Video Transcript
For a metal surface that has a work
function of 2.5 electron volts, the maximum wavelength for light to enable emitting
photoelectrons from this surface is blank. You can use ℎ equals 6.625 times 10
to the power of negative 34 joule seconds and 𝑐 equals three times 10 to the power
of eight meters per second.
Let’s begin by recalling that the
work function of a metal tells the minimum amount of energy needed to remove an
electron from its surface. Thus, in order to induce the
photoelectric effect, an incident photon must have energy that is greater than or
equal to the work function of a given surface. Also, recall that the energy of a
photon is given by ℎ, the Planck constant, times 𝑐, the speed of light, divided by
𝜆, the photon’s wavelength.
Since we want to solve for the
maximum photon wavelength, we’re solving for the minimum photon energy. So, in this case, we should set ℎ𝑐
over 𝜆 equal to the work function 𝑊. Let’s now rearrange the formula to
make wavelength the subject. To do this, we just need to
multiply both sides by 𝜆 over 𝑊. And so the expression becomes 𝜆
equals ℎ𝑐 over 𝑊.
But before we substitute in values
for all these terms on the right-hand side, let’s make sure they’re expressed in
appropriate SI or SI-derived units. ℎ and 𝑐 are good to go, but notice
that the work function is currently given in electron volts. So we should convert it into
joules. To do this, we need to remember
that one electron volt equals 1.60 times 10 to the power of negative 19 joules. And so we can multiply the work
function value by this conversion factor, which itself is just equal to one. Multiplying through and canceling
out units of electron volts, we get that 𝑊 equals 4.0 times 10 to the power of
negative 19 joules.
Finally, we’re ready to substitute
the work function, the Planck constant, and the speed of light into the formula for
wavelength. Doing this and grabbing a
calculator, we get a result of 4.97 times 10 to the power of negative seven
meters. And we have our final answer. This is the maximum wavelength of
light that will induce the photoelectric effect on this metal surface.
