A parallel beam of light of wavelength `100 nm` passes through a sample of atomic hydrogengas in ground state (a)Assume that when a photon suppose some of its energy to a hydrogen atom the rest of the energy appears as another photon moving in the same direction as the incident photon Neglecting the light emitted by the excited hydrogen ato in the direction of the incident beam, ? (b) A radiation detector is placed near the gas to detect radiation coming perpenducular to the incident beam find the wevelength of radiation that may be detected by the detector

Answer

A, B, C, D

Explanation

Here `lambda=100 nm`
`E=(hc)/lambda = 1212/100`
`=12.42 eV`
(a) The Possible transitions may be `E_1` to `E_2`.
Energy absorbed in `E_1` to `E_2`
`=10.2 eV`.
Energy left `=12.42 - 10.2 = 2.22 eV`
`2.22 eV = (hc)/lambda = 1242/lambda`
or `lambda = 559.45 =560 nm`
Energy absorbed in `E_1` to `E_3`
`=12.1 e V`
Energy left `=12.42 -12.1 = 0.31 eV`
`0.32 = (hc)/lambda=1242/lambda`
`lambda = 1242/0.32`
`=3881.2 = 3881 nm`
Energy absorbed in `E_3` to `E_4=0.65`
Energy left `=12.42 -0.65 = 11.77`
`11.77 = (hc)/lambda`
or, `lambda = 1242/11.77 = 105.52`
(b) The energy absorbed by the 'H' atom is now radiated perpendicular to the incident beam.
`rarr10.2 =(hc)/lambda`
or `lambda = 1242/10.2 = 121.76`
`rarr 12.1 =(hc)/lambda`
or `lambda = 1242/12.1 = 102.64 nm`
`rarr 0.65 = (hc)/lambda`
or `lambda = 1242/0.65 = 1910.76 nm`