Question

Match List I with List II :

	List I		List II
A	3 Translational degrees of freedom	I	Monoatomic gases
B	3 Translational, 2 rotational degrees of freedoms	II	Polyatomic gases
C	3 Translational, 2 rotational and 1 vibrational degrees of freedom	III	Rigid diatomic gases
D	3 Translational, 3 rotational and more than one vibrational degrees of freedom	IV	Nonrigid diatomic gases

Choose the correct answer from the options given below:

• A. (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
• B. (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
• C. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
• D. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)

Hint:

Monoatomic gases only have translational degrees of freedom. Diatomic molecules can have translational, rotational, and (if nonrigid) vibrational degrees of freedom. Polyatomic molecules generally have all three types

Answer 1

The Correct Option is B

To solve this problem, we need to match the types of gases in List II with their corresponding degrees of freedom in List I. Let's explain each in detail:

1. Monoatomic gases typically refer to noble gases like Helium, Neon, etc. These gases have only 3 translational degrees of freedom and no rotational or vibrational ones because there is only one atom moving in three-dimensional space. Hence, they correspond to:
   • List I: 3 Translational degrees of freedom
   • List II: I. Monoatomic gases
   Thus, A-I.
2. Rigid diatomic gases such as Nitrogen, Oxygen, etc., have 3 translational and 2 rotational degrees of freedom. Vibrations are not considered here because they are rigid. Therefore, they match:
   • List I: 3 Translational, 2 rotational degrees of freedom
   • List II: III. Rigid diatomic gases
   Hence, B-III.
3. Nonrigid diatomic gases have 3 translational, 2 rotational, and 1 vibrational degree of freedom because they can stretch and contract. So, they correspond to:
   • List I: 3 Translational, 2 rotational and 1 vibrational degrees of freedom
   • List II: IV. Nonrigid diatomic gases
   Thus, C-IV.
4. Polyatomic gases such as methane or water vapor generally have 3 translational, 3 rotational, and multiple vibrational degrees of freedom depending on the structure. Therefore, they match with:
   • List I: 3 Translational, 3 rotational and more than one vibrational degrees of freedom
   • List II: II. Polyatomic gases
   So, D-II.

Therefore, the correct matching of the lists is: (A)-(I), (B)-(III), (C)-(IV), (D)-(II).