Question

Absorption by H CI occurs in the far infrared near = 200 1. cm and the spacing between the neighboring lines is 20.89 cm Find the moment of inertia and the internuclear distance in H CL Solution From Eq. 13.99, with J = 0 (which gives the spacing), %3D

Answer 1

From the separation between the lines, the moment of inertia
can be obtained, and from that the distance between the atoms, i.e. the
bond length.
From the spacing one gets δν = cδν¯ = h/4π²I = 3*10^8*20.89*10^-2 = 6.267*10⁷ Hz .

and that gives I = h/4π² δν = 2.678*10^-43kgm²

. The moment of inertia is I = µr²_b,

Here reduced mass of HCl,µ =1.66*10^-27[(35.5*1)/(35.5+1)]= 1.652*10^-27kg

so,Inter nuclear distance,r_b = (I/µ)^1/2

=[ (2.678*10^-43)​​​)/(1.652*10^-27)]^1/2.

= 1.27*10^-8 m

All the best. Thank you.