Q. The energy of electron in the $n$th orbit of hydrogen atom is expressed as $En = \frac{- 14.6}{n^{2}}$ $eV$. The shortest and longest wavelength of Lyman series will be
A) $910\mathring{\mathrm{A}},\ 1213\ \mathring{\mathrm{A}}$
B) $5463\ \mathring{\mathrm{A}}\ ,\ 7858\ \mathring{\mathrm{A}}$
C) $1315\ \mathring{\mathrm{A}},1530\ \mathring{\mathrm{A}}$
D) None of these
Explanation
(a) $\ \ \ \ \ \ \ \ \ \ \ \frac{1}{\lambda_{\max}} = R\left\lbrack \frac{1}{(1)^{2}} - \frac{1}{(2)^{2}} \right\rbrack$
$\Rightarrow \ \ \ \ \ \ \lambda_{\max}$ = $\frac{4}{3R}\ \approx 1213\ \mathring{\mathrm{A}}$
and$\ \ \ \ \ \frac{1}{\lambda_{\min}} = R\left\lbrack \frac{1}{(1)^{2}} - \frac{1}{\infty} \right\rbrack$
$\Rightarrow \ \ \ \ \ \ \lambda_{\min}$ = $\frac{1}{R} \approx$910 $\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.