Question

When electrons in a hydrogen atom jumps from first orbit to one of the higher energy orbits, the orbital velocity is reduced to (1/3)rd the initial value. If the radius of the first orbit is r, the radius of the higher energy orbit is

• A. 9r
• B. 4r
• C. 3r
• D. 2r

Answer 1

The correct option is A 9r

$v\propto \frac{1}{n}$
$\frac{v_1}{v_2}=\frac{n_2}{1}\Rightarrow \frac{v_1}{\frac{v_1}{3}}=n_2\Rightarrow n_2=3$
$r\propto n^2$
$\Rightarrow \frac{r_1}{r_2}={\left(\frac{n_1}{n_2}\right)}^2$
$\frac{r}{r_2}={\left(\frac{1}{3}\right)}^2\Rightarrow r_2=9r$