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.