Question

For CO molecule, the first line in the pure rotational spectrum appears at 3.8424 cm !. Determine the moment of
inertia of the molecule.
Select one:
O a. 1.458 x 10-49 kg m?
O b. 1.458 X 10-47 kg m2
O c. 1.458 x 10-48 kg
kg me
O d. 1.458 X 10-46 kg m2​

Answer 1

Answer:

The rotational constant is easily obtained from the rotational line spacing for a rigid rotor:

ν~=2B~(J+1), so Δν~=2B~ and B~=1.93cm−1

The rotational constant is related to the bond length R by the equation:

B~=h8π2cμR2(12.E.1)

with the reduced mass μ=mCmOmC+mO=1.14×10−26kg

Therefore, the bond length R is:

R2=h8π2cμB~=1.27×10−20m2(12.E.2)

R=1.13Å