Question

What is the degree of freedom for ${{O}_{2}}$?

Answer 1

Hint: A degree of freedom is an independent physical parameter in the formal description of the state of a physical system in physics and chemistry. The phase space of a system is the set of all states of the system, and the degrees of freedom of the system are the phase space's dimensions.

Complete answer:
Three position coordinates are required to locate a particle in three-dimensional space. Similarly, the direction and speed with which a particle moves may be defined in terms of three velocity components, each referring to one of the three spatial dimensions. A system with six degrees of freedom possesses deterministic time evolution, in which the state at one moment uniquely defines its past and future location and velocity as a function of time. The system has less than six degrees of freedom if the particle's mobility is restricted to a smaller number of dimensions - for example, if the particle must move down a wire or on a fixed surface.
A system with an extended item that may spin or vibrate, on the other hand, can have more than six degrees of freedom.
Degrees of freedom (DOF): A mechanical system's degree of freedom (DOF) is the number of independent factors that define its configuration.
A rigid body's position and orientation in space are specified by three components: one translation and three rotation components, giving it six degrees of freedom.
N = 3A - R, where A is the number of particles in the system and R denotes the number of relations between the particles.
Translation is the movement of a whole body from one location to another. A diatomic gas, such as hydrogen, oxygen, or nitrogen, has two atoms in each molecule. Thus, a diatomic molecule with three translational degrees of freedom and two rotational degrees of freedom is free to travel in space.
In the case of a diatomic gas,
The system's particle count (A) is equal to two.
The number of particle relationships (R) is equal to one.
\[N\text{ }=\text{ }3\text{ }\times \text{ }2\text{ }-1\text{ }=\text{ }5\] is the number of degrees of freedom.
Thus, oxygen molecules have 5 translational degrees of freedom and are free to move in space.

Note:
The state of a point particle at any given time in classical mechanics is frequently represented by position and velocity coordinates in the Lagrangian formalism, or position and momentum coordinates in the Hamiltonian formalism. A degree of freedom is a single scalar number in statistical mechanics that describes the microstate of a system. A point in the system's phase space represents the definition of all microstates.