Question

An electron in a hydrogen atom in its ground state absorbs twice of its ionization energy what is the wavelength of the emitted electron?

Answer 1

$$\begin{gathered} TherelationbetweenenergyandIonisationenergy \\ IE=-E=-(-13.6eV/atom) \\ Itsgiventhattheenergyofhydrogenistwiceofitsionisationenergy \\ 2IE=-E \\ =2\times 13.6eV/atom) \\ =27.2eV=27.2\times 1.6\times {10}^{-19}J(\sin ce1eV=1.6\times {10}^{-19}J) \\ E=\frac{hc}{\lambda } \\ \lambda =\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{27.2\times 1.6\times {10}^{-19}} \\ =0.457\times {10}^{-7}m \\ =45.7\times {10}^{-9}nm \end{gathered}$$