Question

In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to [ $n \rightarrow $ principal quantum number, $Z \rightarrow $ atomic number]

• A. $\frac{Z^{3}}{n^{4}}$
• B. $\frac{n^{3}}{Z^{2}}$
• C. $\frac{Z^{2}}{n^{3}}$
• D. $\frac{n^{4}}{Z^{3}}$

Answer 1

Answer: (A)

The net force on a revolving electron is
$F = \frac{m v^{2}}{r}$
$F \propto \frac{v_{n}^{2}}{r_{n}}$
The velocity of the electron in the $n^{th}$ shell
$v_{n} \propto \frac{Z}{n}$
and the radius of the $n^{th}$ shell
$r_{n} \propto \frac{n^{2}}{Z}$
$\Rightarrow F \propto \frac{Z^{3}}{n^{4}}$