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We will use two light sources of exactly the same frequency and same emitting area in this experiment as shown in figure

The distance of both the sources is adjusted to be the same (indicated as d) and in such a way that both project the photons to the area inside the circle ⭕ and also both are switched on at the same time . If both the sources emit light of exactly the same frequency (above the threshold frequency of the emitter plate) then the number of photons reaching the circle will double and since both are at same distance the two photons will reach simultaneously to the electrons inside the circle and the energy gained by the electrons will be twice the one in the original experiment.

Since the frequency is same and number of photons increases then the total energy reaching the plate increases and hence intensity of light has increased . And again , since single electron gains twice the energy then their kinetic energy will increase.

But from theory, intensity doesn't affect the kinetic energy of photoelectrons.

Aren't the two contradictory ? Am I wrong somewhere ?

Ankit
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    Your assumption of both are at same distance the two photons will reach simultaneously to the electrons inside the circle is incorrect. Emissions are random and arrival time of different photons are uncorrelated. – Superfast Jellyfish Aug 22 '20 at 13:02
  • @Superfast Jellyfish but the distance is same and speed is C . So why can't they reach simultaneously ?? – Ankit Aug 22 '20 at 13:14
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    In order to reach at the same time, two photons must be emitted at exactly the same time and travel the exact same distance. – Superfast Jellyfish Aug 22 '20 at 13:16
  • It is edited now. I left that information by mistake. – Ankit Aug 22 '20 at 13:18
  • @Ankit Why do you think that twice the amount of photons means twice the amount of energy per electron? In practice, it means double the number of electrons with the same energy per electron – Ofek Gillon Aug 22 '20 at 13:21
  • @Ofek Gillon earlier let us say the number of photons reaching the circle was exactly equal to that of the number of electrons in that region. So each photon gave energy to each electron. But if total number of photons doubled then the same electrons will receive twice the number of photons. – Ankit Aug 22 '20 at 13:23
  • The probability of two photons arriving at the same time is like the probability of you picking a 20 digit number and I independently picked the same 20 digit number. Also just turning the two sources on at the same no way ensures photons reaching at the same time. Photon emission is like I said, completely random. – Superfast Jellyfish Aug 22 '20 at 13:24
  • Why can't they reach at the same time ?? – Ankit Aug 22 '20 at 13:26
  • Can you prove it ?? – Ankit Aug 22 '20 at 13:33
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    The interaction time between light and electron is extremely fast $\sim10^{-15}$ seconds. So in that sense electrons are excellent time keepers. For two photons to interact with the same electron, they’d have to arrive within $10^{-15}$ seconds of each other. The probability of this is still not zero. These events do happen. But single photon interactions happen way way way more often. So they overshadow these events – Superfast Jellyfish Aug 22 '20 at 13:40
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    The reason this experiment has not been done is because the design is terrible. By using two sources you reduce the coherence. And by using light above the frequency threshold you dramatically contaminate the signal of interest. This experiment would have essentially no chance of detecting two-photon absorption. – Dale Aug 23 '20 at 03:46
  • @Dale but can it prove that intensity affects kinetic energy of photoelectrons ?? – Ankit Aug 23 '20 at 04:50
  • Can the downvoters tell me the reason for downvoting ?? – Ankit Aug 23 '20 at 04:57
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    I told you exactly why I downvoted. I dislike these sorts of “why hasn’t my exact experiment been done” questions. A useful question would be simply “Is there any way that a single electron can absorb two photons at once so that the excitation of the electron is larger than could be achieved by the individual photons? If so, what experiments have validated this?” But instead when my2cts and SuperfastJellyfish tried to teach you the underlying physics you “double down” on your bad experimental design. You should learn from their corrections, not insist on your exact experiment – Dale Aug 23 '20 at 11:36
  • @ankit said “can it prove that intensity affects kinetic energy of photoelectrons ??” Your experiment cannot. That is what my2cts and SuperfastJellyfish were trying to teach you. They were telling you about other experimental designs that can and do prove that intensity can affect the energy. You should not have dismissed their corrections to your experiment – Dale Aug 23 '20 at 16:43
  • @Dale exactly I want to know that whether it can prove the above mentioned thing but if not then why ?? – Ankit Aug 24 '20 at 04:31
  • They already told you why – Dale Aug 24 '20 at 14:00
  • I have edited my answer to explain further. Hopefully this resolves your misunderstandings. – Superfast Jellyfish Aug 27 '20 at 08:44

3 Answers3

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Though possible, it's extremely unlikely that a single electron absorbs two photons in succession, within a tiny interval in just the right way. As increasing the intensity increases the number of photons incident on the metal surface, the number of photoelectrons that are emitted probablistically increases, though the "observed" kinetic energy does not grow considerably beyond a certain saturation-intensity

(even though there might very few lucky ones, but... as said by @Superfast Jellyfish, these would be overshadowed).

The following link might be helpful Photoelectric effect – Why does one electron absorb one photon?

