Photoelectric Current: Max KE & Intensity Explained

[Janiceleong26]

Homework Statement

I know the fact that increasing frequency of light increases max KE of electrons. Max KE=hf-Φ.
Does this mean increasing frequency, increases photoelectric current?

If max KE of the electrons is independent of the light intensity,
Why is photoelectric current proportional to the light intensity?

Is there any association between max KE of electrons and the photoelectric current ?

 

[ZapperZ]

Homework Statement

I know the fact that increasing frequency of light increases max KE of electrons. Max KE=hf-Φ.
Does this mean increasing frequency, increases photoelectric current?

If max KE of the electrons is independent of the light intensity,
Why is photoelectric current proportional to the light intensity?

Is there any association between max KE of electrons and the photoelectric current ?

This isn't that easy to answer because it depends on the level of complexities and generalities that you want.

Here's the general trend: increasing the photon energy tends to generally increase the photoemission current. Thus, in this case, there is a correlation (but NOT causation) between increasing currrent and increasing max KE of the photoelectrons.

The reason for this is that now, you can no longer just focus on the photons, but you now need to include the photocathode. The band structure of the photocathode can dictate the nature of the emission. The higher photon energy can cause emission from a deeper energy state. And also depending on the material, the higher photon energy may also penetrate deeper below the surface of the material.

But there is a limit to this, because at some point, this penetration depth may be longer than the electron's escape depth. So while the photon may have sufficient energy to excite an electron into the vacuum state, the electron was created too far below the surface to make it out, and will decay back into the Fermi sea.

Zz.

 

[J Hann]

Suppose just 1 photon strikes the surface.
Then only photoelectron can be emitted, right?
Now if two photons strike the surface then 2 electrons can be emitted.
Since the light intensity depends on the number of photons striking the surface then
the photoelectric current must be related to the incident intensity.
Now you should be able to answer the question of the relation of the
emitted photoelectron energy to the photoelectric current since the current
is related to the number of photons being emitted and not to the energy of the
emitted photons.

 

[lychette]

The photoelectric current depends on the intensity of the light (brightness). The energy of the emitted electrons depends on the frequency of the photon (colour of light)

 

[ZapperZ]

Suppose just 1 photon strikes the surface.
Then only photoelectron can be emitted, right?
Now if two photons strike the surface then 2 electrons can be emitted.
Since the light intensity depends on the number of photons striking the surface then
the photoelectric current must be related to the incident intensity.
Now you should be able to answer the question of the relation of the
emitted photoelectron energy to the photoelectric current since the current
is related to the number of photons being emitted and not to the energy of the
emitted photons.

The photoelectric current depends on the intensity of the light (brightness). The energy of the emitted electrons depends on the frequency of the photon (colour of light)

Two of you need to be VERY careful. The Einstein photoelectric effect equation say NOTHING about (i) current density and (ii) about its relationship to the photon energy. So if you are basing this solely on that equation, then you are basing it on incomplete or non-existent information.

The OP asked about the correlation between photon energy and photocurrent. To answer this, you need to look at a larger and broader description of the photoemission phenomenon. You cannot use just the photoelectric effect equation.

One of the things that I do is measure the quantum efficiency of photocathodes. This is where I try to find out how many electrons are emitted per incident photon, and at various photon energies. There is a clear and obvious relationship between these two, whereby increasing the photon energy WILL increase the photocurrent density (up to a point and with the caveat that I mentioned in my earlier post). For example, look at this paper:

http://arxiv.org/pdf/1202.0152v2.pdf

In particular, pay attention to Fig. 6. You can clearly see that the QE increases with decreasing wavelength (i.e. increasing photon energy). This means that for the same number of photons, a higher photon energy will produce MORE photoelectrons, and thus, a higher photocurrent, than photons with lower energy.

Zz.

 

[lychette]

we all need to be VERY careful, this is a post in introductory physics and if you consult introductory physics textbooks regarding photoelectric effect the starting point is photoelectric emission from metals.
The link between KE of ejected electrons and frequency/wavelength of incident radiation is fairly clear and unambiguous. Also the link between photoelectric current and light intensity is fairly straight forward. the photoelectric equation is well known.

 

[Janiceleong26]

Thank you all.
So photoelectric current depends on the number of photoelectrons emitted per unit time but not really the max KE of the photoelectrons, am I right?

 

[lychette]

That is what the textbooks that I use say. The KE depends on the colour(wavelength) of the incident light.
The current (number of electrons per sec) depends on the brightness of the light.

 

[Janiceleong26]

That is what the textbooks that I use say. The KE depends on the colour(wavelength) of the incident light.
The current (number of electrons per sec) depends on the brightness of the light.

Ok thanks!

 

[CrazyNinja]

OK @ZapperZ, in simple terms do you mean that ONE photon can emit MORE than one electron?

