Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 30 - Think and Explain: 79

Answer

The sum of the 2 photon frequencies equals the frequency of the single photon.

Work Step by Step

Energy is conserved. The sum of the two photon energies equals the single photon's energy. $$E_{1} + E_{2} = E_{3}$$ For photons, E = hf, where E is the energy, h is Planck's constant, and f is the photon's vibrational frequency. $$E_{1} + E_{2} = E_{3}$$ $$h(f_{1} + f_{2}) = h f_{3}$$ $$f_{1} + f_{2} = f_{3} $$ So the sum of the two photon frequencies, emitted when the electron transitions from 4 to 3 and then from 3 to 1, is equal to the frequency of light emitted when the electron transitions from quantum level 4 straight down to quantum level 1.
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