Question

The translational degrees of freedom ($f_t$) and rotational degrees of freedom ($f_r$) of $\text{CH}_4$ molecule are:

• A. $f_t = 2 \, \text{and} \, f_r = 2$
• B. $f_t = 3 \, \text{and} \, f_r = 3$
• C. $f_t = 3 \, \text{and} \, f_r = 2$
• D. $f_t = 2 \, \text{and} \, f_r = 3$

Answer 1

Answer: (B)

$f_t = 3 \, \text{and} \, f_r = 3$

Answer 2

Since CH4 is polyatomic Non-Linear D.O.F of CH4:
T. DOF = 3 R DOF = 3

The molecule CH4 (methane) is a polyatomic molecule with a non-linear structure.

For non-linear polyatomic molecules:
The translational degrees of freedom (f t) are 3, corresponding to motion along the x, y, and z axes.

The rotational degrees of freedom (f r) are also 3, as the molecule can rotate about three mutually perpendicular axes.

Thus, for CH4, we have:
$f_{t} = 3 \, \text{and} \, f_{r} = 3.$