Q. The energy of electron in the $n$th orbit of hydrogen atom is expressed as $E_{n} = \frac{- 13.6}{n^{2}}eV$. 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.