# Wavenumber of corresponding isotope peak in IR?

1. Feb 19, 2016

### magnesium12

1. The problem statement, all variables and given/known data
The infrared spectrum of CO shows a vibrational absorption peak at 2170 cm-1
(a) What is the force constant of the CO bond?
(b) At what wavenumber would the corresponding peak for
14CO occur?

2. Relevant equations
k=ω2μ = (2πcv)2μ

3. The attempt at a solution
So I solved part a correctly and the force constant for CO = 1900N/m
For part b I assumed the force constant was the same for both isotopes so :
v12(√μ1214) = v14
I got v14 = 2079cm-1. However, the posted answer is 2083cm-1.
I realize this isn't a very big difference, but I can't see a reason why my answer shouldn't be exact if I'm using the exact wavelength given and amus for the reduced mass (as in 12 and 14 for C, and 16 for O). So am I incorrect in assuming the force constants are the same? If the force constant is different for the isotopes, how would I go about solving this question since I would have two unknowns (k14 and v14).

2. Feb 19, 2016

### Staff: Mentor

Could be a rounding error.
How did you calculate the reduced masses?

The force constant should be the same.