Question

If the velocity of an electron in the second orbit of hydrogen atom is $x$, the velocity in fourth orbit will be:

• A. $x/16$
• B. $0.4x$
• C. $x/4$
• D. $x/2$

Answer 1

The correct option is D $x/2$

Velocity of an electron in an orbit = $\frac{nh}{2\pi mr}$
Therefore$\frac{v_2}{v_4}=\frac{n_2}{n_4}\times \frac{r_4}{r_2}$
$r=0.529$ $n^2$

$n_4^2=16$ and $n_2^2=4$

Therefore, $\frac{v_2}{v_4}=\frac{2}{4}\times \frac{16}{4}=2$
$\therefore \frac{v_2}{v_4}=2$ and $v_4=\frac{v_2}{2}=$ $\frac{x}{2}$