Question

An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transitions. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transitions. The ratio of the velocity of the electron in these two orbits is

• A. $\frac{5}{4}$
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. $\frac{2}{1}$

Answer 1

Answer: (B)

Number of spectral lines obtained due to transition of electrons from $n$ th orbit to lower orbit is,
$N=\frac{n(n-1)}{2}$
I case $6=\frac{n_1\left(n_1-1\right)}{2}$
$\Rightarrow n_1=4$
II case $3=\frac{n_2\left(n_2-1\right)}{2}$
$\Rightarrow n_2=3$
Velocity of electron in hydrogen atom in $n$ th orbit
$v_n\propto \frac{1}{n}$
$\frac{v_n}{v_n^{\prime }}=\frac{n_2}{n_1}$
$\Rightarrow \frac{v_6}{v_3}=\frac{3}{4}$