Question

How do you find degrees of freedom and vibrational nodes?

Answer 1

The degrees of freedom of a molecule is measured as follows :-

If we consider the molecule consists of 'N' number of molecules,whilw each atom moves in the three independent co-ordinates x,y,z directions.Now the each atom having independent degrees of freedom is not useful.Instead that we make the combinations of different degrees of freedom.The important thing that when a particular degrees of freedom does to the atom changes,the standard breakdown of degrees of freedom subtracts out the global movement in each of the three directions.So, we have '3N' degrees of freedom.

For both linear and non-linear molecules there are "3N" degrees of freedom

The number of vibrational modes modes are measured as:-

As,the molecule consists "3N" degrees of freedom.tse "3N" will include the translation ,rotation and vibration modes.Translation corresponds movement of the center of mass whose position can be described by three cartesian co-ordinates.So, the degree of freedom changes to "3N-3"

A non linear molecule can rotate about any of three mutually perpendicular axes and therefore has three rotatinal degrees of freedom.The the number of vibrational modes are "3N-3-3"i.e.,"3N-6"

A linear molecule can rotate only in two rotational degrees of freedom then the number vibrational modes are "3n-3-2" i.e., "3N-5"