The mircowave spectrum of the CO molecule consists of a seri

The mircowave spectrum of the CO molecule consists of a series of lines at wavenumbers 3.86, 7.73, 11.59,15.45, ...cm-1. Find the CO bond length.

Solution

Line separation = 2B = 15.45 - 11.59 = 3.86 cm-1

Rotational constant B = h/(8 x pi^2 x c x I) = 3.86/2 = 1.93 cm-1


Moment of inertia I = h/(8 x pi^2 x c x B)

= 6.626 x 10^(-34)/(8 x 3.1416^2 x 2.998 x 10^10 x 1.93)

= 1.450 x 10^(-46) kg.m^2


Reduced mass of CO = u = m(C) x m(O)/(m(C) + m(O) x atomic mass unit

= 12 x 16/(12 + 16) x 1.6605 x 10^(-27)

= 1.139 x 10^(-26) kg


Since I = u x r^2

Bond length r = (I/u)^(1/2)

= (1.450 x 10^(-46)/1.139 x 10^(-26))^(1/2)

= 1.13 x 10(-10) m (or 1.13 Angstroms)