Question

Discuss rotational spectra of a diatomic molecule and a rigid rotator

Answer 1

Answer:

For a rigid rotor diatomic molecule, the selection rules for rotational transitions are ΔJ = +/-1, ΔMJ = 0 . The rotational spectrum of a diatomic molecule consists of a series of equally spaced absorption lines, typically in the microwave region of the electromagnetic spectrum.

Answer 2

Explanation:

Let us consider HCl, a linear molecule as an example. Let us consider that two atoms having mass m₁ and m₂ are joined together by a line, whose length is-

r = r₁+r₂

Again let that bond length of the molecule doesn’t change during rotation. We also assume that the atoms are point-like. A diatomic molecule whose nuclei are separated by a finite distance behaves as a rigid- rotator.

m₁r₁ = m₂r₂

The moment of inertia of the molecule-

I = m₁r₁²+ m₂r₂²

We know that-

r= r₁+r₂

So, r ₁ = m₂r/m₁+m₂

r₂ = m₁r /m₁+m₂

Putting in I,

I= m₁ (m₂r/m₁+m₂²)² + m₂(m₁r/m₁ + m₂)²

By solving this equation we get-

I = (m₁.m₂/m₁+m₂)r²

I= μr²

Where μ is called reduced mass.

And μ = m₁m₂/m₁+m₂