The figure shows an energy level diagram for the hydrogen atom. Several transiti

Question

The figure shows an energy level diagram for the hydrogen atom. Several transitions are shown and are labeled by letters. a) Which transition corresponds to the absorption of a photon with the longest wave length? b) Determine the energy of the photon involved in transition E. c) Determine the wavelength of the radiation involved in transition B. d) Which transition will occur when a hydrogen atom is irradiated with radiation of wavelength of 103nm? e) Which transition involves the longest wavelength line in the visible (400-700nm) portion of the hydrogen spectrum? f) What is the energy of a photon (in eV) that will cause an electron jump from the n=4 to the n=7 level in a hydrogen atom?

Explanation / Answer

a)photon absorbed having longest wavelength means photon absorbed having minimum energy which corresponds to transition from n = 3 to 4 i.e. C b)energy = 13.6(1/4 - 1/9) = 1.889 eV = 1.889*1.6*10-19J = 3.02*10-19 J c)energy of photon released = 13.6(1/4 -1/16) = 2.55eV = 4.08*10-19J = hc/wavelength => wavelength = hc/4.08*10-19 = 4.872* 10-7 m = 487.2 nm d)wavelength = 103nm energy = hc/wavelength = 12.06eV energy involved in transition D = 13.6(1-1/9) = 12.06eV so, the wavelength corresponds to transition D. e) in visible spectrum, only transition B and E are involved. Longest wavelength means minimum energy which corresponds to E. f) energy released = 13.6(1/16 - 1/49) = 0.572eV = 0.916*10-19J

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