In the hydrogen atom, the electron is making 6.6 × 1015 rps. If the radius of orbit is 0.53 × 10-10 m, then magnetic field produced at the centre of the orbit is

Question

In the hydrogen atom, the electron is making 6.6 × 1015 rps. If the radius of orbit is 0.53 × 10-10 m, then magnetic field produced at the centre of the orbit is (A) 140T (B) 12.5T (C) 1.4T (D) 0.14T

Tardigrade Admin · Accepted Answer

Current, i=q v B=(μ0 i/2 r)=(μ0 q v/2 r) =(4 π × 10-7 × 1.6 × 10-19 × 6.6 × 1015/2 × 0.53 × 10-10) =(2 π × 1.6 × 6.6/5.3)=12.513 T

Q. In the hydrogen atom, the electron is making $6.6 \times 1 0^{15}$ rps. If the radius of orbit is $0.53 \times 1 0^{- 10}$ m, then magnetic field produced at the centre of the orbit is

140T

12.5T

1.4T

0.14T

Current, $i = q v$
$B = \frac{μ _{0} i}{2 r} = \frac{μ _{0} q v}{2 r}$
$= \frac{4 π \times 1 0 ^{- 7} \times 1.6 \times 1 0 ^{- 19} \times 6.6 \times 1 0 ^{15}}{2 \times 0.53 \times 1 0 ^{- 10}}$
$= \frac{2 π \times 1.6 \times 6.6}{5.3} = 12.513 T$

Q. In the hydrogen atom, the electron is making 6.6×1015 rps. If the radius of orbit is 0.53×10−10 m, then magnetic field produced at the centre of the orbit is