Using the expression provided below for vibrational energy, show that the maximum value of the vibrational energy is the value predicted by the Equipartition of Energy principle.

$[5$ marks$]$

$[10$ marks$]$

R $=8\mathrm{.}3145$ J K$-1$ mol$-1$ h $=6\mathrm{.}626$ x $10-34$ J s

$1$ atm $=101325$ N m$-2$

$$ RTx $$ Evib$=$ x $$e $1$

k $=1\mathrm{.}38$ x $10-23$ J K$-1$

NA $=6\mathrm{.}022$ x $1023$ mol$-1($ii$)$ Using the expression provided below for vibrational energy, show that the

maximum value of the vibrational energy is the value predicted by the

Equipartition of Energy principle.

$,E_{\text{v}\text{i}\text{b}}=(\frac{RTx}{e^x-1})$

$R=8\mathrm{.}3145J{K}^{-1}mo{l}^{-1},k=1\mathrm{.}38{10}^{-23}J{K}^{-1}$

$h=6\mathrm{.}626{10}^{-34}J{s}^{23}mo{l}^{-1}$

$1$atm$=101325N{m}^{-2},N_A=6\mathrm{.}022{10}^{-3}{m}^{-1}$