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According to Bohr's hypothesis, the angular momentum of the electron in any stationary orbit of radius r is proportional to _______.

Asked in GSEB Board March 2016 · Postulates, radius, speed and angular momentum

• (1) 1/r
• (2) r
• (3) √r
• (4) r²

Step-by-step solution

Why the other options are wrong

• (1) 1/r is how the size of the electron's energy behaves, |E|=(e²)/(8πε₀r). Angular momentum grows as the orbit gets bigger; it does not shrink.
• (2) r would follow from L=mvr only if the speed were the same in every orbit. In fact v∝1/(√r), which takes a factor √r back off.
• (4) r² treats the electron like a point on a rigid wheel, with the same angular speed ω in every orbit so that L=mω r². The outer orbits are travelled far more slowly than that.

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