The vibrational transition from $v=3$ to $v=4$ for ${?}^1{H}^{35}Cl$ occurs with a force constant of the $HCl$ bond equal to $4\mathrm{.}78{10}^5\frac{g}{se{c}^2}.$ Assume that the vibrational motion of $HCl$ is purely harmonic. Calculate the energy of the transition between the vibrational energy levels in this molecule, in units of ergs.

or $($:$6\mathrm{.}63{10}^{-34}(J)(s),N_A=6\mathrm{.}022{10}^{23}mo{l}^{-1}\}$

a$.5\mathrm{.}27{10}^{-13}$erg

b$.4\mathrm{.}44{10}^{-13}$erg

c$.5\mathrm{.}74{10}^{-13}$erg

d$.1\mathrm{.}61{10}^{-24}$erg

e$.5\mathrm{.}44{10}^{14}$erg