The electron in a hydrogen atom make a transtion `n_(1) rarr n_(2)` where `n_(1) and n_(2)` are the priocipal quantum number of the two states . Assume the Bohr model to be valid . The time period of the electron in the initial state is eight time that in the final state . The possible values of `n_(1) and n_(2)` are

Options

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`

Answer

A, D

Explanation

As `r_(n)propn^(2), v_(n) prop 1/n`, time `t=(2pir_(n))/(v_(n))`
i.e, `t_(n) prop (r_(n))/(v_(n))` or `T_(n) prop n^(3)`, i.e., `(T_(1))/(T_(2))=((n_(1))/(n_(2)))^(3)`
or `8=((n_(1))/(n_(2)))^(3)` or `(2)^(3)=((n_(1))/(n_(2)))^(3)`
hence `n_(1)=2n_(2)`,
`:.` when (a) `n_(1)=4, n_(2)=2` and (d) `n_(1)=6, n_(2)=3`