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(D) According to the Bohr model,the time period $T$ of an electron in an orbit with principal quantum number $n$ is given by $T = \frac{2\pi r}{v}$.Si

Vedclass · Accepted Answer

Both $(a)$ and $(b)$

Vedclass · Answer

(D) According to the Bohr model,the time period $T$ of an electron in an orbit with principal quantum number $n$ is given by $T = \frac{2\pi r}{v}$.Since $r \propto n^2$ and $v \propto \frac{1}{n}$,we have $T \propto n^3$.Given that the time period in the initial state is eight times that in the final state: $T_{n_1} = 8 T_{n_2}$.Substituting the proportionality: $n_1^3 = 8 n_2^3$.Taking the cube root on both sides: $n_1 = 2 n_2$.Checking the options:For option $(a)$: $n_1 = 4, n_2 = 2$. Here $4 = 2(2)$,which is correct.For option $(b)$: $n_1 = 6, n_2 = 3$. Here $6 = 2(3)$,which is correct.Thus,both $(a)$ and $(b)$ are valid possibilities.

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