Question

Explain why particular isotopes are specified in vibrational and rotational calculations, instead of the atomic mass listed in the period table.

Answer 1

Case 1

Energy levels for rotational motion of a molecule is given by

Where J is the rotational quantum number

And I is the moment of inertia about the axis of rotation of the molecule.

For example, Moment of inertia (I) for a diatomic molecule is given by

Where m₁ and m₂ are the masses of atoms in diatomic molecule; r is internuclear distance and is the reduced mass.

Note:

1. Energy is inversely proportional to moment of inertia and moment of inertia is directly related to reduced mass.

2. Isotopes are different by each other on the basis of atomic weight, not by the atomic number.

Case 2:

Natural frequency of vibration of any particular bond is given by the following equation

Where, K is the force constant and is the reduced mass and is given by

Frequency of vibration is inversely related with reduced mass of atoms involved in vibration.

And different isotopes have different atomic masses.

That’s why particular isotopes are specified in Rotational and Vibrational calculations.