The period of revolution of an electron revol | vedclass

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Question

(C) The time period of revolution $T$ of an electron in the $n^{th}$ orbit is defined as the ratio of the circumference of the orbit to the orbital ve

Vedclass · Accepted Answer

$n^{3}$

Vedclass · Answer

(C) The time period of revolution $T$ of an electron in the $n^{th}$ orbit is defined as the ratio of the circumference of the orbit to the orbital velocity of the electron: $T = \frac{2 \pi r_{n}}{v_{n}}$.According to Bohr's theory,the radius of the $n^{th}$ orbit is $r_{n} \propto n^{2}$ and the velocity of the electron in the $n^{th}$ orbit is $v_{n} \propto \frac{1}{n}$.Substituting these proportionalities into the formula for the time period:$T_{n} \propto \frac{r_{n}}{v_{n}} \propto \frac{n^{2}}{1/n} = n^{3}$.Thus,the time period of revolution is proportional to $n^{3}$.

The period of revolution of an electron revolving in $n^{th}$ orbit of $H$-atom is proportional to

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