Describe the total degrees of freedom for monoatomic molecule, diatomic molecule and triatomic molecule.

Explanation

Monatomic molecule
A monoatomic molecule by virtue of its nature has only three translational degrees of freedom.
Therefore f = 3
Example: Helium, Neon, Argon
Diatomic molecule :

(i) At normal temperature
A molecule of a diatomic gas consists of two atoms bound to each other by a force of attraction.
The center of mass lies in the center of the diatomic molecule. So, the motion of the center of mass requires three translational degrees of freedom. In addition, the diatomic molecule can rotate about three mutually perpendicular axes. But the moment of inertia (about y-axis) in the figure). Therefore, it has only two rotational degrees of freedom. Therefore totally there are five degrees of freedom. f = 5
(ii) At High Temperature
At a very high temperature such as `5000K`, the diatomic molecules posses additional two degrees of freedom due to vibrational motion [one due to kinetic energy of vibration and the other is due to potential energy]. So totally there are seven degrees of freedom. f = 7
Examples: Hydrogen, Nitrogen, Oxygen.
(iii) Triatomic molecules
There are two cases.
Linear triatomic molecule:
In this type, two atoms lie on either side of the central atom as shown in the figure. 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 center. At normal temperature, linear triatomic molecule will have five degrees of freedom. At high temperature it has two additional vibrational it has two additional vibrational degrees of freedom. So a linear triatomic molecule has seven degrees of freedom.
Example: Carbon dioxide.
Non-linear triatomic molecule:
In this case, the three atoms lie at the vertices of a triangle as shown in the figure. It has three translational degrees of freedom and three rotational degrees of freedom about three mutually orthogonal axes. The total degrees of freedom, f = 6
Example: Water, Sulphurdioxide.