wavelength of light that a certain silicon photocell can detect is $1.11$ mm. What is the energy gap (in electron volts) between the valence and conduction bands for this photocell?

Calculate the density of states $g\left(E\right)$ for the free-electron model of a metal if $E=7.0$ eV and $V=1.0$ cm³. Express your answer in units of states per electron volt.

Silver has a Fermi energy of $5.48$ eV. Calculate the electron contribution to the molar heat capacity at constant volume of silver, $C_V$, at $300$ K. Express your result as a multiple of $R$.

At the Fermi temperature $T_F$, $E_F=k{T}_F$ (see Exercise $42.22$). When $T=T_F$, what is the probability that a state with energy $E=2E_F$ is occupied?

Pure germanium has a band gap of $0.67$ eV. The Fermi energy is in the middle of the gap. For temperatures of $250$ K, $300$ K, and $350$ K, calculate the probability $f\left(E\right)$ that a state at the bottom of the conduction band is occupied.

Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron–hole pairs. If each pair requires $0.67$ eV of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie?

At a temperature of $290$ K, a certain $p-n$ junction has a saturation current $I_S=0.500$ mA. Find the current at this temperature when the voltage is (i) $1.00$ mV, (ii) $-1.00$ mV, (iii) $100$ mV, and (iv) $-100$ mV.

A forward-bias voltage of $15.0$ mV produces a positive current of $9.25$ mA through a $p-n$ junction at $300$ K. What does the positive current become if the forward-bias voltage is reduced to $10.0$ mV?

The maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (b) Explain why pure silicon is opaque.