Question

An electron moves in Bhor's orbit. The magnetic field at the centre is proportional to

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

Answer 1

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

Magnetic field at the center of a coil=$B=\frac{{\mu }_{0}i}{2r}$

Here the electrons orbits the nucleus and is equivalent to a current carrying coil, where $r$ is the Bohr's orbit, and $i=\frac{e}{T}=\frac{ev}{2\pi r}$

We know that $v\propto \frac{1}{n}$, $r\propto n^2$

$⟹B\propto \frac{i}{r}\propto \frac{\frac{1/n}{n^2}}{n^2}\propto \frac{1}{n^5}$