Photoelectric effect confusion

[sss1]

Homework Statement

Why does wave model of light not explain the photoelectric effect?

Relevant Equations

NA

We know that electrons bound to an atom can only absorb light with certain energies that match the energy difference between two energy levels or otherwise this implies electrons can exist in between energy levels. Then electrons will spiral into the nucleus due to the attractive forces between the electron and the nucleus and so atoms won't exist.
Alright, then if light with frequency f_0 gives the exact amount of energy to free the electrons from the metal, then why can all frequencies above f_0 also work and that the excess energy is all converted into kinetic energy? Or is that where the wave model of light fails to explain the photoelectric effect?

Why does the fact that there is no time delay between the ejection of the electrons and illuminating the metal with light given its above the threshold frequency also suggest that light is a particle instead of a wave? If light were waves then light wave of same energy would be distributed over large number of electrons, and so it will take time for electrons to accumulate enough energy to escape the surface. But I still don't understand how this is supportive of light is a particle? I guess as a particle then it can only transfer energy to one electron, and since electrons can only accept certain energies, combined with the fact that theres no time delay, this suggests that light is a particle with energy equal to E=h_f0? but it can actually be E=hf where f>=f_0? That kinda comes back to the first part of my question..

Also, experimentally, on increasing the intensity of light, the number of ejected electrons increases. However, from many posts that I've read about how the photoelectric effect is unable to explain the wave model of light, it mostly says that the classical wave model of light predicts that higher intensity corresponds to an increase in kinetic energy of the ejected electrons. But to my point of view, higher intensity means more light per unit area right? And so wouldn't this mean the electrons will get ejected faster because now they are "absorbing energy" at a faster rate.

 

[Drakkith]

Alright, then if light with frequency f_0 gives the exact amount of energy to free the electrons from the metal, then why can all frequencies above f_0 also work and that the excess energy is all converted into kinetic energy?

The energy levels in a bulk metal (much, much larger than atomic or molecule size) are incredibly numerous. So much so that they are virtually a continuum. Once you have a minimum amount of energy to eject the electrons in the highest energy states, any photons with an energy above this will eject an electron.

Why does the fact that there is no time delay between the ejection of the electrons and illuminating the metal with light given its above the threshold frequency also suggest that light is a particle instead of a wave?

A time delay could imply that lower frequency and energy waves are 'adding up' their energies until there is enough to eject an electron. But this does not happen. The electrons are ejected immediately, implying that the light either has enough energy to immediately eject an electron or it will never eject one.

But to my point of view, higher intensity means more light per unit area right? And so wouldn't this mean the electrons will get ejected faster because now they are "absorbing energy" at a faster rate.

That may or may not work in a wave model, but since the wave model can't account for everything we have to go with the photon model, in which electrons don't absorb any more energy once they've been ejected from the surface of the metal.

 

[sss1]

The energy levels in a bulk metal (much, much larger than atomic or molecule size) are incredibly numerous. So much so that they are virtually a continuum. Once you have a minimum amount of energy to eject the electrons in the highest energy states, any photons with an energy above this will eject an electron.

By this do you mean they have lots of energy levels so it essentially becomes a continuum? But if it were a continuum, then why can't the electrons just absorb any energy?

in which electrons don't absorb any more energy once they've been ejected from the surface of the metal.

But how is this in favour of the particle model instead of the wave model? Even if light is a particle why couldn't it transfer energy to the electrons once its free?

 

[Drakkith]

By this do you mean they have lots of energy levels so it essentially becomes a continuum? But if it were a continuum, then why can't the electrons just absorb any energy?

As a whole, they can absorb a wide range of energies, but there is a minimum energy needed to eject them from the metal to be seen by the experiment.

But how is this in favour of the particle model instead of the wave model? Even if light is a particle why couldn't it transfer energy to the electrons once its free?

