The ratio of the time period of an electron i | vedclass

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(B) According to Bohr's theory,the time period $(T)$ of an electron in an orbit is given by the relation $T \propto \frac{n^3}{Z^2}$.For a hydrogen at

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$1 : 27$

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(B) According to Bohr's theory,the time period $(T)$ of an electron in an orbit is given by the relation $T \propto \frac{n^3}{Z^2}$.For a hydrogen atom ($H$-atom),the atomic number $Z = 1$,so $T \propto n^3$.For the first orbit $(n_1 = 1)$,$T_1 \propto (1)^3 = 1$.For the third orbit $(n_2 = 3)$,$T_2 \propto (3)^3 = 27$.Therefore,the ratio of the time period is $\frac{T_1}{T_2} = \frac{1}{27}$,which is $1 : 27$.

The ratio of the time period of an electron in the first and third orbit of an $H$-atom would be:

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