# More detailed explanation of photoelectric effect ?

1. Oct 8, 2012

### mraptor

I get confused when I read that the Energy of wave in classical mechanics is correlated to the amplitude E ~ A^2
(pls. point me to a doc which shows that, couldn't find any exact formula on internet), but then when we are talking about atoms,photons,electrons
they say it is dependent on the freq. i.e. E = hf.
Here is how I do my interpretation on those explanations.
If I imagine a ocean wave (similar to sound wave) I will expect that I will measure the energy of the wave impacted on specific area.
From this follow that I'm looking at the Intensity which is defined as Power over area i.e. I = P/Area..
We know that Power is Work done over time i.e. P = W/t, Work is the Energy dispensed to do a job i.e. W = F*d.
Following this line of thought I then figure out Energy transported from a wave is correlated i.e. depend on
E ~ Amplitude * velocity * area ? The bigger any of them more energy is transferred.
Making logical jump for the small world that velocity is synonymous for frequency...
E ~ Amplitude * frequency * area ?
... we conclude then that when doing photo-electric experiment we are expecting that the energy transferred by the
"impact wave" (remember we dont know yet, we are speculating that light is a wave, still) will be dependent on the Amplitude in our case
brightness of the light.
So when later we measure the fleeting electrons off the metal we would expect that when we increased the the brightness(Amplitude) we would get faster
electrons (more Energy), but we don't.
But when the scientists changed the color(freq) of light they saw that they got their faster electrons.
This then proved that the Amplitude does not have impact on the velocity of the electrons (which was expected from classical mech) i.e. kinetic-energy,
but only on the number of the electron emitted (if emitted at all) i.e. Intensity of the output!

Did I made the correct assumptions and explanations.

I'm looking for the connection of disregarding the Amplitude. I know we are talking about specific electrons, but their wave quality still implies amplitude right? Or is it because the amplitude is bit wave amplitude , but probabilistic ? Still in 1900+ they didn't knew that , yet.

2. Oct 8, 2012

### Staff: Mentor

The wave quality of the electrons? I'm not quite sure what you are asking here.

Last edited: Oct 8, 2012
3. Oct 8, 2012

### mraptor

How did the scientists decided that Energy is not dependent on Amplitude ?
Also a derivation in clasical physics that shows that Energy of the wave is dependent on Amplitude (belive it or not, i couldn't find any on google !).

Example how normally this relation is mentioned :
http://www.physicsclassroom.com/class/waves/u10l2c.cfm

Last edited: Oct 8, 2012
4. Oct 8, 2012

### Staff: Mentor

For the photoelectric effect it was simply that you could reduce the intensity of the light and still have the same energy of ejected electrons, you just had less of them per second. It was when you reduce the frequency of the light that the electron energy fell.

Keep in mind that the energy DOES go up as you increase the intensity of the light, but only because you have more photons. For example, a radio antenna will have a large voltage and subsequent current induced in it from a very high amplitude signal, whereas a low amplitude signal may get lost in the background noise since it is barely registered.

I don't think I can provide a derivation, as I am not formally trained in physics. All I know is that the amplitude is what determines the energy of the wave. For example, a sound wave has a higher amplitude the louder it is, irregardless of it's frequency.

5. Oct 8, 2012

### mraptor

thanks,

So in a sense, the scientists saw that increasing the brightness(amplitude) increases the current, but if the light that was shone was of specific colors you didnt get any current at all and in other colors you got current.
So they saw that the frequency act like a switch and amplitude still increases energy if correct frequency is selected, so they decided frequency is what carries the energy and because we are talking about such a small particles and Plank law already showed by that time that the energy is recieved and released in bundles, amplitude was prescribed to the number of bundles released. (Intensity is anyway related to Amplitude via Power i.e. P ~ A^2 * v)

I'm also not trained in Physics, that is probably ask such questions ;)

6. Oct 8, 2012

### Staff: Mentor

Hold on, I want to make sure you understand exactly what is going on. When an electromagnetic wave interacts with matter it does so in quanta called photons. That means that if an EM wave with a wavelength of 600 nm, each interaction will transport just over 2 electron volts of energy into a material.