Sorry, I was simplifying things. Ejected electrons could probably still be affected by incoming light, but likely not enough to make a difference in the experiment. I confess I don't know the details of photon-electron interaction well enough to expand on this.

 

[sss1]

As a whole, they can absorb a wide range of energies, but there is a minimum energy needed to eject them from the metal to be seen by the experiment.

Oh alright, yeah I understand. So threshold frequency can be explained by the wave model? Instead the timing is a problem for the wave model since electrons can absorb a whole range of energies that means it can just simply accumulate until it has enough energy to escape, but that doesn't happen.
Which suggests that light is a particle? Here I get kind of confused between how waves and particles work in terms of transferring energy to electrons? Do the energy of waves get split between many electrons whereas the energy of photons is only transferred to one? If thats true then it makes sense from the fact that theres no time delay that light is indeed a particle.

 

[sss1]

So threshold frequency can be explained by the wave model?

actually on second thought the wave model can't explain threshold frequency because if light was a wave then the electrons can just keep absorbing until it gets enough energy to escape so there wouldn't be such a thing as threshold frequency?
And also what's stopping electrons from absorbing energy from many low energy photons and then accumulate enough energy to escape as in the wave model case? Why is it that the particle model of light not allow a time delay?

 

[sss1]

actually on second thought the wave model can't explain threshold frequency because if light was a wave then the electrons can just keep absorbing until it gets enough energy to escape so there wouldn't be such a thing as threshold frequency?
And also what's stopping electrons from absorbing energy from many low energy photons and then accumulate enough energy to escape as in the wave model case? Why is it that the particle model of light not allow a time delay?

Idk why theres a duplicate, and when I delete one it just deletes both of my replies so I have no choice but to keep two of them. They basically say the same things.

 

[Drakkith]

Instead the timing is a problem for the wave model since electrons can absorb a whole range of energies that means it can just simply accumulate until it has enough energy to escape, but that doesn't happen.
Which suggests that light is a particle?

That's right.

Here I get kind of confused between how waves and particles work in terms of transferring energy to electrons? Do the energy of waves get split between many electrons whereas the energy of photons is only transferred to one? If thats true then it makes sense from the fact that theres no time delay that light is indeed a particle.

Remember that light has both particle and wave properties. A high intensity light wave has a huge number of photons and can eject many electrons at once. The wave properties of light show up in how light moves, in things like diffraction and interference. The particle properties show up in how light interacts, such as quantized interactions as the photoelectric effect shows.

And also what's stopping electrons from absorbing energy from many low energy photons and then accumulate enough energy to escape as in the wave model case?

Electrons excited into a slightly higher energy band can quickly give up their extra energy via several processes. So unless the light intensity is extremely high the average electron will lose energy at least as fast as it can gain it.

Why is it that the particle model of light not allow a time delay?

It's not about disallowing it, it's simply that the transfer of energy is instant.

Idk why theres a duplicate, and when I delete one it just deletes both of my replies so I have no choice but to keep two of them. They basically say the same things.

I've deleted the duplicate post.

 

[sss1]

Remember that light has both particle and wave properties. A high intensity light wave has a huge number of photons and can eject many electrons at once. The wave properties of light show up in how light moves, in things like diffraction and interference. The particle properties show up in how light interacts, such as quantized interactions as the photoelectric effect shows.

But does the same thing happen to waves? Like electrons can absorb low energy waves which might excite them to jump to a higher energy level but not enough to escape the surface. Then won't the same energy be released in the form of light instantly again as in the case of absorbing low energy particles?

Electrons excited into a slightly higher energy band can quickly give up their extra energy via several processes. So unless the light intensity is extremely high the average electron will lose energy at least as fast as it can gain it.

Yup, makes sense.

 

[sss1]

actually on second thought the wave model can't explain threshold frequency because if light was a wave then the electrons can just keep absorbing until it gets enough energy to escape so there wouldn't be such a thing as threshold frequency?

Also is this correct?

