Q 12-12-031JEE MainJEE Main 2026 (2 Apr, Shift 2)Medium
Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{\text{nd}}$ and $4^{\text{th}}$ orbits of hydrogen atom ______.
Numerical value type. Enter your answer.
Answer: 32
The orbiting electron is a current loop, so the field at the nucleus is $B=\dfrac{\mu_0I}{2r}$ with $I=\dfrac{ev}{2\pi r}$:
$$B=\frac{\mu_0ev}{4\pi r^2}$$
In Bohr's model $v\propto\dfrac1n$ and $r\propto n^2$, so $B\propto\dfrac{1/n}{n^4}=\dfrac{1}{n^5}$.
$$\frac{B_2}{B_4}=\left(\frac42\right)^5=32$$
Solution by Sreeraj P, M.Sc Physics