Two excited energy levels are separated by the very small

Chapter 41, Problem 41.85

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Two excited energy levels are separated by the very small energy difference E. As atoms in these levels undergo quantum jumps to the ground state, the photons they emit have nearly identical wavelengths l. a. Show that the wavelengths differ by l = l2 hc E b. In the Lyman series of hydrogen, what is the wavelength difference between photons emitted in the n = 20 to n = 1 transition and photons emitted in the n = 21 to n = 1 transition?

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