 

[Drakkith]

But does the same thing happen to waves? Like electrons can absorb low energy waves which might excite them to jump to a higher energy level but not enough to escape the surface. Then won't the same energy be released in the form of light instantly again as in the case of absorbing low energy particles?

No, otherwise low frequency light would eject electrons. But it doesn't.

Edit: Misread the question. See post # 13

Also is this correct?

Yes it is.

 

[sss1]

No, otherwise low frequency light would eject electrons. But it doesn't.

Why will that mean electron will be ejected? if the absorbed energy is released back in the form of light very quickly as in the case of low energy photons then the electrons won't be able to accumulate enough energy?

 

[Drakkith]

Why will that mean electron will be ejected? if the absorbed energy is released back in the form of light very quickly as in the case of low energy photons then the electrons won't be able to accumulate enough energy?

Oh I'm sorry, I completely misread your question.

But does the same thing happen to waves? Like electrons can absorb low energy waves which might excite them to jump to a higher energy level but not enough to escape the surface. Then won't the same energy be released in the form of light instantly again as in the case of absorbing low energy particles?

Generally, in a system such as a bulk metal with huge numbers of particles, the electrons can lose energy through many processes, not just radiation emission. It's more likely that an excited electron will transfer its energy to several other electrons/ions as is interacts with them, gradually losing energy in several steps as it makes its way back down to a low energy state. The net result of this is that the light energy is turned into thermal energy, heating the metal up, before that energy is lost as radiation at a longer wavelength or conducted away through direct contact.

 

[apostolosdt]

Homework Statement: Why does wave model of light not explain the photoelectric effect?
Relevant Equations: NA

We know that electrons bound to an atom can only absorb light with certain energies that match the energy difference between two energy levels or otherwise this implies electrons can exist in between energy levels. Then electrons will spiral into the nucleus due to the attractive forces between the electron and the nucleus and so atoms won't exist.
Alright, then if light with frequency f_0 gives the exact amount of energy to free the electrons from the metal, then why can all frequencies above f_0 also work and that the excess energy is all converted into kinetic energy? Or is that where the wave model of light fails to explain the photoelectric effect? […]

By wave model of light I guess you mean classical model. Now, you should realise that, at the time of Einstein’s explanation of “strange” experimental data, metal surfaces were contaminated with absorbed gaseous molecules. Even today, purifying samples to no contamination at all is highly unlikely. So, in photoelectric effect, what do you really observe? You, in fact, observe interaction of light with a—-in simplified terms—-new state, the so-called adsorbate state. In such a state, a number of effects are in play. The metal substrate has undergone an important change in the surface structure, known as relaxation. Think of this picture: The uppermost metal atoms are now at larger distances between them and thus the forces in the crystal are modified, a bit weaker now. On the other hand, the gaseous molecules are bound on the metal but still keep their physical and chemical properties.

Therefore, all in all, the infalling light interacts with both discrete electron orbits and those immensely symmetrical and cooperative metal atomic states. Al a result, you observe an extremely complicated process. Even today, there isn’t a fully understood explanation.

I know I am not answering your questions in a direct way. You may find the previous posts more illuminating. My intention was to set a more accurate foundation of the photoelectric effect to organise your thoughts on. Hope I helped.

 

[sss1]

Generally, in a system such as a bulk metal with huge numbers of particles, the electrons can lose energy through many processes, not just radiation emission. It's more likely that an excited electron will transfer its energy to several other electrons/ions as is interacts with them, gradually losing energy in several steps as it makes its way back down to a low energy state. The net result of this is that the light energy is turned into thermal energy, heating the metal up, before that energy is lost as radiation at a longer wavelength or conducted away through direct contact.

If electrons lose energy so quickly after absorbing energy, then electrons either get enough energy to escape the surface or they never do? Which is why threshold frequencies exist?
But that in a way doesn't differentiate the wave model and the particle model of light? In wave model you can have low energy waves whereas in particle model you can have low energy photons. And an electron absorbing energy from any of these two will not gain enough energy to escape the surface. So there won't be such a thing as accumulation of energy because the electrons simply lose energy they gain so fast? Electrons can escape the metal if they can gain enough energy whether that be from photons or waves?