 

[ZapperZ]

OK @ZapperZ, in simple terms do you mean that ONE photon can emit MORE than one electron?

You misread what I wrote. The number of electrons emitted per photon need not be whole numbers greater than one. It can be 0.2, which is a typical high-QE for many photocathodes in photomultiplier tubes.

Most metals have QE in the 10^-3 or less range. It means that you need 1000 photons or more to get one electron.

Zz.

 

[lychette]

You misread what I wrote. The number of electrons emitted per photon need not be whole numbers greater than one. It can be 0.2, which is a typical high-QE for many photocathodes in photomultiplier tubes.

Most metals have QE in the 10^-3 or less range. It means that you need 1000 photons or more to get one electron.

Zz.

By this do you mean that only 1 in 1000 photons ejects an electron, that is the way I understand it. A probability feature.
Not quite the same as 1000 photons needed to eject an electron?

 

[ZapperZ]

By this do you mean that only 1 in 1000 photons ejects an electron, that is the way I understand it. A probability feature.
Not quite the same as 1000 photons needed to eject an electron?

Doesn't matter, because the outcome is the same. And yes, it is a matter of statistics. The Spicer's 3-Step model involves probabilities for each of the steps, from the photon absorption cross section to diffusion in the vacuum state towards the surface of the material.

Zz.

 

[lychette]

Doesn't matter, because the outcome is the same. And yes, it is a matter of statistics. The Spicer's 3-Step model involves probabilities for each of the steps, from the photon absorption cross section to diffusion in the vacuum state towards the surface of the material.

Zz.

It does matter! The outcome may be the same but there are 2 different mechanisms implied in the statements.
1 photon ejects an electron or 1000 photons eject an electron are not equivalent statements.
1 photon ejects an electron but only 1 in 1000 actually do so.

 

[ZapperZ]

It does matter! The outcome may be the same but there are 2 different mechanisms implied in the statements.
1 photon ejects an electron or 1000 photons eject an electron are not equivalent statements.
1 photon ejects an electron but only 1 in 1000 actually do so.

I state that it doesn't matter because you cannot distinguish between the two. There is no way to know because it is a matter of probability, and you can't follow a single photon to know what it is doing. Or do YOU?

Until there is an experiment to distinguish the two, this is a matter of taste and philosophy. I do not have the time or patience to argue on favorite color.

Zz.

 

[lychette]

I state that it doesn't matter because you cannot distinguish between the two. There is no way to know because it is a matter of probability, and you can't follow a single photon to know what it is doing. Or do YOU?

Until there is an experiment to distinguish the two, this is a matter of taste and philosophy. I do not have the time or patience to argue on favorite color.

Zz.

There is a way, If an electron has to wait to collect 1000 photons before it ie ejected then there would be a time delay between emission of an electron and incidence of radiation. There is no such time delay.
everything here comes down to philosophy if we want it to but there is experimental evidence. lack of patience is not to be encouraged. Sorry to have bothered you.

 

[ZapperZ]

There is a way, If an electron has to wait to collect 1000 photons before it ie ejected then there would be a time delay between emission of an electron and incidence of radiation. There is no such time delay.
everything here comes down to philosophy if we want it to but there is experimental evidence. lack of patience is not to be encouraged. Sorry to have bothered you.

I suggest you look up "photocathode response time" before you claim that there is no time delay.

Zz.

 

[lychette]

I state that it doesn't matter because you cannot distinguish between the two. There is no way to know because it is a matter of probability, and you can't follow a single photon to know what it is doing. Or do YOU?

Until there is an experiment to distinguish the two, this is a matter of taste and philosophy. I do not have the time or patience to argue on favorite color.

Zz.

Why do YOU feel the desire to shout?
Of course I (nor anyone else) cannot follow a single photon but when there 1000 I can !
I know (with some certainty) that one of the 1000 photons will eject an electron. I don't know which one but I also know that 999 photons will have no part in the ejection of an electron.
As you rightly point out the figure could be as high as 1 in 5 photons in some photo cathode materials.
The fact remains 1 photon ejects 1 electron.
There is a time delay but it is insignificant (less than 10^-7 secs) and it does not depend on light intensity.
I will make no further contributions to this post.

 

[ZapperZ]

1 first you claim that there is no time delay.

2 then you now claim that there is a delay but it is insignificant. This is silly because when we are dealing with picosecond time scale response, this IS significant! Fast photodetectors and photocathodes for FELs do care about such large time response!

3 here is an example of a lecture material that we teach students with at a particle accelerator school. Maybe you might, just might, learn something from it.
http://uspas.fnal.gov/materials/12UTA/Lecture1.pdf

Zz.

 

[CrazyNinja]

@ZapperZ nd @lychette .. guys calm down. If you have a difference of opinion, sort it out in a conversation. Let us maintain decorum here. This is a public forum.