Abstract:
Planck’s constant is the relation between a frequency of light, and its energy. This
experiment seeks to measure Planck’s constant from the principles of the photoelectric
effect. This is achieved by determining the energy of electrons, which have been imparted
with energy from photons of different frequencies. We will also explore the photoelectric
effect by varying the intensity of the incident light. We predicted a value of 2.841 ± .254
eVs for Planck’s constant, and inconclusively proved the lack of relation between
incident intensity and stopping potential. We were unable to discern a relationship
between incident intensity and photocurrent, even though theory predicts it.
Motivation and Theory:
Energy in light propagates in discrete packets called photons. Their energy can be related
to the frequency by this expression:
Incident photons on a conductor are absorbed and their energy is transferred to electrons.
If the energy imparted is above a specific threshold, called the work function, the electron
will be emitted from the metal, containing all the energy of the photon, minus the work
function energy. With a constant stream of incident photons on metal, a photocurrent of
photoelectrons can be created. The electrons will have a range of kinetic energies because
some will have collided with atoms on their way out of the metal. The most energetic of
these photoelectrons will contain all of the energy, minus the work function, imparted by
the photon. This is only true for the most energetic electrons because they did not lose
energy to collisions. The relation, with K as kinetic energy, h as Planck’s constant, ν as
the incident light frequency, and Φ as the work function, is:
The formula only gives the energy of the most energetic electrons. We can determine K
max
by applying a retarding voltage across the anode and cathode. When the retarding voltage
is high enough, it will stop the most energetic electrons, and the current will go to zero.
Therefore, the retarding voltage, at the point where the current cancels out, gives us a
way to find the exact energy needed to stop the electrons, and therefore, the amount of
energy they possess. Once we have this relation for multiple frequencies, we can illustrate
the Planck constant with the slope of K
max
versus frequency, according to the above
relation.
Another factor to consider is the effect of intensity. As we vary intensity with
polarizers, the photocurrent should increase; however, the maximum kinetic energy
should not depend on the current. The reason for this is that the energy imparted to the
electrons depends only on the incident frequency of the individual photons and not on