Bohr atom: Light shines through atomic hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.63 nm. What is the value of n of the level to which the hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level. (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J; the Rydberg constant is R = 1.097 × 10⁷ m^-1.) A) 14 B) 16 C) 11 D) 21

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Quizplus · Accepted Answer

The energy of a photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. The energy of a photon absorbed by an atom is equal to the difference in energy between the two levels involved in the transition. The energy of an electron in the nth level of a hydrogen atom is given by En = -13.6 eV/n^2. The energy difference between the n = 1 level and the n = 2 level is given by ΔE = E2 - E1 = -13.6 eV/2^2 - (-13.6 eV/1^2) = 10.2 eV. The wavelength of a photon with energy of 10.2 eV is given by λ = hc/E = (6.626 × 10^-34 J ∙ s)(3.00 × 10^8 m/s)/(10.2 eV)(1.60 × 10^-19 J/eV) = 91.63 nm. Therefore, the hydrogen is being excited to the n = 2 level by the absorption of light of this wavelength.

Bohr Atom: Light Shines Through Atomic Hydrogen Gas