Energy of 10 non rigid diatomic molecules at temperature T is :

Solution

Physics sir · 2 steps

Count every quadratic energy term, give each one 1/2k_BT, then multiply by 10 molecules.

1. Count energy terms. A non-rigid diatomic molecule moves in 3 directions and rotates about 2 axes. It also vibrates, and vibration carries two terms: kinetic energy and potential energy of the stretched bond.

   Motion	Quadratic terms	Energy per molecule
   Translation	3	3/2k_BT
   Rotation	2	k_BT
   Vibration (KE + PE)	2	k_BT
   Total	7	7/2k_BT

   E = 10 × 7/2k_BT = 35 k_BT

2. So. The question counts molecules, not moles, so the constant is k_B, not R. The energy of 10 molecules is 35 k_BT, option (d).

The idea to keep. Each quadratic energy term gets 1/2k_BT per molecule, and a vibration mode always brings two terms. Use k_B when you count molecules and R when you count moles.

Answer from the NTA final answer key. Solution by PrepWiser.