Question

The velocity of an electron in its fifth orbit, if the velocity of an electron in the second orbit of sodium atom $(Z+11)$ is $v$, will be

• A. $v$
• B. $\frac{22}{5}v$
• C. $\frac{5}{2}v$
• D. $\frac{2}{5}v$

Answer 1

The correct option is D $\frac{2}{5}v$

Velocity in nth orbit $v_n=2.18\times {10}^6\frac{Z}{n}$ m/s

Ratio of velocity in different orbits $\frac{v_n}{v_m}=\frac{m}{n}$

Given : $n=5$ $m=2$

$\therefore$ $\frac{v_5}{v}=\frac{2}{5}$ $⟹v_5=\frac{2v}{5}$