In the hydrogen atom, an electron revolves around the nucleus in a circular orbit of radius \( 5.11 \times 10^{-11}\,\mathrm{m} \) with a frequency of \( 6.8 \times 10^{15}\,\mathrm{Hz} \). The magnetic field at the centre of the orbit is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 13.4 T
A revolving electron is a current loop: the charge \( e \) passes a point \( f \) times every second, so the equivalent current is \( I = e f \). The field at the centre of a circular loop of radius \( r \) is \( B = \mu_0 I/2r \).
\( \displaystyle I = e f = 1.6\times10^{-19} \times 6.8\times10^{15} = 1.088\times10^{-3}\,\mathrm{A} \)
\( \displaystyle B = \frac{\mu_0 I}{2r} = \frac{4\pi\times10^{-7} \times 1.088\times10^{-3}}{2 \times 5.11\times10^{-11}} \approx 13.4\,\mathrm{T} \)