Question

Frequency of $1$ line of paschen series of ${}^{\prime }{H}^{\prime }$ atom $2.34\times {10}^{14}Hz$ suggest quantum no which can produce thin transition.

Answer 1

For paschen series : -

$hv=E_{\circ }[\frac{1}{3^2}-\frac{1}{n^2}]J,$ where $E_{\circ }=13.6eV=13.6\times 1.6\times {10}^{-19}J$

$\therefore 6.6\times {10}^{-34}\times 2.34\times {10}^{14}=13.6\times 1.6\times {10}^{-19}[\frac{1}{3^2}-\frac{1}{n^2}]$

$\frac{1.544}{21.76}=\frac{1}{9}-\frac{1}{n^2}$

$n=5$

$\therefore$ Quantum no. producing this transition $=5$.