Question

The average energy associated with a monoatomic molecule is

• A. \( K_B T \)
• B. \( \frac{1}{2} K_B T \)
• C. \( \frac{3}{2} K_B T \)
• D. \( 2 K_B T \)

Hint:

Each translational degree of freedom contributes \( \frac{1}{2} K_B T \) to the energy. Monoatomic gases have 3 such degrees.

Answer 1

The Correct Option is C

A monoatomic molecule has only 3 translational degrees of freedom (no rotational or vibrational ones). From the equipartition of energy principle, each degree contributes: \[ \frac{1}{2} K_B T \] So, total average energy: \[ E = 3 \times \frac{1}{2} K_B T = \frac{3}{2} K_B T \]