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)
- (a) nh/(2 π r)
- (b) (n h)/(2 r)
- (c) nh/(2 π)
- (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.
- Bohr's condition. Bohr's postulate says the electron's angular momentum in the nᵗʰ orbit is quantised: L = mvr = nh/2π.
- 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)
- 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.