### Video Transcript

The graph shows the maximum kinetic
energy of photoelectrons when different metals are illuminated with light of
different frequencies. Which metal has the lowest work
function? Which metal has the highest work
function?

Looking at our graph, we see that
the maximum kinetic energy of electrons ejected from metal surfaces is plotted
against photon energy. The idea is that we have metal of
some type, whether cesium, calcium, aluminum, beryllium, or platinum, and photons of
various frequencies are incident on that metal. If an incident photon has enough
energy, then when it’s absorbed by the metal, it will cause the ejection of an
electron from that surface. The minimum amount of energy
required for a photon to cause that electron ejection is called the work function of
the metal.

We can think of the work function as
an energy barrier that an electron must overcome in order to leave the surface. According to our graph, the work
function varies for our different metals. Something important about the work
function is that it’s the very minimum amount of energy required to eject an
electron from a surface.

In identifying the work functions of
the metals on our graph, we want to look for the energies at which these metals will
emit an electron, but one with zero kinetic energy. These energies occur where our five
lines meet the horizontal axis. It’s these photon energies which,
if transferred to these five different types of metals, would just barely eject an
electron from that surface. The electron would no longer be
part of the metal, but it wouldn’t be moving.

The first part of our question asks,
which metal has the lowest work function? This is the metal that will require
the least amount of photon energy to eject an electron. Of our five metals, we see that
cesium has the lowest work function. The curve for this metal intersects
the horizontal axis at a smaller value than any of the other metals. So cesium has the lowest work
function of all the metals.

And now we want to know which metal
has the highest work function. This will be the metal whose curve
intersects the horizontal axis at the highest value. And we see that this corresponds to
platinum. The lowest work function of our
metals then belongs to cesium with a value of about 2.1 electron volts, while
platinum has the highest work function with a value of about 6.3 electron
volts.