Harmonic Oscillator- Energy levels

[quantumech]

Homework Statement

Predict the wavenumber (cm^-1) position of infrared absorption due to fundamental vibration from v=0 to v=1 and 2nd overtone from v=0 to v=3. For a harmonic occilator whose frequency=8.00x10¹³ s.

Homework Equations

Energy expression for harmonic oscilator:

E_v= (v+1/2)hv v=1, 2, 3...

The Attempt at a Solution

I am not at all sure of my answers, but this is what I did:

Fundamental Vibration:

E₀= (0+1/2)*6.626x10^-34*8.00x10¹³ s
= 2.504 x 10^-20

E₁= (1+1/2)*6.626x10^-34*8.00x10¹³ s
= 7.9512 x 10^-20

E₃= (3+1/2)*6.626x10^-34*8.00x10¹³ s
= 1.85528 x 10^-19

Then I found difference between energies:
E₁-E₀=5.4472*10^-20 and

E₃-E₀=1.60488*10^-19

I have no clue how to find the infrared absorption from this. Please help me ASAP. Thanks.

 

[Redbelly98]

You need the equation for energy of a photon of a particular wavelength. Your book or professor must have given you this, in order to be asking this question.

Another question, do you know what the units are for the energies you calculated?