Question

state number of degrees of freedom possessed by the monoatomic molecule in a space also give expression for total energy possessed by it at a given temperature hence five the total energy of atom at 300k

Answer 1

The number of independent way in which a body or a particle may absorb energy is called degree of freedom of that body or system of particle.
let n be no. of particle in a system or r be tha relation among them,
so
no. of dgree of freedom = 3n - r

for example
in monoatomic gas molecules
since there is only one atom so there would be no relation with other atom

so the no of degree of freedom of that gas molecule is
3(1) - 0
so
= 3
so for monoatomic molecule the no. of degree of freedom is 3.

Answer 2

Answer:

The number of degrees of freedom of monoatomic molecule is 3. Total energy possessed by it is 3/2 KT. Total energy of atom at 300 K is $6.21×10^{-21} J$.

Explanation:

Degrees of freedom

Degrees of freedom is defined as the number of independent co-ordinates the particle has without the constraints. Constraints are the limitations in motion of the particles. If there are constraints then these are substracted from degrees of freedom.

Here monoatomic molecule can freely move to X-axis, Y-axis and Z-axis. Also, it has no constraint. It can move freely. So, it has three degrees of freedom.

The total energy of the molecule is given by

(f/2)KT

where f is degrees of freedom, K is Boltzmann constant and T is temperature.

The value of Boltzmann constant is $1.38×10^{-23} J/K$

Here, there is monoatomic molecule. So, f = 3. So, total energy of molecule is 3/2 KT.

Total energy at 300 K =$(3/2)×1.38×10^{-23}×300$

= $6.21×10^{-21} J$