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The total energy of molecules is divided...

The total energy of molecules is divided equally amongst the various degrees of freedom of a molecule. The distribution of kinetic energy along x, y, z axis are `E_(K_(x)), E_(K_(y)), E_(K_(z))`
Total K.e `=E_(K_(x)) + E_(K_(y)) + E_(K_(z))`
Since the motion of molecule is equally probable in all the three directions, therefore
`E_(K_(x)) = E_(K_(y)) = E_(K_(z)) =1/3 E_(K) =1/3 xx 3/2 kT = 1/2 kT`, where `k =R/N_(A)` = Botzman constant.
`K.E. = 1/2 kT` per molecule or `=1/2 RT` per mole.
In vibration motion, molecules possess both kinetic energy as well as potential energy. This means energy of vibration involves two degrees of fiuedom.
Vibration energy `=2 xx 1/2kT =2 xx 1/2RT` [`therefore` two degrees of freedom per mole]
If the gas molecules have `n_(1)` translational degrees of freedom, `n_2` rotational degrees of freedom and `n_(3)` vibrational degrees of freedom, that total energy = `n_(1)[(kT)/2] + n_(2) [(kT)/2] + n_(3) [(kT)/2] xx 2`

Where 'n' is atomicity of gas.
How many total degrees of freedom are present in `H_(2)` molecules in all types of motions ?

A

3

B

5

C

6

D

4

Text Solution

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The correct Answer is:
C
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