Questions & Answers

Question

Answers

A. 6

B. 4

C. 2

D. 8

Answer
Verified

We have to find the Degree of freedom of a triatomic molecule. A triatomic gas molecule has 3 atoms in it.

Consider a triatomic gas molecule as shown in the figure above.

We now consider the possible movements of this molecule in the x, y and z axis.

Here this triatomic gas can have a translatory motion along the x, y, and z axis. I.e. triatomic molecules can move along x direction, y direction and z direction.

Hence the translatory degree of freedom of this molecule is 3

Now let us consider the rotational degree of freedom of this molecule.

For that we place two atoms of the molecule on the x axis. Then it can rotate about y axis and z axis. It also has a significant rotation about x axis because here the third atom has a moment of inertia about x axis even if the other two atoms do not have the inertia.

And thus the rotational degree of freedom of this molecule is also three.

Hence the degree of freedom= Translatory degree of freedom + Rotational degree of freedom

=3+3=6

Therefore at moderate temperature the degree of freedom of a triatomic gas equals to 6.

Degree of freedom, $\text{DF=3N-n}$ where N is the total number of particles and n is holonomic constraints.

We have a triatomic molecule. And hence the number of particles, $\text{N=3}$. And since the separation between 3 atoms is fixed, the number of holonomic constraints, $\text{n=3}$.

Therefore we have,

$\begin{align}

& \text{DF=3 }\!\!\times\!\!\text{ 3 - 3} \\

& \text{DF=9 - 3} \\

& \text{DF=6} \\

\end{align}$

Thus the degree of freedom of a triatomic molecule is 6.