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# Predicting the Phonon Number of an Oscillator

## The Prompt

**If the frequency of a normal mode is** $\omega_{mode}=10^{12}rads^{-1}$**, what phonon number,** $n_{phonon}$**, does the equipartition theorem predict at room temperature?**

## Context

This SWBQ demonstrates to students how the energy stored in a normal mode is directly proportional to the frequency of the normal mode and how the equipartition theorem is useful for finding the phonon number of a normal mode as long as not on the scale $n_{phonon}\, \sim \, 1$. In particular, students must recall that the energy stored in a single normal mode is $k_{B}T$.