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^(2))/(z^(3))`
B. `(n^(4))/(Z)`
C. `(z^(2))/(n^(3))`
D. `(z^(3))/(n^(5))`

Answer

4

Explanation

Current produced orbiting `e^(-)` is
`I =(qv)/(2pir)`
`therefore` Magnetic field at centre
`B =(mu_(0)i)/(2pi)=(mu_(0))/(2)((qv)/(2pir)) (1)/(r)`.
`=(mu_(0) ev)/(4pir^(2))`
As `V prop (Z)/(n) and r prop (n^(2))/(Z)`.
`therefore B prop (Z)/(n)=(Z//n)((Z)/(n^(2)))^(2)`
`B prop (Z^(3))/(n^(5))`