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Question

(A) According to Bohr's quantization postulate, the angular momentum $L$ of an electron in an orbit is given by $L = mvr = nh / 2\pi$.For the first or

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$h / 4\pi^2mr^2$

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(A) According to Bohr's quantization postulate, the angular momentum $L$ of an electron in an orbit is given by $L = mvr = nh / 2\pi$.For the first orbit, $n = 1$, so $mvr = h / 2\pi$.The velocity $v$ is given by $v = h / (2\pi mr)$.The number of revolutions per second $f$ is the frequency, which is defined as $f = v / (2\pi r)$.Substituting the value of $v$ into the frequency formula: $f = (h / 2\pi mr) / (2\pi r) = h / 4\pi^2mr^2$.Thus, the correct option is $A$.

The number of revolutions per second made by an electron in the first Bohr orbit of a hydrogen atom is ($h$ = Planck's constant, $m$ = mass of electron, $r$ = radius of the orbit).

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