What is the ratio of time periods (T_1 / T_2) | vedclass

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(B) The time period $(T)$ of an electron in the $n^{th}$ orbit is given by the formula $T \propto \frac{n^3}{Z^2}$.Therefore,the ratio of time periods

Vedclass · Accepted Answer

$32/27$

Vedclass · Answer

(B) The time period $(T)$ of an electron in the $n^{th}$ orbit is given by the formula $T \propto \frac{n^3}{Z^2}$.Therefore,the ratio of time periods for two different species is given by $\frac{T_1}{T_2} = \frac{n_1^3}{Z_1^2} 	imes \frac{Z_2^2}{n_2^3}$.For the second orbit of hydrogen atom $(n_1 = 2, Z_1 = 1)$ and the third orbit of $He^{+}$ ion $(n_2 = 3, Z_2 = 2)$:$\frac{T_1}{T_2} = \frac{2^3}{1^2} 	imes \frac{2^2}{3^3} = \frac{8}{1} 	imes \frac{4}{27} = \frac{32}{27}$.Thus,the ratio is $32/27$.

What is the ratio of time periods $(T_1 / T_2)$ in the second orbit of a hydrogen atom to the third orbit of a $He^{+}$ ion?

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