In a hydrogen atom the electron moves in an orbit of radius ~ 0.5 Å, making 10 revolutions per second. The magnetic moment associated with the orbital motion of the electron would be-
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.256 x 10−38 Am2
The revolving electron is a current loop. The current is the charge passing a point per second, \( I = ef \), and the magnetic moment of a loop is current times area.
\( e = 1.6\times10^{-19}\,\mathrm{C},\ f = 10\,\mathrm{s^{-1}} \)
\( r = 0.5\times10^{-10}\,\mathrm{m} \)
\( \displaystyle I = ef = 1.6\times10^{-19}\,\mathrm{C} \times 10\,\mathrm{s^{-1}} = 1.6\times10^{-18}\,\mathrm{A} \)
\( \displaystyle A = \pi r^{2} = 3.14 \times (0.5\times10^{-10}\,\mathrm{m})^{2} = 7.85\times10^{-21}\,\mathrm{m^{2}} \)
\( \displaystyle \mu = IA = 1.6\times10^{-18}\,\mathrm{A} \times 7.85\times10^{-21}\,\mathrm{m^{2}} \)
\( \displaystyle \mu = 1.256\times10^{-38}\,\mathrm{A\,m^{2}} \)