Question

The average current due to an electron orbiting the proton in the $n^{th}$ Bohr orbit of the hydrogen atom is

• A. $\propto n$
• B. $\propto n^3$
• C. $\propto n^{-3}$
• D. None of these

Answer 1

The correct option is C $\propto n^{-3}$

Current $i=\frac{q}{t}$
Time taken for one orbit $t=\frac{2\pi r}{v}$
where $r$ is radius and $v$ is velocity of electron
But we know $v\propto \frac{Z}{n}$
and $r\propto \frac{n^2}{Z}$
Hence $t\propto \frac{n^3}{Z^2}$
For hydrogen atom, $Z=1$
Putting this proportionality expression in the first equation
$i\propto n^{-3}$