The electron in a hydrogen atom makes a transition `n _(1) to n _(2)` where `n_(1) and n_(2)` are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. What are the possible values of `n _(1) and n _(2)` ?

Explanation

The time period T of an electron in a Bohr orbit of principle quantum number n is :
`T = ( 2 pi n ^(3) h ^(3))/( k ^(2) mZ ^(2) e ^(4))`
Thus `T alpha n ^(3)` As ` T _(1) = 8 T _(2),` the above relation give
`((n _(1))/( n _(2)) ) ^(3) = 8`
`or n _(1) = 2n _(2)`
Thus the possible values of `n _(1) and n _(2)` are
`n _(2) = 2, n _(2)=1, n _(1) = 4, n _(2) = 2, n _(1) = 6, n _(2) = 3, and ` so on....