Adorable Cherry
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    In your link the case used is the one which has been done by the scientists i.e. the one with single source but here I have two sources sending photons at the same time and same part of the emitter. – Ankit Aug 22 '20 at 15:13
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The interaction time between light and electron is extremely fast $\sim10^{−15}$ seconds. So in that sense electrons are excellent time keepers. For two photons to interact with the same electron, they’d have to arrive within $10^{-15}$ seconds of each other. The probability of this is still not zero. These events do happen. But single photon interactions happen way way way more often. So they overshadow these events.

One way to observe two photon absorption is to send high intensity light of photon energy that is lower than the threshold energy. This way, single photon interactions don’t lead to ejection of electron. And the only way any electron will be ejected is via multiple photon interaction.

One last attempt

I’ll try one last time to explain why two photon interactions are very rare without special setups. Fundamentally, it is a interesting question.

I think the source of your confusion is your mental picture of light. You might know that light is made up of photons. Now there can be different kinds of light. Light from lasers, light from bulb and so on. The main distinguishing feature between these different kinds of light is how the photons are distributed in a given time window. Here’s a cartoon depicting some of them:

enter image description here

As you can see, for the most common type of light (from bulb and so on), thermal light is made up of photons that are randomly distributed. Lasers on the other hand are still randomly distributed, but average number of photons in a subframe is constant (three in the cartoon). What you might be thinking of as the distribution (equally spaced photons) is actually an extremely rare one called number state. These are generated under very special circumstances.

Coming to the photoelectric effect, consider a stream of photons coming towards a metal sheet. The electrons interact within a small time frame depicted by a blue box in the following cartoon.

enter image description here

You can see that it’s very rare to have two photons inside the box simultaneously. And whatever electrons you’ll be getting will be mostly because of single photon excitation.

However, if we increase the intensity (number of photons in a time window) much higher then the probability of two photons coming within the blue box is higher.

enter image description here

Now if you want to detect these two-photon excitation, then you’ll have to filter out single photon excitations. One easy way to do that is to choose photons such that individually they don’t have enough energy to excite the electron. But two together they do.

Superfast Jellyfish
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  • but you are taking the scenario of the experiment in which single source was used and thus we didn't notice two photons interaction but here two photons are striking at the same time to the same area . – Ankit Aug 22 '20 at 15:10
  • Has this experiment be done with two sources ?? If yes can you share me the link . – Ankit Aug 22 '20 at 15:11
  • Can the downvoter explain their reason to do? – Superfast Jellyfish Aug 22 '20 at 15:37
  • Why didn't you reply ? – Ankit Aug 22 '20 at 15:47
  • @Ankit The link I shared earlier is essentially the experiment I described. https://iopscience.iop.org/article/10.1088/1367-2630/9/10/368 – Superfast Jellyfish Aug 22 '20 at 15:50
  • PS if you were the downvoter, you should review https://physics.stackexchange.com/help/privileges/vote-down – Superfast Jellyfish Aug 22 '20 at 15:52
  • If the interaction time is very small between photons and electrons then does that mean that the reaction time of electrons due to each photon is also very less ?? – Ankit Aug 22 '20 at 15:59
  • Also why should I consider the case in which frequency of each photon is less than that of threshold frequency ?? – Ankit Aug 22 '20 at 16:08
  • can it be filtered this way : suppose we set the stopping potential corresponding to the energy of single photon. So the electron influence by single photon doesn't come out ?? – Ankit Aug 27 '20 at 09:28
  • In this way we don't need to take such photon whose energy is less than work function. – Ankit Aug 27 '20 at 09:31
  • Yes that can be done but it will filter out some two-photon excited electrons as well. Remember that the emission is in random direction so only the component of velocity in the required direction counts. – Superfast Jellyfish Aug 27 '20 at 09:39
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At very high intensity non-linear absorption may occur. You will have to make more than a few modifications to your setup to measure this. "Two-photon absorption (TPA) is the absorption of two photons of identical or different frequencies in order to excite a molecule from one state (usually the ground state) to a higher energy, most commonly an excited electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, typically several orders of magnitude weaker than linear absorption at low light intensities. It differs from linear absorption in that the optical transition rate due to TPA depends on the square of the light intensity, thus it is a nonlinear optical process, and can dominate over linear absorption at high intensities." https://en.wikipedia.org/wiki/Two-photon_absorption

my2cts
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  • Can you tell me why do we need modifications ?? And why does non linear absorption occur at high intensities ?? – Ankit Aug 22 '20 at 15:51
  • You need A to be a laser source and you can drop B. – my2cts Aug 22 '20 at 15:57
  • No I don't want to drop any of these two sources and I want to know what will happen with both at work at the same time ?? – Ankit Aug 22 '20 at 16:00
  • You have been explained that things do not work this way. If you want to observe nonlinear effects you should have a strong coherent source. With one or any number of incoherent sources the linear effect dominates everything. – my2cts Aug 22 '20 at 16:08
  • @my2acts but why ?? – Ankit Aug 22 '20 at 17:21