JEE Main 2022 · 25 July · morning · Single correct · +4 / −1

The momentum of an electron revolving in nᵗʰ orbit is given by :
(Symbols have their usual meanings)

  1. (a) nh/(2 π r)
  2. (b) (n h)/(2 r)
  3. (c) nh/(2 π)
  4. (d) (2 π r)/nh
Answer and solution

Answer (a) nh/(2 π r)

Solution

Physics sir · 3 steps

Bohr fixes angular momentum, not momentum: divide nh/2π by the radius and you are done.

  1. Bohr's condition. Bohr's postulate says the electron's angular momentum in the nᵗʰ orbit is quantised: L = mvr = nh/2π.
  2. Link L and p. For circular motion, angular momentum is linear momentum times radius: L = pr, where p = mv.

    p = mv = L/r = nh/(2π r)

  3. So. The momentum of the electron in the nᵗʰ orbit is nh/(2π r), which is option (a).

The idea to keep. In Bohr's model, mvr = nh/2π is the starting point. Need linear momentum? Divide by r. Need speed? Divide by mr.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 110 times in JEE Main since 2020. This question is from 2022.