Question

In a hydrogen atom, the electron makes a transition from $n=2$ to $n=1$. The magnetic field produced by the circulating electron at the nucleus

• A. Decreases 16 times
• B. Increases 4 times
• C. Decreases 4 times
• D. Increases 32 times

Answer 1

Answer: (D)

Increases 32 times

Magnetic field produced at the center due to a circulating electron is:

$\left|\overrightarrow{B}\right|=\frac{{\mu }_0}{4\pi }\frac{e{v}_n}{r^2}$

And, $v_n={\left(\frac{Z{k}_e{e}^2}{m_{e}r}\right)}^{\frac{1}{2}}$

$\therefore \left|\overrightarrow{B}\right|\alpha \frac{1}{r^{\frac{5}{2}}}\Rightarrow \left|\overrightarrow{B}\right|\alpha \frac{1}{n^5}asr\alpha n^2$

Hence, magnetic field increases 32 times when electron makes a transition from n=2 to n=1.