Question

HCl has a bond force constant of 480 N/m, oscillates at 8.66x10^13 Hz and an equilibrium bond length of 0.127nm.

(a) At what wavelength (in μm) and wavenumber (in cm−1) would you expect such a molecule to absorb light?

(b) When the molecule is in its ground energy state, the two atoms do not simply rest at a fixed distance of 0.127 nm and, instead, they are constantly in motion. What is the maximum and minimum distance of separation between H and Cl in this state?

(c) Repeat (b) but now for the first excited vibrational energy state.

Answer 1

1)

As we know that

v- = 1/2c  ( k /) ^1/2   as = m1 m2 / m1+m2 = 1 * 10^-27 Kg *35.5 * 10^-27 Kg / 35.5 * 10^-27 Kg +1* 10^-27 Kg

= 0.9726 * 10^-27 Kg

above   = reduced mass , k = force constant ,

v- = 1/2 *3.14 ( 3 *10¹⁰ cm s^-1 ) ( 480 kg s^-2 / 0.9726 * 10^-27 Kg )^1/2   

= 0.05308 *10^-10 *(493.52 *10²⁷)^1/2    =   0.05308 *10^{-10 *} (49.352 *10²⁸)^1/2

=   0.05308 *10^{-10 *} 7.0250 * 10¹⁴ = 3728.87 cm^-1