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The electron in a hydrogen atom makes a ...

The electron in a hydrogen atom makes a transition from `n = n_(1)` to `n = n_(2)` state. The time period of the electron in state `n_(1)` is eight times that in state `n_(2)`. The possible values of `n_(1)` and `n_(2)` are

A

`n_(1) = 4, n_(2) = 2`

B

`n_(1) = 8, n_(2) = 2`

C

`n_(1) = 8, n_(2) = 1`

D

`n_(1) = 6, n_(2) = 3`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Time period,
`T_(n)=(2pi r_(n))/v_(n)` (in `n^(th)` state) i.e. `T_(n) prop r_(n)/v_(n)`
But `r_(n) prop n^(2)` and `v_(n) prop 1/n`
Therefore, `T_(n) prop n^(3)` given `T_(n1)=8T_(n2)`
Hence, `n_(1)=2n_(2)`
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