The Quantization of Energy 171
day. No one was able to explain why the intensity did not continue to
increase with frequency.
Max Planck devoted a great deal of effort trying to derive the
experimentally observed distribution from a strictly theoretical point of
view. Not meeting with success, he attacked the problem from a
phenomenological point of view. Rather than trying to derive the correct
formula from first principle, he first searched for an algebraic formula,
which would just describe the experimental data. Using trial and error
and guided by previous attempts at a solution, Planck finally found a
formula, which represented the data. Working backwards from the
answer, Planck then searched for a way to derive his formula. He
discovered he could obtain his formula if he made the assumption that
the radiation of frequency, f, was absorbed and emitted in bundles of
energy equal to hf where h is a constant, called Planck’s constant, and is
an extremely small number. The bundles of energies are called quanta
(quantum is the singular) or photons.
The implication of Planck’s result is that the energy of light is not
continuous but is packaged in discreet bundles of energy called quanta or
photons. According to Planck’s hypothesis, a frequency, f, cannot be
excited unless an amount of energy, hf, is provided to create a photon.
Planck’s constant, h, is extremely small and, hence, the amount of energy
to excite a particular frequency is not much, however, it takes more
energy to create the higher frequency photons than the lower frequency
photons, and, hence, the probability of exciting the higher frequencies is
not always greater than that of exciting the lower frequencies. Also, there
is a cutoff of frequencies in Planck’s model so that the infinite number of
high frequencies can no longer contribute to the black body radiation. If
the total amount of energy available for thermal radiation is Eo, then, the
frequency fo, such that Eo = hfo is the highest possible frequency that can
contribute. There just would not be enough energy available to create a
photon with frequency greater than fo.
Planck’s hypothesis that the energy of light is quantized explained the
distribution of energy of black body radiation. Because Planck’s constant
is so small and, hence, each quantum or photon actually carries such a
small amount of energy, Planck’s hypothesis does not conflict with the
experimentally observed continuity of light. Light rays are composed of
literally millions and millions of tiny bundles of energy or photons, each
of which carry a minuscule amount of energy. The amount of energy
carried by the most energetic photon conceivable, for example, a photon