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The angular momentum of the electron revolving in \(2^{nd}\) orbit is

  • A.\(\frac{h}{\pi}\)
  • B.\(\frac{h}{2\pi}\)
  • C.\(\frac{2h}{\pi}\)
  • D.\(\frac{3h}{2\pi}\)
  • E.\(\frac{h}{3\pi}\)

Answer: A

The angular momentum is \(\frac{h}{\pi}\).

Bohr's quantisation condition gives \(L = \frac{nh}{2\pi}\). For the second orbit, \(n = 2\):

\[ L = \frac{2h}{2\pi} = \frac{h}{\pi} \]

\(\frac{h}{2\pi}\) is the first orbit, \(\frac{3h}{2\pi}\) the third, and \(\frac{2h}{\pi}\) would be the fourth.

In general the angular momentum in the \(n\)th orbit is an integral multiple of \(\frac{h}{2\pi}\), so successive orbits differ by exactly \(\frac{h}{2\pi}\).

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