174 The Poetry of Physics and The Physics of Poetry
prisoner in the metal. If one increases the frequency, f, such that hf is
greater than the binding energy, then, the photons can deliver enough
energy to the electrons to allow them to escape. This explains the
threshold effect.
The photon model also explains the instantaneous appearance of the
electrons once the threshold frequency is surpassed. The electron does
not absorb the required energy for ejection from the metal accumatively
from a wave, but, rather, all at once from a single photon. The electron is
ejected because it suffers a collision with a particle of light. Therefore, as
soon as the collision occurs, the escape of a photoelectron is possible
which is why electrons appear immediately after the metal has been
irradiated by a ray of light, which is nothing more than a beam of
photons.
The quantum hypothesis also explains why increasing the intensity
does not increase the energy of an individual photoelectron. The energy
of an ejected electron depends only on the frequency of the single
photon, which knocks it out of the metal. Increasing the intensity of
the light does not change the frequency of the photons, it only increases
the number of them. This is why increasing the intensity increases the
number of photoelectrons without increasing the energy of individual
photoelectrons. The fact that the energy of the photoelectron depends on
the frequency of the photon explains why the energy of the ejected
electrons increase as the frequency increases.
Thus, Einstein was able to account for all the observationally known
facts concerning the photoelectric effect by assuming the particle-
like behaviour of light. Not only did he explain all of the observations
known at the time he wrote his paper in 1905, but he also made exact
mathematical predictions relating the energy of the ejected photo-
electrons to the frequency of the light inducing the effect. Let W
represent the binding energy and fo the threshold frequency at which the
photoelectric effects first occur. Then the energy of the photons of
frequency fo is hfo and equals the binding energy W. (In terms of an
equation, we have W = hfo or fo = W/h). The energy of the escaped
electrons ejected by photons with frequency f greater than fo is equal to
the energy hf imparted by the photon minus the binding energy, W.
Defining E as the energy of the ejected electron and using an equation
once again, we have E = hf – W for the photoelectron.
This precise mathematical prediction, made by Einstein in 1905, was
not verified until eleven years later in a series of experiments performed