Magnetic field at the center (at nucleus) of the hydrogen like atom `("atomic number" = z)` due to the motion of electron in nth orbit is proporional to

Options

A. `(n^3)/(Z^5)`
B. `(n^4)/(Z)`
C. `(z^4)/(n^3)`
D. `(Z^3)/(n^5)`.

Answer

D

Explanation

`B_(n) =(mu_0I_n)/(2 r_n) or B_(n) prop (I_n)/( r_n) , prop ((f_n))/( r_n)`
`therefore B_(n) prop ((v_n//r_n))/(r_n) prop (v_n)/(r_n)^2 prop ((z//n))/(n^2//z)^2 prop (z^3)/(n^5)`.