Question

How do you find degrees of freedom and vibrational nodes?

Answer 1

Degree Of Freedom- Degree of freedom the the total number of co-ordinates or you can say that the number of variable used to describe the motion of a particle completely. OR degrees of freedom refer is the number of ways a molecule in the gas phase may move, rotate, or vibrate in space.For a single atom that is moving in space i,e in three dimensional space ,so here only three co-ordinate is sufficient to describe the motion of the atom completely.So, the degree of freedom for a atom moving in space is 3.

If we have a molecule made up of N atoms the degree of freedom of the molecule is 3N,because each atom that is present in the molecule has 3 degree of freedom , so for the molecule the degree is 3N.

There are three  types of degrees of freedom - translational, rotational, and vibrational.

Vibrational Modes-The number of vibrational degrees of freedom (or vibrational modes) of a molecule is determined by examining the number of unique ways the atoms within the molecule may move relative to one another, such as in bond stretches or bends.

The degrees of vibrational modes for linear molecules can be calculated using the formula: 3N-5

The degrees of freedom for nonlinear molecules can be calculated using the formula:3N-6

To find the vibrational modes we have to look the follwing way;

1) Determine if the molecule is linear or non linear for the linear molecule use the formula 3N-5 and for the non-linear molecule use the formula 3N-6.

2) Calculate the no. of atoms in the molecule i.e N.

3) Put your value in the formula and solve.