Question

The ratio of the wave number corresponding to the first line of Lyman series of $H$-atom and third line of Paschen series of a hydrogen-like sample is $9:16$. Then find the third excitation potential in terms of volt for this $H$-like samples.

Answer 1

Answer: 204

Wave number
$N=\frac{1}{\lambda }=R{z}^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
$\frac{N_1}{N_2}=\frac{z_1^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)}{z_2^2\left(\frac{1}{n_1^{{}^{\prime }2}}-\frac{1}{n_2^{{}^{\prime }2}}\right)}$
$=\frac{(1-1/4)}{z^2\left(\frac{1}{9}-\frac{1}{36}\right)}$
$\Rightarrow \frac{N_1}{N_2}=\frac{9}{z^2}=\frac{9}{16}$
$\Rightarrow z=4$
Hence third excitation potential $=12.75\times 16=204V$.