Question

A hydrogen atom initially in ground level absorbs a photon,which excites it to the n=4 level.Determine the wavelength and frequency of the photon.

Answer 1

For ground state $n_1=1$ and $n_2=4$

Energy of photon absorbed $E=E_2-E_1$

$=13.6(\frac{1}{1^2}-\frac{1}{4^2})$

$=13.6\times \frac{15}{16}ev$

$=\frac{13.6\times 15}{16}\times 1.6\times {19}^{-9}$

$E=2.04\times {10}^{-18}J$

$\lambda =\frac{hc}{E}=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{2.04\times {10}^{-18}}$

$\lambda =9.7\times {10}^{-8}m$

$\gamma =\frac{c}{\lambda }$

$=\frac{3\times {10}^8}{9.7\times {10}^{-8}}$

$=3.1\times {10}^{-15}$