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 is also equal to the difference in energy between two energy levels, ΔE = E2 - E1. In this case, the photon is absorbed by the hydrogen atom, which means that the atom is excited to a higher energy level. The energy of the photon is equal to the difference in energy between the ground state and the excited state, ΔE = E2 - E1. The energy of the ground state is given by E1 = -13.6 eV, and the energy of the excited state is given by E2 = -3.4 eV. Therefore, the difference in energy between the two levels is ΔE = E2 - E1 = -10.2 eV. The wavelength of the photon is given by λ = hc/ΔE, where h is Planck's constant, c is the speed of light, and ΔE is the difference in energy between the two levels. Substituting the values of h, c, and ΔE into the equation, we get λ = hc/ΔE = (6.626 × 10^-34 J ∙ s)(3.00 × 10^8 m/s)/(-10.2 eV) = 91.63 nm. Therefore, the correct answer is A.

Light Shines Through Atomic Hydrogen Gas