Question
Find the average energy of an oscillator at (a) $T=10 h f / k$,(b) $T=h f / k,$ and(c) $T=0.1 \mathrm{hf} / \mathrm{k},$ and compare your results with those from the equipartition theorem.
Step 1
Step 1: The average energy of an oscillator is given by the formula: \[ \langle E \rangle = \frac{hf}{e^{hf/kT} - 1} \] Show more…
Show all steps
Your feedback will help us improve your experience
Suzanne W. and 70 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Calculate the average energy $\bar{E}$ per mode of oscillation for $(a)$ a long wavelength $\lambda=10 h c / k T,(b)$ a short wavelength $\lambda=0.1 h c / k T,$ and compare your results with the classical prediction $k T$ (see Equation 3-9). (The classical value comes from the equipartition theorem discussed in Chapter $8 .)$
At high temperature, the average energy of a classical one-diniensional oscillator is $k_{\mathrm{h}} T,$ and tor an atom in $\mathrm{u}$ monatomic ideal gas. it is $\frac{1}{2} k_{B} T$, Explain the difference. using the equipartition theorem.
For the three-dimensional isotropic harmonic oscillator, $k_{x}=k_{y}=k_{z}$ (see Problem 9.54 ), write the formula for the energy levels. Give the energies and degeneracies of the first 10 states.
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD