Question

Infrared absorption by CO gives rise to an R branch from v = 0. What is the wavenumber of the line originating from the rotational state with J = 2? Assume v = 0 to 1 transition. The rotational constant is 1.92252 cm^-1. Ignore centrifugal distortion. Please show all work.

Answer 1

ANSWER--

We treat the molecule's rotations as those of a rigid rotor (ignoring centrifugal distortion). The energy of a rotation is also quantized in discrete levels given by

Er=h28π2IJ(J+1)

In which I is the moment of inertia, given by

I=μr2 where μ is the reduced mass from above and r is the equilibrium bond length.

Experimentally, frequencies or wavenumbers are measured rather than energies, and dividing by h or hc gives more commonly seen term symbols, F(J) using the rotational quantum number J and the rotational constant B in either frequency

F(J)=Erh=h8π2IJ(J+1)=BJ(J+1)

or wavenumbers

F(J)=Erhc=h8π2cIJ(J+1)=BJ(J+1)   ..............................................(eqt 1)

Note- rotational constant is always represented as B, whether in frequency or wavenumbers.

Now puttiing the values in (eq1)

wave number= 1.92252 x 2(2+1)

wave number = 11.54                             ~ Answer