The Rydberg Equation
Using the quantum mechanical resonance model for the electron cloud in atoms, we can
understand the absorption or emission of photons as resulting from the electron cloud
expanding out to a larger shell or contracting inward to a smaller one, respectively. The
difference in energy between the shells gives the energy—and therefore the frequency
and wavelength—of the photon. We know that the energy level of a given shell can be
found in units of
electronvolts
from
E
= 13.6/n
.
Notice, however, that a hydrogen atom cannot produce photons of every possible
wavelength. Since the principal quantum number
n
is an integer, and since the energy in a
shell depends on
n
, there are certain values of energy difference that the electron clouds
can never create. It’s somewhat like the sound pitches that a piano can never produce
because they lie in between two adjacent keys. If we are dealing with photons coming
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 Spring '11
 Tibbets
 Atom, Photon, Balmer, Rydberg equation

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