The frequency of photons released in such transitions is approximately .
Explanation:
The Rydberg Equation gives the wavelength (in vacuum) of photons released when the electron of a hydrogen atom transitions from one main energy level to a lower one.
Let denote the wavelength of the photon released when measured in vacuum.
Let denote the Rydberg constant for hydrogen. .
Let and denote the principal quantum number of the initial and final main energy level of that electron. (Both and should be positive integers; .)
The Rydberg Equation gives the following relation:
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Rearrange to obtain and expression for :
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In this question, while . Therefore:
.
Note, that is equivalent to . That is: .
Look up the speed of light in vacuum: . Calculate the frequency of this photon:
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Let represent Planck constant. The energy of a photon of wavelength would be .
Look up the Planck constant: . With a frequency of (,) the energy of each photon released in this transition would be: