The time taken for an electron to complete on | vedclass

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Question

(C) The distance travelled in one revolution is the circumference of the orbit, which is $2 \pi r$. Velocity $(v)$ is given by the ratio of distance t

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$\frac{4 \pi^2 m r^2}{n h}$

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(C) The distance travelled in one revolution is the circumference of the orbit, which is $2 \pi r$. Velocity $(v)$ is given by the ratio of distance to time $(T)$: $v = \frac{2 \pi r}{T}$. From Bohr's postulate, the angular momentum is $mvr = \frac{nh}{2 \pi}$, which gives $v = \frac{nh}{2 \pi mr}$. Equating the two expressions for velocity: $\frac{2 \pi r}{T} = \frac{nh}{2 \pi mr}$. Solving for $T$: $T = \frac{2 \pi r 	imes 2 \pi mr}{nh} = \frac{4 \pi^2 m r^2}{nh}$.

The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is

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