Question

The microwave spectrum of the 12C16O molecule consists of a series of lines separated by 3.913 cm−1. Draw the corresponding energy level diagram for this spectral line spacing for the first 5 energy levels, assuming the rigid rotor model. Give the value for the energy gap between each level.

Answer 1

Microwave spectrum of 12C16O

wavenumber = 3.913 cm-1

energy for first line E1 = hv = 6.626 x 10^-34 x 3 x 10^10 x 3.913 = 7.8 x 10^-23 J

energy for second line E2 = hv = 6.626 x 10^-34 x 3 x 10^10 x 2 x 3.913 = 1.6 x 10^-22 J

energy for third line E3 = hv = 6.626 x 10^-34 x 3 x 10^10 x 3 x 3.913 = 2.34 x 10^-22 J

energy for second line E4 = hv = 6.626 x 10^-34 x 3 x 10^10 x 4 x 3.913 = 3.12 x 10^-22 J

energy for second line E5 = hv = 6.626 x 10^-34 x 3 x 10^10 x 5 x 3.913 = 3.9 x 10^-22 J

A representative design of spectral series is given below