In hydrogen atom, an electron is revolving in the orbit of radius `0.53 Å` with `6.6xx10^(15) rotations//second`. Magnetic field produced at the centre of the orbit is

Options

A. `6.28Wb/m^(2)`
B. `9 Wb//m^(2)`
C. `12.56Wb//m^(2)`
D. `15 Wb//m^(2)`

Answer

C

Explanation

The circulating electron is equivalent to a circular current loop carrying a current I.
`I =(dQ)/(dt) =e/R =(e)/(1//n)=n e`
`=6.25 xx10^(15)xx1.6 xx10^(-19) =10xx10^(-4) =10^(-3) A`
and B at the curcle `=(mu_(0))/(4pi) ((2pi n i)/(r))`
In this case `=1 and r=0.5 xx10^(-10) m`
`therefore B =(10^(-7)xx2xx3.14xx10^(-3))/(1/2xx10^(-10))`
`therefore B =4xx3.14 =12.56 Wb//m^(2)`