Binding Energy

${}_7^{14}\mathrm{N}$ contains 7 protons and 7 neutrons.

Mass defect,  $\left({}_{}{}_{}\right)\left(\begin{array}{c}\\ \end{array}\right)$ $\mathrm{\Delta }m=\left(7m_H+7m_n\right)-m\left(\begin{array}{c}14\\ 7\end{array}\right)=(7*1.00783u)+(7*1.00867u)-14.00307u$

$=0.11243u$

Binding energy $=0.11243*931.5\mathrm{M}\mathrm{e}\mathrm{V}=104.7\mathrm{M}\mathrm{e}\mathrm{V}$

Sol. $\Rightarrow \mathrm{}{\stackrel{?}{\mathrm{V}}}_1=2\stackrel{?}{{\mathrm{U}}_{\mathrm{c}\mathrm{m}}}-\stackrel{?}{{\mathrm{U}}_1}\Rightarrow \mathrm{}2\left[\frac{\mathrm{m}/2{\mathrm{V}}_{\mathrm{o}}}{\frac{\mathrm{m}}{2}+\frac{\mathrm{m}}{3}}\right]-{\mathrm{V}}_{\mathrm{o}}$

$\Rightarrow \mathrm{}\frac{6}{5}{\mathrm{V}}_{\mathrm{o}}-{\mathrm{V}}_{\mathrm{o}}\Rightarrow \frac{{\mathrm{V}}_0}{5}$

$\Rightarrow \mathrm{}{\lambda }_{\mathrm{o}}=\frac{\mathrm{h}\mathrm{c}}{\left(\frac{\mathrm{m}}{2}{\mathrm{V}}_{\mathrm{o}}\right)}\mathrm{}{\lambda }_{\mathrm{f}}=\frac{\mathrm{h}\mathrm{c}}{\left(\frac{\mathrm{M}}{2}\frac{{\mathrm{V}}_{\mathrm{o}}}{5}\right)}$

$\Rightarrow \mathrm{\Delta }\lambda =\frac{8\mathrm{h}\mathrm{c}}{{\mathrm{m}\mathrm{V}}_{\mathrm{o}}}$