An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^{6}$ ms$^{-1}$ in an orbit of radius $0.52$ Å. The magnetic field produced at the nucleus of the hydrogen atom is ______ T.

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Magnetic Effects of Current

An electron in a hydrogen atom revolves around its nucleus with a speed of

6.76 \times 1 0^{6}

^{- 1}

in an orbit of radius

0.52

Å. The magnetic field produced at the nucleus of the hydrogen atom is ______ T.

Answer: 40

Solution

A charge circulating with speed

v

at radius

r

is equivalent to a current loop, producing at its centre

B = \frac{μ _{0}}{4 π} \frac{e v}{r ^{2}}

. Substituting

e = 1.6 \times 1 0^{- 19} C

v = 6.76 \times 1 0^{6} m s^{- 1}

and

r = 0.52 \times 1 0^{- 10} m

B = \frac{1 0 ^{- 7} \times 1.6 \times 1 0 ^{- 19} \times 6.76 \times 1 0 ^{6}}{( 0.52 \times 1 0 ^{- 10} ) ^{2}} = 40 T

. The magnetic field at the nucleus is

40 T

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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