question about the photoelectric effect

[gib65]

I'm writing a paper on the "basics" of quantum mechanics, and I'd like to start a thread to ask questions on the subject.

 

First of all, I'm trying to explain how the quantization of energy (and the idea of the photon) explain the photoelectric effect. Based on what I've read, I'm lead to assume that an electron can only obsorbe one photon at a time. I understand that an increase in the frequency of the incident radiation correlates with a greater amount of energy carried by the photons that make up that radiation. I also understand that an increase in the intensity of the radiation correlates with more photons making up that radiation. So, if it's only the frequency of the radiation that causes electrons to be ejected with more force, then the number of photons the electrons are douced with wouldn't be making a difference. Essential, I assume this means electrons can't obsorbe more than one photon at a time, otherwise you'd see the same effect wither by increasing the frequency or by increasing the intensity. Am I right?

[Klaynos]

Ejected with more energy, not force.

Yes only one absorbtion at a time. BUT! an electron can have it's energy level raised by absorbtion, and in this excited state absorb anoter photon, raising it to an even higher level.

[YT2095]

it depends on the material used in the PV/PE cell, they each have their own frequency response curve, some peak at one freq others at a different one, over saturation can kill the cell too.

 

if you have a cell that peaks in the Yellow, and you give it Red at the same intensity you will lose a little charge, it won`t be as effective.

you have to increase the intensity to compensate (more red photons per sqr whatever).

[gib65]

Ejected with more energy, not force.

Yes only one absorbtion at a time. BUT! an electron can have it's energy level raised by absorbtion, and in this excited state absorb anoter photon, raising it to an even higher level.

 

See, this is what I'm having trouble with. If an electron can obsorbe more than one photon, let's say one after the other rather than at the same time, then the energy with which it is emitted should also increase. Why don't we see this with the photoelectric effect?

[swansont]

See, this is what I'm having trouble with. If an electron can obsorbe more than one photon, let's say one after the other rather than at the same time, then the energy with which it is emitted should also increase. Why don't we see this with the photoelectric effect?

 

It will happen, but rarely unless it's very high intensity. The electron typically doesn't stay in the excited state for very long. Plus, if you are looking at PEE, then you are talking about ionizing radiation, so excitations aren't under consideration.

[gib65]

I think I get the general picture (Still a little confusing though ). Thanks.

 

Onto my next question: atomic line spectra. I understand the general theory behind it (electrons dropping to lower energy levels, and the photons emitted carrying the difference in energy between those levels - thus corresponding to a certain frequency of light and to a specific spot and color in the range of spectral lines). What I'd like to understand better is why these spectral lines are unique from one gas to another. For example, between hydrogen and helium. It seems to me that if hydrogen and helium contain electrons in the same orbital (though helium would have 2 in that orbital where hydrogen would only have one), there shouldn't be any difference in the spectral lines. The electrons should be raised and dropped to the same energy levels. The only difference would be that it would be happening twice as often in helium since it's got two electrons, and so the spectral lines for helium would be twice as intense. But this doesn't seem to be the case in the research I've done, and I'm not sure why.

[Klaynos]

For solids....

 

Simply because the energy bands are different for all atoms. The number of protons and electrons alters the positions of the bands. More photons mean that the electrons are attracted to the centre more.... (*handwavy argument that isn't 100% true but the perturbation you apply is pretty much that*)

 

I'm strugling to remember my solid state about band structure which is not good considering what I'm currently working on.

 

But I think to derive the structures you need to use quantum mechanics, starting with hydrogen and then using perturbation theory, I'm sure the same applies for gases...

[swansont]

Helium has two protons, so the force of attraction on an electron is twice as large. That changes the energy right there - the electrons (classically) will try and be as far apart as possible, so the repulsion will be a smaller effect. Right there you can see the dynamics are different.

 

Even without delving into QM, if you solve the Bohr equation you'll see that the energy terms depend on Z² for a single electron system. The only way you could get the same spectrum is if the second electron completely screened the extra proton, which would require that the electron be in the nucleus. And we already know that's not the case.

[gib65]

Helium has two protons, so the force of attraction on an electron is twice as large. That changes the energy right there - the electrons (classically) will try and be as far apart as possible, so the repulsion will be a smaller effect. Right there you can see the dynamics are different.

 

Even without delving into QM, if you solve the Bohr equation you'll see that the energy terms depend on Z² for a single electron system. The only way you could get the same spectrum is if the second electron completely screened the extra proton, which would require that the electron be in the nucleus. And we already know that's not the case.

