Question

According to Bohr model of hydrogen atom, the electric current due to motion of electron in $n^{th}$ orbit is proportional to

• A. $\frac{1}{n^3}$
• B. $\frac{1}{n^5}$
• C. $n^3$
• D. $n^5$

Answer 1

Answer: (A)

Electric current due to motion of electron in $n^{th}$ orbit is, $I_n=e{\upsilon }_n$
For hydrogen atom,
Frequency of electron in $n^{th}$ orbit is
${\upsilon }_n={\left(\frac{1}{4\pi {\epsilon }_0}\right)}^2\frac{4{\pi }^2{e}^{4}m}{n^3{h}^3}\dots \left(i\right)$
$\therefore I_n={\left(\frac{1}{4\pi {\epsilon }_0}\right)}^2\frac{4{\pi }^2{e}^{5}m}{n^3{h}^3}$ (Using $\left(i\right)$)
Thus, $I_n\propto \frac{1}{n^3}$