Question

In Physical Chemistry, what are the formulas for Zero Point Energy and Fundamental Vibrational Frequency? Please tell me what the constants are.

Answer 1

1. Zero point energy

--------------------------------(1)

where

zero point energy implies the energy of the oscillator when the vibrational quantum number i.e. V = 0

by substituting V = 0 we get the corresponding equation (1) = Zero point energy

2. Fundamental vibration frequency:

at room temperature most of the molecules will be in the ground state i.e at V = 0 energy level.

for simple harmonic motion the selection rule for vibrational transition is:

So the only transition possible at the room temperature is from V = 0 to V = 1 state.

The vibrational frequency corresponding to this transition is called Fundamental Vibration Frequency

here:

where E₁ = vibrational energy when V = 1

E₀ = vibrational energy when V = 0 i.e.zero point energy