Conceptual Photoelectric Effect Question

[trogtothedor]

Homework Statement

"A blue laser beam is incident on a metallic surface, causing electrons to be ejected from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed,

a)the rate of ejected electrons will remain the same but the maximum kinetic energy will increase.

b)the rate of ejected electrons will increase and the maximum kinetic energy will increase.

c)the rate of ejected electrons will remain the same but the maximum kinetic energy will
decrease.

d)the rate of ejected electrons will decrease and the maximum kinetic energy will increase.

Homework Equations

Kmax = hf - E0

The Attempt at a Solution

I arrived at the correct answer by trial and error. The Kmax equation tells me that if the frequency of the beam increases, then the kinetic energy will increase. I also know that electron flow is proportional to the intensity of the light.

There is also a graph in my book that has the electron current vs frequency, which looks rather linear. The current is at 0 until the threshold frequency is reached, then it jumps to a consistent current for f > f-threshold.

So I chose answer A at first, given these statements. The electron flow related to intensity is steady, and from the graph, increases in frequency result in no change in current. Also, just from Kmax = hf - E0, with E0 constant, Kmax increases with an increase in f.

However, these are wrong. The correct answer according to MasteringPhysics is D, where both the current and maximum kinetic energy decrease. I do not understand why this is true. We did not really go over this section well in class and our book does a rather poor job explaining this area.

Thank you in advance for the help!

 

[Doc Al]

However, these are wrong. The correct answer according to MasteringPhysics is D, where both the current and maximum kinetic energy decrease. I do not understand why this is true. We did not really go over this section well in class and our book does a rather poor job explaining this area.

Hint: What determines the intensity of the beam? If the frequency is increased, what must change to keep the intensity fixed?

 

[trogtothedor]

Would the wavelength have to change in order for the intensity to be the same?

If so, I still have no idea how that relates tot he correct answer.

 

[Doc Al]

Would the wavelength have to change in order for the intensity to be the same?

No, that's not it. The wavelength and frequency are two sides of the same coin, so you can't change one without changing the other (at least in this context).

Hint: Intensity refers to the energy of the beam. Keeping the intensity fixed means that the total energy (per second) of the beam does not change.

Hint2: What does the laser beam consist of?

 

[trogtothedor]

I guess I'm just not getting it. We also sort of breezed over light intensity, so I wasn't really sure of how they related.

The laser beam would consist of waves with photons clustered at each maxima of the wave.
I don't think I'm going to make the connection you're trying to steer me toward.

 

[Doc Al]

The laser beam would consist of waves with photons clustered at each maxima of the wave.

You're getting warmer. The key insight is that the beam consists of photons. (The wave and photon are two different ways of describing the same beam. Do not picture the photons as clustered at the maxima of the wave.) What determines the energy of each photon?

 

[trogtothedor]

The energy of each photon is given by Planck's constant multiplied by the frequency of the photon.

Again I must be making a conceptual mistake. That leads me to believe that since the intensity of the beam is constant, and that the energy of each individual photon is increasing in the beam since the frequency is increasing, then the energy added by the increase in frequency must be transferred to the electrons in the metal. I guess that isn't correct?

 

[Delphi51]

Constant intensity means the same overall energy per second.
But your photons get more energetic . . .

 

[trogtothedor]

I'm still not making the connection. I've been rather off today, so things just aren't making sense right now.

Also the question I'm asking isn't part of the homework, so you anyone willing to help can tell me whatever I am missing and have no ethical dilemmas. I got the problem wrong and am just at a loss as to why it works the way that it does.

 

[Doc Al]

The energy of each photon is given by Planck's constant multiplied by the frequency of the photon.

Good. And since the frequency is increasing, so is the energy of each individual photon. Since the energy per photon is greater, but the overall energy (per second) of the beam must remain fixed, what can you say about the number of photons per second in the beam? And how does that matter?

 

[trogtothedor]

Ah yes thank you. I get it now. I was thinking frequency was proportional to the number of photons, such as photons per second. This clears things up!

I understand the idea of each photon transmitting its energy to an electron, so a decrease in the number of photons would lead to a decrease in the number of electrons receiving energy, thus slowing the current. At least I think that's the idea.

Thank you for your help!

 

[Doc Al]

I understand the idea of each photon transmitting its energy to an electron, so a decrease in the number of photons would lead to a decrease in the number of electrons receiving energy, thus slowing the current. At least I think that's the idea.

Good! Fewer photons hitting the material means fewer electrons ejected. And since each photon now has greater energy, the maximum KE of the ejected electrons will be greater.