Question

A gas of mono atomic hydrogen is excited by an energy of $12.75$ eV/atom. Which spectral lines of the following are formed in Lyman, Balmer and Paschen series respectively?

• A. $3,2,1$
• B. $2,3,1$
• C. $1,3,2$
• D. $1,2,3$

Answer 1

The correct option is A $3,2,1$

Energy of the electron in various orbits are
Energy in $1^{st}$ orbit $=-13.6ev$
$E\propto \frac{1}{n^2}$
$2^{nd}orbit=\frac{-13.6}{4}ev=-3.4ev$
$3^{rd}orbit=\frac{-13.6}{9}ev=-1.51ev$
$4^{th}orbit=\frac{-13.6}{16}ev=-0.85ev$
$\to$ electrons is excited to $4^{th}$ orbit
Lyman $n_{1}ton=1$ $n_1=3$ [13.6ev-0.85ev]
Balmer $n_{2}ton=2$ $n_2=2$ [=12.75]
Paschen $n_{3}ton=3$ $n_3=1$