Question

According to equipartition principle, the energy contributed by each translational degree of freedom and rotational degree of freedom at a temperature T are respectively ($k_B = \text{Boltzmann constant}$):

• A. $\frac{1}{2} k_B T, \frac{1}{2} k_B T$
• B. $k_B T, \frac{1}{2} k_B T$
• C. $k_B T, k_B T$
• D. $\frac{1}{2} k_B T, k_B T$
• E. $\frac{3}{2} k_B T, \frac{1}{2} k_B T$

Hint:

Remember that the equipartition theorem states each degree of freedom contributes $\frac{1}{2} k_B T$ to the total energy.

Answer 1

The Correct Option is A

According to the equipartition theorem, each degree of freedom contributes $\frac{1}{2} k_B T$ to the energy of a system at thermal equilibrium.
This applies equally to both translational and rotational degrees of freedom.