 

[sss1]

By wave model of light I guess you mean classical model. Now, you should realise that, at the time of Einstein’s explanation of “strange” experimental data, metal surfaces were contaminated with absorbed gaseous molecules. Even today, purifying samples to no contamination at all is highly unlikely. So, in photoelectric effect, what do you really observe? You, in fact, observe interaction of light with a—-in simplified terms—-new state, the so-called adsorbate state. In such a state, a number of effects are in play. The metal substrate has undergone an important change in the surface structure, known as relaxation. Think of this picture: The uppermost metal atoms are now at larger distances between them and thus the forces in the crystal are modified, a bit weaker now. On the other hand, the gaseous molecules are bound on the metal but still keep their physical and chemical properties.

Therefore, all in all, the infalling light interacts with both discrete electron orbits and those immensely symmetrical and cooperative metal atomic states. Al a result, you observe an extremely complicated process. Even today, there isn’t a fully understood explanation.

I know I am not answering your questions in a direct way. You may find the previous posts more illuminating. My intention was to set a more accurate foundation of the photoelectric effect to organise your thoughts on. Hope I helped.

Although this doesn't answer my question as you mentioned, it was definitely very inspirational! I'll research into it sometime. Appreciate your effort for writing all this :)

 

[Drakkith]

If electrons lose energy so quickly after absorbing energy, then electrons either get enough energy to escape the surface or they never do? Which is why threshold frequencies exist?

That's right. Light with a frequency below the threshold frequency just heats up the material. It doesn't eject electrons.

But that in a way doesn't differentiate the wave model and the particle model of light? In wave model you can have low energy waves whereas in particle model you can have low energy photons. And an electron absorbing energy from any of these two will not gain enough energy to escape the surface. So there won't be such a thing as accumulation of energy because the electrons simply lose energy they gain so fast? Electrons can escape the metal if they can gain enough energy whether that be from photons or waves?

In a purely wave model, raising the intensity of the light would cause ejected electrons to have increasing kinetic energy since more energy is deposited per unit of time when the intensity is higher. But instead we see that the kinetic energy remains the same, only the number of electrons (specifically the current in the detectors circuit) is larger with increasing intensity.

This only makes sense if energy is deposited in discrete 'chunks' of all roughly the same energy, which supports the idea of quantized energy and photons.

Remember to look at the combination of:

1. Minimum frequency threshold for electron ejection.
2. Electron KE scales with frequency, not intensity.
3. Electron current scales with intensity, not frequency.

All of this is counter to how waves normally behave. It can only be explained if light energy is quantized. Hence photons.

 

[sss1]

In a purely wave model, raising the intensity of the light would cause ejected electrons to have increasing kinetic energy since more energy is deposited per unit of time when the intensity is higher. But instead we see that the kinetic energy remains the same, only the number of electrons (specifically the current in the detectors circuit) is larger with increasing intensity.

This only makes sense if energy is deposited in discrete 'chunks' of all roughly the same energy, which supports the idea of quantized energy and photons.

So wave model suggests that more intensity means same amount of waves but each individual waves have more energy? Not sure if I interpreted that correctly. Which predicts increased kinetic energy of ejected photons, and that doesn't happen.
And this only makes sense if there are more waves of the same energy, which keeps the kinetic energy the same but increases the amount of ejected photons instead.
^And that's the particle model?

 

[Lord Jestocost]

One should never think of a light as stream of traveling "particles" across space. Quantization of electromagnetic radiation means that the radiation field energy can only be changed by integer numbers of energy portions (called photons) of amount $h\nu$, where $ν$ is a light frequency and $h$ is Planck's constant.

