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^(2))/(n^(3))`
D. `(z^(3))/(n^(5))`

Answer

D

Explanation

`B_(n) = (mu_(0)l_(n))/(2 r_(n))`
or `B_(n) prop (l_(n))/(r_(n))`
`prop ((f_(n)))/(r_(n))`
`:. 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))`