Video Transcript
In the photoelectric effect, which
of the following should be done to increase the velocity of the emitted
electrons? (A) Increasing the number of the
incident photons that are of the critical frequency. (B) Decreasing the number of the
incident photons that are of the critical frequency. (C) Increasing the frequency of the
incident photons beyond the critical frequency. (D) Decreasing the frequency of the
incident photons below the critical frequency.
To begin, let’s recall a formula
that can help us here. 𝐸 max equals ℎ𝑓 minus 𝑊, where
𝐸 max is the maximum kinetic energy of a photoelectron. ℎ is the Planck constant. 𝑓 is the frequency of the incident
photon. And 𝑊 is the work function of a
metal surface. This question is asking about how
to increase the velocity of photoelectrons, and we know that their kinetic energy
increases with their velocity. So our goal is to increase the
value of this entire expression. Let’s think about how this could be
done.
Well, we know that ℎ represents a
constant, so there’s nothing we can do to increase its value. And for a given metal surface, the
work function 𝑊 is also constant, so its value can’t really be modified either. This leaves us with one option: to
increase the value of 𝑓, the frequency of the incident photons. This is a good hint that the
correct answer is option (C). Option (D) also talks about the
frequency of the incident photons. But since 𝐸 max is proportional to
𝑓, we want to increase the frequency, not decrease it. So let’s eliminate answer option
(D).
Answer options (A) and (B) suggest
another approach entirely: to change the number of incident photons. But all this could do is change the
number of photoelectrons that are produced. As we saw before, the energy of the
emitted electrons depends on the frequency of the incident photons. It doesn’t depend on the number of
incident photons. Further, we should recall that the
critical frequency, also known as the threshold frequency, gives the minimum
frequency of an incident photon that can overcome the work function of a metal
surface and induce the photoelectric effect. When an incident photon has this
critical frequency, 𝐸 max is equal to zero since the energy of the incident photon
is just enough to overcome the work function.
Therefore, if we want the emitted
electrons to have greater energy and speed, we should definitely be using incident
photons that have a greater frequency than the threshold frequency. Let’s eliminate options (A) and
(B). Thus, we know the correct answer is
option (C). Increasing the frequency of the
incident photons beyond the critical frequency will increase the velocity of emitted
electrons.