 

[sss1]

One should never think of a light as stream of traveling "particles" across space. Quantization of electromagnetic radiation means that the radiation field energy can only be changed by integer numbers of energy portions (called photons) of amount $h\nu$, where $ν$ is a light frequency and $h$ is Planck's constant.

But why does photoelectric effect suggests that photon energy is quantised?

 

[PeroK]

If electrons lose energy so quickly after absorbing energy, then electrons either get enough energy to escape the surface or they never do? Which is why threshold frequencies exist?
But that in a way doesn't differentiate the wave model and the particle model of light? In wave model you can have low energy waves whereas in particle model you can have low energy photons. And an electron absorbing energy from any of these two will not gain enough energy to escape the surface. So there won't be such a thing as accumulation of energy because the electrons simply lose energy they gain so fast? Electrons can escape the metal if they can gain enough energy whether that be from photons or waves?

Where are you getting this from?

But why does photoelectric effect suggests that photon energy is quantised?

Photon energy is not quantised. Photons are the quanta of the EM field.

 

[sss1]

Where are you getting this from?

Electrons excited into a slightly higher energy band can quickly give up their extra energy via several processes.

here

Photon energy is not quantised. Photons are the quanta of the EM field.

I don't quite understand that, can you maybe expand on it?

 

[PeroK]

here

I see little or no comparison between what @Drakkith is saying and your posts.

I don't quite understand that, can you maybe expand on it?

A single photon can have any amount of electromagnetic energy. But, all photons of the same frequency have the same energy.

That means that light of a given frequency exchanges energy with matter in multiples of a given energy. If a process such as absorption of energy by an atom requires a certain amount of energy, then only light of a given frequency can do the job.

Ultimately, what is an isn't possible is governed by QED (Quantum Electrodynamics). Hypothetically, an atom simultaneously absorbing two photons each of half the required energy may be possible, but with a very low probability. Whereas, an atom absorbing a single photon with the required energy may be very likely. Note that technically a range of energies may be absorbed. I.e. each line in the spectrum has a non-zero width. But, the closer the energy is to the mean energy, the more likely the absorption.

 

[PeroK]

PS the hypothetical processes you are imagining will either be forbidden under the rules of QED or have a very low probability. The processes we typically see take place in nature are the ones with the highest probability within QED.

 

[Drakkith]

So wave model suggests that more intensity means same amount of waves but each individual waves have more energy?

That's right.

Which predicts increased kinetic energy of ejected photons, and that doesn't happen.

I believe so, yes.

And this only makes sense if there are more waves of the same energy, which keeps the kinetic energy the same but increases the amount of ejected photons instead.
^And that's the particle model?

No, the intensity is the strength of the electric and magnetic fields of the EM wave. Raising the intensity keeps the same number of 'waves' per unit of time, just with stronger fields. If you draw a diagram of a wave a stronger intensity is how high and low the crests are. More intensity equals more photons equals more electrons ejected.

 

[Lord Jestocost]

But why does photoelectric effect suggests that photon energy is quantised?

Maybe, the following text from “Experiments in Modern Physics” by Adrian C. Melissinos (Academic Press, 1966) might be of help:

"4. The Photoelectric Effect
4.1 GENERAL

It was observed as early as 75 years ago that most metals under the influence of radiation (light), especially ultraviolet radiation, emit electrons. This phenomenon was termed photoelectric emission, and detailed study of it has shown:

(a) That the emission process depends strongly on the frequency of the light, and that for each metal there exists a critical frequency such that light of lower frequency is absolutely unable to liberate electrons while light of higher frequency always does. Indeed, for a given surface, if the frequency of the incident radiation is increased, the energy of the emitted electrons increases in some linear relation.
(b) The emission of the electrons occurs within a very short time interval after the arrival of the radiation, and the number of electrons emitted is strictly proportional to the intensity of the radiation.
The experimental facts given above are among the strongest evidence for our present-day belief that the electromagnetic field is quantized. They cannot be explained in terms of a continuous energy distribution in the radiation field, but it must be assumed that the field consists of “quanta" of energy
$$E=h\nu$$
where $\nu$ is the frequency of the radiation and $h$ is Planck's constant (an expression we have already used in Section 3). These quanta are called photons."

