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What will be the angular momentum in the fourth orbit, if L is the angular momentum of the electron in the second orbit of a hydrogen atom?

Asked in GUJCET 2008 · Postulates, radius, speed and angular momentum

(1) (2L)/3
(2) L/2
(3) 2L
(4) (3L)/2

Answer: (3) 2L

Step-by-step solution

Idea: Bohr's quantisation condition is Lₙ=(nh)/(2π), so L∝ n.

(L₄)/(L₂)=4/2=2.

L₄=2L.

Why the other options are wrong

(1) No single slip gives (2L)/3. Sanity check: it is smaller than L, but Bohr's rule L=(nh)/(2π) makes the angular momentum grow with n, so the fourth orbit must carry more than the second.
(2) L/2 takes the angular momentum as inversely proportional to n, giving L×2/4; it is directly proportional to n.
(4) (3L)/2 is the angular momentum of the third orbit, L×3/2 — the next orbit out, not the fourth.

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