The frequency and amplitude only describe properties of the wave. It is the interaction between the wave and the material that transports the energy. So saying the frequency is what transports the energy is misleading in my opinion. I think it is best to think of it as energy transported over time, in which case both the frequency AND intensity of the light are important.

7. Oct 8, 2012

### mraptor

Ok, can I rephrase it like this then :

The electromagnetic wave carries the energy but deposits it only when there is "impedance" of the frequency between the EM-wave and the materail and the transfer of energy happens only when there is a match of frequencies (resonanse).

8. Oct 8, 2012

### Staff: Mentor

As long as you are aware the in many materials, especially metals, the range of energy levels is practically infinite, so they can absorb all wavelengths.

9. Oct 8, 2012

### Darwin123

In those days (<1905), quantum physicists didn't picture quantization has involving particles. Quantization involved quantization of amplitude.
Amplitude is constrained to be at certain discrete values. The changes in energy corresponding to this discrete values are constrained to be integer numbers of hf (where h is Plancks constant).
If one integrates the square of the amplitude of any mode in a cavity over the volume of the cavity, and then multiplies it by hf, one gets the total energy of that mode. The Planck law as originally stated implies that his energy has to be an integer number times hf. Of course, zero point radiation is now known to add about hf/2 to that number. However, the changes in energy of the mode still have to be an integer times hf.
The concept where amplitude is constrained to discrete values is equivalent to the concept of wave-particle duality. It is sometimes better to picture the photon as being a sudden change in amplitude then of being a particle. It is still anti-intuitive.
In the classical world, there is no constraint to the amplitude of a wave. Amplitudes can change continuously according to Newton's Laws. However, Planck came up with a sort of phenomenological fit to the black body radiation using the idea that amplitude changed in discrete steps. Einstein and deBroglies reinterpreted this idea as describing wave-particle duality.
Planck was the first scientist to come up with the idea of "quantization." He came up with the idea by analyzing black body radiation. However, his concept of quantization is clearly tied to quantization of amplitude. He had no idea that quantization of amplitude had anything to do with particles.
The probability part comes in when one tries to predict when the amplitude changes its constrained value. The transition can occur at any time. This is analogous a particle colliding at any time. So you have to think of the transitions in amplitude as being stochastic in time.
Frequency can be discrete even in classical Newtonian theory. The modes of vibration of a tense string have discrete wavelengths and hence discrete frequencies. The quantum mechanics part comes in by picturing the amplitude of the string being constricted to fixed values. There is no Newtonian counterpart to that.
The two ideas are equivalent on some level. A phonon can be thought of as discrete steps in the amplitude of a vibration. However, it is also called a "quasiparticle." The two interpretations are very close together.
Think of it this way. Suppose that the amplitudes of a wave on a string are confined to discrete values. Now use just a very small amount of energy to vibrate the string. In order to be consistent in terms of energy, only a small segment of string can be excited. The small region of string that contains all the energy from this small amount of energy is a quasiparticle.

10. Oct 9, 2012

### mraptor

Ok, I see the Amplitude is quantized...makes more sense.
Thanks alot, have to ponder abit, before I come with the next question.

"The probability part comes in when one tries to predict when the amplitude changes its constrained value. The transition can occur at any time. This is analogous a particle colliding at any time. So you have to think of the transitions in amplitude as being stochastic in time."

Ha, very nice explanation... quantized amplitude, which changes in time as a stochastic process. So the hf provides the quantization amounts possible, but can be predicted only on average i.e. statistically

11. Oct 9, 2012

### soothsayer

mraptor--you seem to get it now.

