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

Degrees of Freedom for Different Types of Gases: 

Type of Gas	No. of Degrees of Freedom
1. Monoatomic	3 (Translational)
2. Diatomic + rigid	3 (Translational) + 2 (Rotational) = 5
3. Diatomic + non-rigid	3 (Translational) + 2 (Rotational) + 1 (Vibrational)
4. Polyatomic	3 (Translational) + 2 (Rotational) + more than 1 (Vibrational)

Explanations:

• (A) 3 Translational degrees of freedom: This corresponds to movement along the x, y, and z axes. Monoatomic gases, consisting of single atoms, only have these three translational degrees of freedom. Thus, (A) matches with (I).
• (B) 3 Translational, 2 Rotational degrees of freedom: Diatomic molecules can translate in three directions and rotate about two axes perpendicular to the bond axis. Rigid diatomic molecules do not have vibrational degrees of freedom as the bond length is considered fixed. Thus, (B) matches with (III).
• (C) 3 Translational, 2 Rotational, and 1 Vibrational degrees of freedom: Non-rigid diatomic gases have the ability to vibrate along the bond axis, adding one vibrational degree of freedom in addition to the 3 translational and 2 rotational degrees. Thus, (C) matches with (IV).
• (D) 3 Translational, 3 Rotational, and more than 1 Vibrational degrees of freedom: Polyatomic gases, having more than two atoms, can rotate about all three axes. They also have multiple vibrational modes depending on the number of atoms and the molecular structure. Thus, (D) matches with (II).