A group of hydrogen atom are prepered in `n = 4` states list the wavelength that are emitted as the atoms make transition and return to `n = 2` states

Answer

A, D

Explanation

Here `n_1=1`, `n_2 = 2`
`n_1 = 4 rarr 3rarr2`
implies `1/lambda = 1.097 xx 10^7((1-4)/(16))`
`1/lambda = (1.097 xx 10^7 xx 3)/(16)`
implies `lambda =(16 xx 10^-7)/(3 xx 1.097)`
`=-4.8617 xx 10^-7
`=-486.1 xx 10^-9`
`=-487 nm`
Again `n_1 = 4` and `n_2 = 3`
`1/lambda = 1.097 xx 10^7((1)/(16)-(1)/(9))`
implies `(1)/(lambda) = 1.097 xx 10^7((9-16)/144)`
implies `1/lambda = (1.097 xx 10^7 xx 7)/144`
implies `lambda = 144/(1.097 xx 10^7 xx 7)`
`=-1875 nm`
`When transition is
`n_1 = 3` to `n_2 =2`
`1/lambda = 1.097 xx 10^7((1)/(9)-(1)/(4))`
implies `1/lambda = 1.097 xx 10^7((4-9)/(36))`
implies `1/lambda = (1.097 xx 10^7)/(36)`
implies `lambda = (36 xx 10^7)/ (1.097 xx 5) = -656 nm`