Question

Calculate the energy required to ionize a hydrogen atom to an excited state where the electron is initially in the n = 5 energy level. Report your answer in kilojoules.
What is the longest wavelength of electromagnetic radiation capable of ionizing this hydrogen atom in an excited state? Report your answer in nanometers.

Answer 1

Energy of electron in any energy level n is given by$\frac{-13.6}{n^2}\ eV$

In 5th energy level

$E=\frac{-13.6}{5^2}eV$

Energy required$=E$ = $\frac{13.6}{25}=0.544\ eV=1.602\times 10^{-19}\times 0.544\times 10^{-3}\ kJ=8.71\times10^{-23}\ kJ$

Now

$E=\frac{hc}{\lambda}$

$\lambda=\frac{hc}{E}$ $=\frac{6.626\times 10^{-34}\times 3\times 10^8}{8.71\times 10^{-23}\times 10^3}=$ $2.282\times 10^{-6}\ m=2282\times 10^{-9}m=2282 \ nm$

Maximum Wavelength$=2282 \ nm$