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?

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.

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=(\(\frac\)12)I\(\omega\)^2$, for the $l = 1$ level, what is the rotational period (the time for one rotation)?

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=(\(\frac\)12)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 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?

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.