 

Thanks. I guess what confuses me most is the idea that if energy is quantized, subtle changes in atomic number and repulsion/attraction forces wouldn't have much effect. Take the minor repulsion force of the electron you mentioned as an example. Supposing this force is indeed minor compared to the force with which the electron is pulled from one orbital to the next one down, then the amount of energy carried by the photon emitted in that event would be just slightly less than what it would be if no repulsion force was present (as in the hydrogen atom). Now, I'm assuming that the energy carried by the emitted photon is indivisible (that's what it means to be quantized - right?). So how is it possible to get a photon with such a minute degree less energy due to the presence of a repulsion force? Wouldn't you have to take that minute difference of energy and consider it as a removable fraction of the total energy you would have without the repulsion force?

 

Maybe I'm thinking of these energy particles too much like matter particles. For example, if you had some particle and found that under some conditions, you could get a slightly smaller or less massive particle out of it, you'd assume the original particle was divisible. But tell me if this alternate conception of energy particles is correct: the energy carried by a photon can come in any amount - it is not limited to predefined quantities. But as a photon, no smaller amount can be extracted from it, thus rendering the photon suitable for treatment as though it were fundamental and indivisible. This way, you don't have to think of different frequencies of electromagnetic radiation as coming only in descrete amounts - it can be smooth and continuous. Would this be a better understanding (am I making sense)?

[Klaynos]

What do you mean by "energy particle"?

 

When a photon is absorbed, either the absorption event happens and the photon no longer exists, or it doesn't and there is no energy transfer and the photon keeps on going. It can't be partially absorbed...

 

I don't believe there is any reason why the energy bands have to be quantised, but they are because there are only so many configurations of atom (and then bonded states change it as does applying external fields but for the sake of simplicity we can ignore that at present)... I think that's what you're getting at?

[gib65]

What do you mean by "energy particle"?... I think that's what you're getting at?

 

I think what you're saying is what I'm saying. What I mean by an "energy particle" is the fundamental unit of energy that Plank postulated and Einstein dubbed the "photon". I call it a "particle" because it's said to be indivisible like a particle of matter.

 

I must apologize for my poor lingo. I'm not in my own waters here so it's difficult for me to be clear in my questions. Please bare with me.

 

Basically, what I'm asking is this: is there any constraints on the amount of energy carried by a single photon?

 

The context from which I ask this is as follows: when I first understood the basic principle from which quantum mechanics stems - namely, that energy comes in discrete packets or "quanta" - I assumed this to mean that the amount of energy one could ever encounter in anything is a multiple of n, where n is the smallest amount of energy possible... period. This puts a constraint on the amount of energy that a given photon can carry. A photon can carry n, 2n, 3n,... but never (3/2)n or (6/5)n and so on. I also understood from the photoelectric effect that as the frequency of the incident elecrtomagnetic radiation increase, the amount of energy carried by the photons absorbed by the electrons increases proportionally. Putting these two (mis?)understandings together, I took this to mean that the frequency likewise comes only in discrete amounts (knHz, 2knHz, 3knHz... where k is some constant). This would have to be the case since a frequency of, say, (3/2)knHz would correspond to a photon of energy (3/2)n which was not possible.

 

But now I'm considering this alternate understanding: that the frequency of electromagnetic radiation and the amount of energy carried by a single photon has no constraints - it can be (3/2)n or whatever amount from the domain of the positive real numbers. What's quantized, or "indivisible", is the photon itself. That is to say, although a single photon can carry any amount of energy, as a photon, that energy cannot be partially removed or divided (or absorbed as you put it, klaynos). For all intents and purposes, it is fundamental and indivisible. It is the fundamental "quanta" that Plank proposed.

 

Is this right?

 

In any case, I think if I understand this stuff, my understanding of the atomic line spectra will follow.

[Klaynos]

Well IIRC there is a n that you describe, which is the plank energy. Might be worth reading about it on wikipedia or hyperphysics.

[swansont]

The quantization occurs in individual systems, but will not be identical in different ones. In Hydrogen, for example, the difference between the n=1 and n=2 energy level is 10.2 eV, but in another element it will be different, depending on the number of protons you have.

 

But that's not the only way to get photons, and while the energy is quantized, the available states in free space are much closer together than in atomic systems. You can look at a photon confined to a potential well, and you have standing waves with (n/2) wavelengths being possible. [math]\lambda = \frac{n}{2} L[/math] But the potential well is the universe, so L is really big, and the possible wavelengths (and thus frequencies) are really close together.

[Severian]

Quantum Mechanics is actually a really bad name for Quantum Mechanics since most things in Quantum Mechanics aren't actually quantised. Even worse, there are plenty of classical systems which are quantised. For example, the frequencies of a (unheld, or whatever the musical term is) guitar string are quantised for exactly tha same reasons as the hydrogen atoms energy levels are quantised.

 

 

Non-commutative Mechanics might have been better.

[gib65]

The quantization occurs in individual systems, but will not be identical in different ones. In Hydrogen, for example, the difference between the n=1 and n=2 energy level is 10.2 eV, but in another element it will be different, depending on the number of protons you have.

