The atoms of a certain mono-atomic gas have five energy levels: E1 = 0, E2 = 5.4

Question

The atoms of a certain mono-atomic gas have five energy levels: E1 = 0, E2 = 5.4 eV, E3 = 8.2 eV, E4 = 8.6 eV, and E5 = 12.4 eV, all measured up from E1. (a) If infrared light with wavelengths in the range from 3000 to 3200 nm shines through the gas, what transitions could it cause? If the gas was so cool that all atoms were in the ground state; would you expect to observe these transitions? (b) Answer the same questions for UV with wavelengths 95 to 105 nm (c) What wavelength light could de-excite the atoms from level 3 to level 2?

Explanation / Answer

(a) all atoms are in the ground state The energy difference E5 -E0   =   12.4eV wavelength ranges     from = hc /E   Here h = 6.63*10^-34 j.s 1eV   = 1.6*10^-19 j c = light velocity   = 3*10^8 m/s E   = 12.4 eV we get = 100.25 nm    hence infrared lignt   3000 nm > 100.25 nm energy transition energies are more than the energy of the infra red light hence it doesn't give any transions    from E0 to   E5   ------------------------------------------ For   UV light E  = E5  -  E0   =   12.4 eV For UV   light   the wave length range   =     ( 105 -95)nm   = 10nm the possible energy E = hc /      1J    = 1 / ( 1.6*10^-19 eV) plug all values   we get the answer   E   = 12.4 eV which is equal to the E5  -  E0   =   12.4 eV hence for cool gas the transision 1 -->   5 is possible (c) difference wavelength in   E3 to E2   E = E3   - E2      = 2.8 eV 1eV   = 1.6*10^-19 j = hc / E    =   4.439*10^-7 m    = 443.9 nm E = E3   - E2      = 2.8 eV 1eV   = 1.6*10^-19 j 1eV   = 1.6*10^-19 j = hc / E    =   4.439*10^-7 m    = 443.9 nm

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