Question

Magnetic field at the center (at nucleus) of the hydrogen like atoms (atomic number =Z) due to the motion of electron in n the 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)

$\frac{Z^3}{n^5}$

Answer 2

$B_n = \frac{\mu_0 I_n}{2 r_n}$ or $B_n \propto \frac{I_n}{r_n} \propto \frac{(f_n)}{r_n}$ $B_n \propto \frac{(\nu_n / r_n)}{r_n} \propto \frac{\nu_n}{(r_n)^2}$ $\propto \frac{(Z/n)}{(n^2 /Z)^2} \propto \frac{Z^3}{n^5}$