A sample of atomic hydrogen gas is irradiated by a beam of ultraviolet radiation having a wavelength between 100 nm and 200 nm . Assuming that the atoms are in the ground state, the wavelength which will have low intensity in the transmitted beam is

Question

A sample of atomic hydrogen gas is irradiated by a beam of ultraviolet radiation having a wavelength between 100 nm and 200 nm . Assuming that the atoms are in the ground state, the wavelength which will have low intensity in the transmitted beam is, 104 nm, 103 nm, 105 nm, 100 nm

MARKS App · Accepted Answer

The energy of a photon corresponding to λ = 100 nm is, 1 2 4 2 eV nm 1 0 0 nm = 1 2 · 4 2 eV Similarly, the corresponding to λ = 200 nm is 6 . 21 eV . The energy needed to take the atom from the ground state to the first excited state is E 2 - E 1 = 13 . 6 eV - 3 . 4 eV = 10 . 2 eV The energy needed to take the atom from the ground state to the second excited state is E 3 - E 1 = 13 . 6 eV - 1 . 5 eV = 12 . 1 eV The energy needed to take the atom from the ground state to the third excited state is E 4 - E 1 = 13 . 6 eV - 0 . 85 eV = 12 . 75 eV , and so on. Thus, 10 . 2 eV photons and 12 . 1 eV photons have a large probability of being absorbed from the given range of 6 . 21 eV to 12 . 42 eV . The corresponding wavelengths are λ 1 = 1 2 4 2 eV nm 1 0 · 2 eV = 1 2 2 nm λ 2 = 1 2 4 2 eV nm 1 2 · 1 eV = 1 0 3 nm These wavelengths will have low intensity in the transmitted beam.

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