Question

$H$ - atoms is exposed to electromagnetic radiation of $1026$ $\dot{A}$ and gives out induced radiations (radiations emitted when $e^{-}$ returns to ground state). Calculate $\lambda$ (in $\dot{A}$) of induced radiations.

Answer 1

H-atom is exposed to UV radiation having wavelength 102.8nm

the energy of photon corresponding to 102.8 nm waveegth is

$E=hc/\lambda =1242eV-nm/102.8nm$

= 12.42 eV

The energy needed to take athe H atom frm ground state to first excited state is

E2-E1 - 13.6 eV - 3.4 eV = 10.2 eV

and to the second excited

E3-E1 - 13.6 eV - 1.5 eV = 12.1 eV

and to the third excited state is

E4-E1 - 13.6 eV - 0.85 eV = 12.75 eV

thus 12.42 eV photon has large probability of being absorbed in 12.1 eV

The corresponding waveegth is:$\lambda$ = 1242/12.1 =103 nm