An electron in a hydrogen atoms makes a transition form `n_1` to `n_2` where `n_1 and n_2` are two principal quantum numbers of two states. If time period of electron in state `n_1` is 8 times the time period in state `n_2`, find the ratio `(n_2//n_1)`, assuming Bohr model to be true.
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Based on Bohr's model, orbital radius `r=(n^2h^2)/(4pi^3mKe^2)` and velocity v of orbiting electron `v=(2piKe^2)/(nh)` Time period, `T=(2pir)/v=2pi(n^2h^2)/(4pi^3mKe^2)xx(nh)/(2piKe^2)` `T=(n^3h^3)/(4pi^2mK^2e^4)` `:. (T_2)/(T_1)=(n_2^3)/(n_1^3)=1/8=[1/2]^3` `(n_2)/(n_1)=1/2`
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