 

But that's not the only way to get photons, and while the energy is quantized, the available states in free space are much closer together than in atomic systems. You can look at a photon confined to a potential well, and you have standing waves with (n/2) wavelengths being possible. [math]\lambda = \frac{n}{2} L[/math] But the potential well is the universe, so L is really big, and the possible wavelengths (and thus frequencies) are really close together.

 

Hmm, so it's a combination of the two views I'm toying with. When an electron in a particular atom (say helium) drops from one energy level to the next one down, the difference in energy need not be considered even close to the fundamental unit of energy of the universe-well (i.e. the smallest amount of energy possible - the difference between successive wavelengths). In other words, there's plenty of room for minor adjustments from one atomic system to another. Is this right?

[Severian]

As far as we know, there is no 'smallest amount of energy possible'.

[gib65]

As far as we know, there is no 'smallest amount of energy possible'.

 

Okay, so the set of possible wavelengths that swansont was referring to (determined by the "universe-well") is a constraint put on electromagnetic waves only, not on energy in general (sorry if this is tedious).

[Severian]

Not really - there is no restriction on free electromagnetic waves either. You can have a photon with arbitrarily long wavelength and as far as we know for sure arbitrarily short wavelength.

 

The only energy restriction you can come up with for free particles is that they should possibly not have energies above the Planck Mass. This is because we expect gravity to become very strong at that very very high energy scale and space-time will foam. Then your minimum waveleght would be the Planck length. But that is very speculative, is unproven, and forms no part of our current model of physics (the Standard Model).

 

(I suppose you could also argue that the universe itself might be a finite size, but that is even more speculative, epsecially since we know it is topologically open.)

[swansont]

Hmm, so it's a combination of the two views I'm toying with. When an electron in a particular atom (say helium) drops from one energy level to the next one down, the difference in energy need not be considered even close to the fundamental unit of energy of the universe-well (i.e. the smallest amount of energy possible - the difference between successive wavelengths). In other words, there's plenty of room for minor adjustments from one atomic system to another. Is this right?

 

 

A Severian notes, the "photon-in-a-box" solution tends toward a continuum once that box is the universe, so any frequency is possible. Photons coming from bound systems is where you will see the quantization. The behavior of the photons in free space isn't going to modify that, only interactions with some other system that alters the energy structure/changes the boundary consitions will do that.

 

Non-commutative Mechanics might have been better.

 

Then we'd have people jabbering about "non-commutative leaps." Meh.

[gib65]

A Severian notes, the "photon-in-a-box" solution tends toward a continuum once that box is the universe, so any frequency is possible. Photons coming from bound systems is where you will see the quantization. The behavior of the photons in free space isn't going to modify that, only interactions with some other system that alters the energy structure/changes the boundary consitions will do that.

 

Okay, this is starting to make some sense to me. In any case, it's more than I need to explain the photoelectric effect and atomic line spectra. I think if I delve any deeper than this, I might as well take a university level course that's heavy on the math (*shutter*).

 

Thanks for all your answers... and stay tuned for my next question .

[gib65]

Here's my next question: What were some of the experiments that lead to the discovery that some outcomes in quantum mechanics are random?

[swansont]

Here's my next question: What were some of the experiments that lead to the discovery that some outcomes in quantum mechanics are random?

 

Double-slit and crystal lattice interference. (Davisson-Germer)

[gib65]

Double-slit and crystal lattice interference. (Davisson-Germer)

 

I take it these experiments came before Heisenburg proposed his uncertainty principle, correct?

 

What was it about these experiments that proved randomness in natue. Was it the random scattering of impact points on the screen as the interference pattern built up (like this)?

[swansont]

I take it these experiments came before Heisenburg proposed his uncertainty principle, correct?

 

What was it about these experiments that proved randomness in natue. Was it the random scattering of impact points on the screen as the interference pattern built up (like this)?

 

 

 

That, and also the fact that you can do it one particle at a time (showing self-interference). Then you have the solutions to atomic orbitals not being classical, and being able to match that up with spectroscopy, and just about every other system that is solved with the Schroedinger equation.

 

Davisson-Germer was 1927, which was the same year as the HUP, but electrons as waves was proposed by deBroglie in 1924.

[gib65]

How do measurements of a particle's momentum reduce the certainty in its position? I understand how this works the other way around - when you bump a photon off a particle, like an electron, it will change its momentum. In order to have as little effect on the momentum as possible, we need to fire photons of long wavelength since the longer the wavelength, the less they disturb the particle being measured. But the photon still has to bounce back, right? And when it bounces back, you can get the time it took, and thereby figure out the position of the particle being measured just as accurately as you could when the photon had a shorter wavelength.

 

I'm wondering if the uncertainty in position comes from the fact that, with a long wavelength, the position of the photon becomes less certain (it's "spread out" more), and so where and when it collides with the particle being measured is more uncertain. Is this right?