Question

The magnetic field induction produced at the centre of orbit due to an electron revolving in $n^{th}$ orbit of hydrogen atom is prportional to

• A. $n^{-3}$
• B. $n^{-5}$
• C. $n^5$
• D. $n^3$

Answer 1

The correct option is B $n^{-5}$

$\text{Solution:-}$

The magnetic field induced at the centre of an orbit due to an electron revolving in the nth orbit of hydrogen atom is given by

B = ${\mu }_o{I}_n$/2$r_n$

where $I_n$ is the current in the nth orbit, $r_n$ is the radius of the nth orbit and ${\mu }_o$ is the magnetic permeablity of free space. Now

$r_n$ ∝ $n^2$
$I_n$ ∝ $n^{-3}$
Therefore
B ∝ $n^{-5}$

$\text{Hence the correct option is B}$