Question

Given below are two statements :

Statement $1$ : In a diatomic molecule , the rotational energy at a given temperature obeys Maxwell's distribution .

Statement $2$ : In a diatomic molecule , the rotational energy at a given temperature equals the translational kinetic energy for each molecule.

In the light of above statements, choose the correct answer from the options given below:

• A. Both statement $1$ and statement $2$ are false .
  
• B. Both statement $1$ and statement $2$ are true .
• C. Statement $1$ is false but statement $2$ is true
• D. Statement $1$ is true but statement $2$ is false .

Answer 1

The correct option is D Statement $1$ is true but statement $2$ is false .

The translational kinetic energy and rotational kinetic energy both obey Maxwell's distribution , independent of each other .

$\text{T.K.E}$ of diatomic molecule $=$ $\frac{3}{2}$ $KT$ (Translational degree of freedom $=$ $3$ )

$\text{R.K.E}$ of diatomic molecule $=$ $\frac{2}{2}$$KT$ (Rotational degree of freedom $=$ $2$)

So , Statement $1$ is true but statement $2$ is false .

Option (d) is the correct answer .