Question

The velocity of an electron in the second orbit of sodium atom (atomic number $=11$ ) is $v .$ The velocity of an electron in its fifth orbit will be

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

Answer 1

Answer: (D)

Velocity of electron in nth orbit
$v_{n}=\frac{Z e^{2}}{2 \varepsilon_{0} n h}$
$\Rightarrow v \propto \frac{1}{n}$
$v_{1}=v, n_{1}=2, n_{2}=5$
$\therefore \frac{v}{v_{2}} =\frac{n_{2}}{n_{1}}$
$\therefore \frac{v}{v_{2}}=\frac{5}{2}$
$\Rightarrow v_{2}= \frac{2 v}{5}$