Question

The velocity of an electron in the second orbit atom 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. $\frac{5}{2}v$
• D. $\frac{2}{5}v$

Answer 1

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

According to Bohr's model, velocity of an electron in an orbit is-

$V_n=\frac{Z{e}^2}{2nh}$

$\Rightarrow V_n\propto \frac{1}{n}$

$\therefore \frac{V_5}{V_2}=\frac{2}{5}$

Given that:- $V_2=v$

$\Rightarrow V_5=\frac{2}{5}v$

Hence the velocity of an electron in its fifth orbit will be $\frac{2}{5}v$.