In a diatomic molecule, the rotational energy at a given temperat… - Vidyadip

MCQ

In a diatomic molecule, the rotational energy at a given temperature.

A
Obeys Maxwell’s distribution.
B
Have the same value for all molecules.
C
Equals the translational kinetic energy for each molecule.
D
Is (2/3)rd the translational kinetic energy for each molecule.

✓

Answer

Obeys Maxwell’s distribution.

Is (2/3)rd the translational kinetic energy for each molecule.

Explanation:

Consider a diatomic molecule along z-axis so its rotational energy about z-axis is zero. So energy of diatomic molecule,

$\text{E}=\frac{1}{2}\text{mv}_\text{x}^2+\frac{1}{2}\text{mv}_\text{y}^2+\frac{1}{2}\text{mv}_\text{z}^2+\frac{1}{2}\text{I}_\text{x}\omega_\text{x}^2+\frac{1}{2}\text{I}_\text{y}\omega_\text{y}^2$ (as moment of inertia along z axis is zero)

The independent terms in the above expression is 5.

As we can predict velocities of molecules by Maxwell’s distribution.

Hence the above expression also obeys Maxwell’s distribution.

As 2 rotational and 3 translational energies are associated with each molecule.

So the rotational energy at given temperature is 2/3 of its translational Kinetic energy of each molecule.

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