Q$3$ Vibrational spectroscopy and Simple harmonic oscillator:

$($a$)$ In the infrared spectrum of $H^{127}$I $($Hydrogen iodide where the su$-$

perscript of $127$ represents the atomic mass of Iodine in Daltons or

atomic mass units$),$ there is an intense line at $2309c{m}^{-1}.$ Calculate

the force constant of $H^{127}$I and the period of vibration ofH ${?}^{127}$I.

$($b$)$ Using the following infrared absorption spectroscopic data for iodine

chloride ${(}^{127}{I}^{35}Cl),$ show that the vibrational terms $($vibration energy

levels$)$ can be parametrized as

$G(v)=$tilde$($

$u{)}_e(v+\frac{1}{2})+$tilde$(x{)}_e$tilde$(v{)}_e(v+\frac{1}{2}{)}^2$;$v=0,1,2,$dots