 

[sss1]

No, the intensity is the strength of the electric and magnetic fields of the EM wave. Raising the intensity keeps the same number of 'waves' per unit of time, just with stronger fields. If you draw a diagram of a wave a stronger intensity is how high and low the crests are. More intensity equals more photons equals more electrons ejected.

Alright. I think I get it:
Wave model:
Increased intensity means stronger E fields and B fields so more energy, predicting higher kinetic energy of ejected electrons
Increased frequency means more waves per unit time so more ejected electrons.
But the observed is the exact opposite.
Particle model:
Increased intensity means more photons per unit time with same energy so there are more electrons being ejected.
Increased frequency means more energy per photon according to E=hf so more kinetic energy for the electrons.
But how exactly can a photon have a frequency?

 

[sss1]

(b) The emission of the electrons occurs within a very short time interval after the arrival of the radiation, and the number of electrons emitted is strictly proportional to the intensity of the radiation.
The experimental facts given above are among the strongest evidence for our present-day belief that the electromagnetic field is quantized. They cannot be explained in terms of a continuous energy distribution in the radiation field, but it must be assumed that the field consists of “quanta" of energy
E=hν
where ν is the frequency of the radiation and h is Planck's constant (an expression we have already used in Section 3). These quanta are called photons."

I did a bit of researching on this and overcame this video which I think gives a pretty good explanation
https://www.nagwa.com/en/videos/497182585713/
So basically every wave has energy equal to E=hf so when you have n waves the amount of energy you will have is E=nhf and so that means you can't have 0.5hf? That means you can't have 0.5 of a wave for example?

 

[Drakkith]

But how exactly can a photon have a frequency?

The EM wave has a frequency. The photon is the quanta of interaction between the EM wave and everything else. We commonly say that the photon has some frequency, but what we mean is that the EM wave the photon is from has a frequency.

So basically every wave has energy equal to E=hf so when you have n waves the amount of energy you will have is E=nhf and so that means you can't have 0.5hf? That means you can't have 0.5 of a wave for example?

I wouldn't say you had n waves, just one wave with some energy that's a multiple of hf.

 

[sss1]

I wouldn't say you had n waves, just one wave with some energy that's a multiple of hf.

I was thinking of a wave as something like this:

Maye you are thinking of something like this? One long wave?

 

[Drakkith]

A single wave (or wavefront) can have any energy as long as it's a multiple of hf.

 

[sss1]

Is it because a single wave is made of many photons and each individual photon has an energy E=hf?
So the energy of an individual photon is not quantised but the energy of a wave is quantised?

 

[Drakkith]

We're really just getting into semantics and what a 'single' wave is. It's not important. If an EM wave comes in, no matter if it has one or many 'waves' or 'wavefronts', its energy will be some integer multiple of hf.

So the energy of an individual photon is not quantised but the energy of a wave is quantised?

The photon IS the quantization of the wave. The wave is quantized and that shows up as a photon.

 

[sss1]

The photon IS the quantization of the wave. The wave is quantized and that shows up as a photon.

But a photon can have any energy it wants? Whereas the energy of a wave needs to be a multiple of hf?

 

[PeroK]

But a photon can have any energy it wants? Whereas the energy of a wave needs to be a multiple of hf?

That's the wrong way round. Classically the energy of a wave is not determined by its frequency. The Classical wave model cannot explain certain phenomena like the photoelectric effect.

So, you need to quantize the EM field and introduce quanta of that field, called photons.

White light is a mixture of frequencies. But, monochromatic light has a single frequency and can only deliver energy in discrete quanta, which depend on the frequency.

Light is neither a classical wave nor a classical particle. It's a product of the quantized EM field.