Question

Magnetic field at the centre (at Nucleus) of the hydrogen like atoms (atomic No. Z) due to motion of electron in $n^{t h}$ orbit is proportional to

• A. $\frac{n^{3}}{Z^{5}}$
• B. $\frac{n^{4}}{Z}$
• C. $\frac{Z^{2}}{n^{3}}$
• D. $\frac{Z^{3}}{n^{5}}$

Answer 1

Answer: (D)

$B_{n}=\frac{\mu _{0} I_{n}}{2 r_{n}}$
or $B_{n} \propto \frac{I_{n}}{r_{n}} \propto \frac{f_{n}}{r_{n}} \propto \frac{v_{n}}{r_{n}^{2}}$
$\Rightarrow B_{n} \propto \frac{z / n}{\left(n^{2} / z\right)^{2}} \propto \frac{z^{3}}{n^{5}}$