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Question
In a diatomic molecule, the rotational energy at a given temperature ______.
- obeys Maxwell’s distribution.
- have the same value for all molecules.
- equals the translational kinetic energy for each molecule.
- is (2/3)rd the translational kinetic energy for each molecule.
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Solution
a and d
Explanation:
Consider a diatomic molecule as shown in the diagram.
The total energy associated with the molecule is
`E = 1/2 mv_x^2 + 1/2 mv_y^2 + 1/2 mv_z^2 + 1/2 I_xω_x^2 + 1/2 I_yω_y^2`
This above expression contains translational kinetic energy `(1/2 mv^2)` corresponding to velocity in each x, y and z-directions as well as rotational KE `(1/2 Iω^2)` associated with the axis of rotations x and y.
The number of independent terms in the above expression is 5.
As we can predict the velocities of molecules by Maxwell's distribution, hence the above expression also obeys Maxwell's distribution.
∵ 2 rotational and 3 translational energies are associated with each molecule.
∴ Rational energy at a given temperature is `(2/3)`rd of translational KE of each molecule.
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