A beam of light having wavelength distributed uniformly between `450 nmto 550 nm` passes through a sample of hydrogen gas which wavelength will have the least intensity in the transition beam?

Answer

D

Explanation

The energies associated with 450 nm radiation
`=1242/450 = 2.76 eV`
Energy associated with 550 nm radiation
`=1242/550 = 2.228 =2.26 eV`.
The light comes under visible range,
thus, `n_1 =2`, `n_1 = 3,4,5…….`
`E_2-E_3 = 13.6 ((1)/(4)-(1)/(9))`
`=(12.6 xx 5)/(30) = 1.9eV`
`E_2 -E_4 = 13.6((1)/(4)-(1)/(16))`
`=2.55eV`
`E_2-E_5 = 13.6((1)/(4)-(1)/(25))`
`=(10.5 xx 21)/(100) = 2.856 eV`
Only `E_2-E_4` comes in the range of energy provided. So the wave length corresponding to that energy will be absorbed.
`lambda= (1242)/(2.55) = 487.05 nm`
`=487 nm`
487 nm wavelength will be absorbed