Question

According to Bohr's theory, the time averaged magnetic field at the centre (i.e nucleus) of a bydrogen atom due to the motion of electrons in the $n^{th}$ orbit is propotional to : $(n=$ principal quantum number$)$

• A. $n^{-3}$
• B. $n^{-4}$
• C. $n^{-5}$
• D. $n^{-2}$

Answer 1

Answer: (C)

$n^{-5}$

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

$B={\mu }_0{i}_{n/\left(2r_n\right)}$,

Where $i_n$ is the current in the nth orbit $r_n$ the nth orbit and ${\mu }_0$ the magnetic permeablity of free space.

$r_n\alpha n^2$

$i_n\alpha n^{-3}$

Therefore

$\beta \alpha n^{-5}$

So the answer is (c) $n^{-5}$.