Which statements are correct about degrees of freedom ?
(A) A molecule with n degrees of freedom has n² different ways of storing energy.
(B) Each degree of freedom is associated with 1/2 RT average energy per mole.
(C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom.
(D) CH₄ has a total of 6 degrees of freedom.
Choose the correct answer from the options given below :

Solution

Physics sir · 2 steps

Test each statement against one rule: every independent way to move is one degree of freedom.

1. Count the motions. A degree of freedom is one independent way a molecule can move and so store energy. Translation along x, y, z gives 3. Rotation adds 2 for a linear molecule and 3 for a non-linear one. At ordinary temperatures, vibrations are ignored.

   E_(per mole, per degree) = 1/2RT

   Statement	Check	Verdict
   (A)	n degrees of freedom means n ways to store energy, not n²	false
   (B)	Equipartition gives 1/2k_BT per molecule, so 1/2RT per mole	true
   (C)	A point-like monatomic molecule has 0 rotational degrees of freedom. A diatomic one does have 2.	false
   (D)	CH₄ is non-linear: 3 + 3 = 6	true

2. So. Only (B) and (D) are correct, which is option (b).

The idea to keep. Translation always gives 3. Rotation gives 0 for monatomic, 2 for linear and 3 for non-linear. Each degree of freedom carries 1/2RT per mole.

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