Question

Find the longest and shortest wavelength when a hydrogen atom in the ground state is excited by radiations of wavelength $975$ $\stackrel{o}{A}$.

Answer 1

$E=\frac{hc}{\lambda }=\frac{6.636\times {10}^{-34}\times 3\times {10}^4}{975\times {10}^{-10}}\times \frac{{10}^{19}}{1.6}$
$=\frac{6.636\times 3}{9.75\times 1.6}\times {10}^{35-34}$
$E_n=-13.6+12.75eV$
$=-85eV$
$u=4$
Now longest wavelength $\frac{1}{\lambda }=R_n[\frac{1}{9}-\frac{1}{16}]$
$4\to 3$
Shortest wavelength $\frac{1}{\lambda }=R_n[\frac{1}{1}-\frac{1}{16}]$
$4\to 1$