Question

If an electron is moving in the $n ^{\text {th }}$ orbit of the hydrogen atom, then its velocity $\left(v_{n}\right)$ for the $n^{\text {th }}$ orbit is given as:

• A. $v _{ n } \propto n$
• B. $v _{ n } \propto \frac{1}{ n }$
• C. $v _{ n } \propto n ^{2}$
• D. $v _{ n } \propto \frac{1}{ n ^{2}}$

Answer 1

Answer: (B)

We know velocity of electron in $n ^{\text {th }}$ shell of hydrogen atom is given by
$v =\frac{2 \pi k Ze ^{2}}{ nh }$
$\therefore v \propto \frac{1}{ n }$