Question

The average energy of a diatomic gaseous molecule at temperature T is $\frac{5}{2} k_B T$. The average energy per degree of freedom is

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

Hint:

Equipartition theorem always gives $\frac{1}{2} k_B T$ per degree of freedom.

Answer 1

The Correct Option is A

Step 1: Recall the equipartition theorem.
Each degree of freedom contributes $\frac{1}{2} k_B T$ to the average energy.
Step 2: Identify degrees of freedom.
A diatomic molecule at normal temperature has 5 degrees of freedom (3 translational + 2 rotational).
Total energy = $\frac{5}{2} k_B T$.
Step 3: Energy per degree of freedom.
Divide total energy by 5: $\frac{\frac{5}{2} k_B T}{5} = \frac{1}{2} k_B T$.
Step 4: Conclusion.
Each degree of freedom contributes $\frac{1}{2} k_B T$.