Suppose that the energy difference between adjacent energy levels for an oscillator in an Einstein solid is $\varepsilon=$ $0.005 \mathrm{eV}$. We would expect the average energy of this oscillator when it is in contact with a reservoir at room temperature to be
A) negligible.
B) smaller than $\frac{1}{2} k_{B} T$.
C) about equal to $\frac{1}{2} k_{B} T$.
D) about equal to $k_{B} T$.
E) significantly larger than $k_{B} T$.
F) One doesn't have enough information to tell.

Question

Quizplus · Accepted Answer

At room temperature ($T \approx 300 \, \mathrm{K}$), the thermal energy $k_B T$ is about $0.025 \, \mathrm{eV}$. Since the energy difference between levels ($\varepsilon = 0.005 \, \mathrm{eV}$) is much smaller than $k_B T$, the average energy of an oscillator will be about equal to $k_B T$, as many energy levels can be populated.

Suppose That the Energy Difference Between Adjacent Energy Levels for an Oscillator