Question

The atom of a hydrogen like gas are in a particular excited energy level. When these atoms de-excite, they emit photons of different energies. The maximum and minimum energies of emitted photons are $E_{\max }=204eV$ and $E_{\min }=10.5\overline{7}eV$ respectively. The principal quantum number of initially excited energy level is_________.

Answer 1

Answer: 4

$E_{\max }=13.6z^2\left(1-\frac{1}{n^2}\right)=204$
$z^2\left(1-\frac{1}{n^2}\right)=\frac{2040}{136}$
$13.6z^2=10.5\overline{7}$
$z^2\left(\frac{1}{(n-1{)}^2}-\frac{1}{n^2}\right)=\frac{10.5\overline{7}}{13.6}=\frac{7}{9}$
try. $Z=4,n=4$
$16\left(\frac{1}{9}-\frac{1}{16}\right)=\frac{7}{9}$
$16\left(1-\frac{1}{16}\right)=15$
$n=4$