Question

An electron makes a transition from $n=2$ to $n=1$ state in a hydrogen like atom.
Choose the correct statements.

• A. Magnetic field at the site of nucleus is decreased by $16$ times
• B. Magnetic field at the site of nucleus is increased by $32$ times
• C. Angular momentum of electron is decreased
• D. Angular momentum of electron is increased

Answer 1

Answer: (B), (C)

The correct options are
B Magnetic field at the site of nucleus is increased by $32$ times
C Angular momentum of electron is decreased

From Bohr's theory, we know
$r_n=\frac{n^2}{Z}\times 0.53\stackrel{\circ }{A}$

$V_n=\frac{Z}{n}\times \frac{c}{137}m{s}^{-1}$
The angular momentum is,
$L_n=n\left(\frac{h}{2\pi }\right)$
$\Rightarrow L_n\propto n$
The effective current is,
$i_n=\frac{e{V}_n}{2\pi r_n}$
$\Rightarrow i_n\propto \frac{1}{n^3}$
The B-field at the nucleus is
$B_n=\frac{{\mu }_0{i}_n}{2r_n}$
$B_n\propto \frac{1}{r^5}$
Since the transition is from $n=2$ to $n=1$

Ratio of angular momentun
$\frac{L_2}{L_1}=\frac{2}{1}$
$\Rightarrow L_1=\frac{L_2}{2}$
Angular momentum is reduced.

and
Ratio of magnetic field
$\frac{B_2}{B_1}=\frac{1^5}{2^5}$
$\Rightarrow B_1=32B_2$
Magnetic field at centre increases $32$ times.