Does this experiment VIOLATE Einstein's theory of photoelectric effect?

Question

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 ?

Answer 1

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?

Answer 2

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:

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.

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.

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.

Answer 3

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