A hydogene sample is prepared in a particular excited state A of quantum number `n _(A) =3.` The ground state energy of hydrogen atom is `-|E|.` The photons of energy `(|E|)/(12)` are absorbed in the sample with results in excitation some electrons to excited state B of quantum number `n _(B),` whose value is

Options

A. 6
B. 4
C. 5
D. 7

Answer

A

Explanation

Given,
For a hydrogen sample,
quantum number of exited state, `A i.e., n_(A)=3`
Ground state energy of hydrogen atom,
`E_(gr) =-|E|`
Energy of electrons from excited state nA to `nB - (|E|)/(12)`
Then,
`En_(B) - E n _(A) = (|E|)/(12)`
`(|E|)/(n _(B) ^(2))- (-|E|)/(n _(A) ^(2)) = (|E|)/(12)`
` (-1)/(n _(B) ^(2)) + (1)/( n _(A) ^(2)) = (1)/( 12)`
`(-1)/( n _(B) ^(2)) + (1)/( 3 ^(2)) = (1)/(12)`
`(-1)/(n _(B) ^(2)) = (1)/(12) - 1/9`
`(-1)/(n _(B) ^(2))= (-3)/(108)`
`n _(B) ^(2) = (108)/(3)`
`implies n _(B) ^(2) = 36`
`therefore n _(B) =6 `