Define the term degrees of freedom.

Explanation

Monoatomic molecule : A monoatomic molecules has only three translational degrees of freedom by virtue of its nature.
`:. f = 3`
Eg : Helium , Neon , Argon
Diatomic molecule : There are two cases.
(i) At Normal temperature : A molecule of a diatomic gas consists of two atoms bound to each other by a force of attraction. The centre of mass lies in the centre of the diatomic molecule. So the motion of the centre of mass requires three translational degrees of freedom.

`implies` Degree of freedom of diatomic molecule
In addition , the diatomic molecule can be rotated about three mutually perpendicular axes.

`implies` Degree of freedom of diatomic molecule
But the moment of inertia about its own axis of rotation is negligible. Hence , it has only two rotational degrees of freedom . So totally there are five degrees of freedom.
f = 5
(ii) At high temperature : At a very high temperature such as 5000 K , the diatomic molecules possess additional two degrees of freedom due to vibrational motion [ one due to kinetic energy of vibration and the other is due to potential energy ] .

`implies` Degree of freedom of diatomic molecule
So totally there are seven degree of freedom.
f = 7
Eg : Hydrogen , Nitrogen , Oxygen.
Triatomic molecule : There are two cases.
(i) Linear triatomic molecule : Linear triatomic molecule has three translational degrees of freedom . It has two rotational degrees of freedom because it is similar to diatomic molecule except there is an additional atom at the centre.
At normal , linear triatomic molecule will have five degrees of freedom . It has two additional vibrational degrees at high temperature.

`implies` A linear triatomic molecule
So a linear triatomic molecule has seven degree of freedom
Eg : Carbon dioxide.
(ii) Non - linear triatomic molecule : It has three translational degrees of freedom and three rotational degrees of freedom about three mutually orthogonal axes. So, the total degrees of freedom .
f = 6

`implies ` None - linear triatomic molecule
Eg : Water , Sulphurdioxide .