The time period of revolution of an electron | vedclass

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(C) The time period of revolution of an electron in the $n^{	ext{th}}$ orbit is given by $T \propto \frac{n^3}{Z^2}$.For a hydrogen atom,$Z = 1$,so $

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$7.8 	imes 10^{14}$

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(C) The time period of revolution of an electron in the $n^{	ext{th}}$ orbit is given by $T \propto \frac{n^3}{Z^2}$.For a hydrogen atom,$Z = 1$,so $T \propto n^3$.The ground state corresponds to $n_1 = 1$,and the first excited state corresponds to $n_2 = 2$.Given $T_1 = 1.6 	imes 10^{-16} \; s$.Using the proportionality,$\frac{T_2}{T_1} = \left(\frac{n_2}{n_1}ight)^3 = \left(\frac{2}{1}ight)^3 = 8$.Therefore,$T_2 = 8 	imes T_1 = 8 	imes 1.6 	imes 10^{-16} = 12.8 	imes 10^{-16} \; s$.The frequency $f_2$ is the reciprocal of the time period: $f_2 = \frac{1}{T_2} = \frac{1}{12.8 	imes 10^{-16}} \approx 0.078125 	imes 10^{16} \; s^{-1} = 7.8 	imes 10^{14} \; s^{-1}$.

The time period of revolution of an electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \; s$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is:

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