Question

$\lambda = \frac{h}{\sqrt{2mE}} \Rightarrow \Delta E = \frac{h^{2}}{2m}\left( \frac{1}{\lambda_{2}^{2}} - \frac{1}{\lambda_{1}^{2}} \right)$

$= \frac{\left( 6.626 \times 10^{- 34} \right)^{2}}{2 \times 9 \times 10^{- 31}}\left( \frac{1}{\left( 50 \times 10^{- 9} \right)^{2}} - \frac{1}{\left( 100 \times 10^{- 9} \right)^{2}} \right) $$$= 7.24 \times 10^{- 23}\text{ J = 4.5} \times \text{1}\text{0}^{- 4}\text{ eV}$$