Question

The O-H bond in water vibrates at a frequency of 3650cm-1. What wavelength and frequency of light would be required to change the vibrational quantum number from n=0 to n=4 assuming 0-H acts as a Harmonic oscillator?

Answer 1

For a Harmonic oscillator the enery is given by

where n =0,1,2............. and is the frequency which is given by

wher k is the spring constant and is the reduced mass given by

where    are the atomic masses.

Here wavenumber is given as 3650 cm-1 for the O-H bond.

The energy difference between n = 0, n = 4

h = 6.62 * 10-34 Kg m²/s

is the frequency required for this transition.

= 43932 * 10⁶ Hz