This same topic came up not long ago. You might refer to this thread for further insight, though the thread became a bit muddled after a while and some topics are still up for debate

12. Oct 9, 2012

### mraptor

Let me do another summation that just popped to me mind, let me know if I'm correct.
The energy output from the impact of EM-wave is still dependent on the Amplitude as in classical mechanics, the difference is that this amplitude now can be clearly linked to the particles which (in a sense provide the "medium" for propagation) provide the quantization of this amplitude (instead of smoothness expected from previous experience).
One additional observation, which was not observed in large scale phenomena was that in EM-wave the transfer of energy happens only if there was frequency match, which act like on/off switch.

13. Oct 9, 2012

### Darwin123

Particle number is a stochastic quantity, too. This is a direct consequence of the fact that amplitude is a stochastic quantity. This is well established in terms of the electromagnetic field (photons).
. The amplitude is a stochastic quantity, as seen by the fact that the amplitude is intrinsically uncertain. One can accurately determine an average value for the amplitude, but one can’t know it precisely. Since the particle number is proportional to the square of the amplitude, particle number is also is a stochastic quantity.
The uncertainty in particle number and in amplitude isn’t apparent in the first quantization theory presented in as an introduction to quantum mechanics. However, it is very important in quantum electrodynamics. In fact, it is very important to engineers building instruments to measure light intensity. The uncertainty in photon number causes most of the noise in measurements with high frequency electromagnetic radiation.
The phase can be considered a type of conjugate variable to amplitude. One can’t know the particle and the phase simultaneously. The product of the uncertainty in photon number and the uncertainty in phase has to be greater than one. Just as one can’t know both the energy and time simultaneously, or both the momentum and position simultaneously.
The uncertainty in particle number is for me easier to visualize in terms of stochastic amplitude than stochastic particle number. However, it still bothers me. It is anti intuitive. Never mind it has a lot of experimental support and engineering applications. The idea that there can sometimes be two of me (randomly speaking) is disturbing.

Amplitude is a stochastic quantity, just as particle number is a stochastic quantity. This can easily be seen by the fact that there are uncertainty relations involving both There is a fundamental uncertainty in amplitude that is implicit in quantum mechanics.

Here are links referring to uncertainties in amplitude, particle number and phase.

http://en.wikipedia.org/wiki/Coherent_states
”A coherent state distributes its quantum-mechanical uncertainty equally between the canonically conjugate coordinates, position and momentum, and the relative uncertainty in phase [defined heuristically] and amplitude are roughly equal—and small at high amplitude.”

http://en.wikipedia.org/wiki/Quantum_noise
“In the case of uncertainty of electric field in some lasers, the quantum noise is not just shot noise; uncertainties of both amplitude and phase contribute to the quantum noise.”

http://www.ino.it/~azavatta/References/PRA48p3159.pdf
“We have mathematically determined all of the quantities involved in the uncertainty relation for phase and photon number...”

The concept that particle number is a stochastic quantity may be helpful when thinking about virtual particles. What is generally considered photon number is really just the expectation of photon number. Therefore, the expectation number of photons can be considered the number of "real" photons. However, the stochastic fluctuations in photon number can be considered the number of "virtual photons".

14. Oct 9, 2012

### mraptor

And that is because...
-- You can measure the EM field with classical instrument and calculate from there the probably the photon count and their average parameters.
-- And you can detect individual photons and get information about them...
-- But you can not measure all the photons one by one and calculate from there the EM fields characteristics.(you can only work with averages in this case and sum the parameters based on probable statistical distribution).
Right ?

15. Oct 9, 2012

### Darwin123

Basically. Of course, there are more than averages in statistics. There are all sorts of statistical moments. For example, there are standard deviations, correlation functions.
The EM fields are determined by the statistical moments of the photons. However, there are an infinite number of statistical moments. The properties of the EM field can be determined precisely by an infinite series that includes a subset of the statistical moments.
Mostly what physicists and engineers work with are the first two statistical moments. If you know the average number of real photons, and the standard deviation of the real photons, then you know a lot about the electromagnetic wave.
A coherent wave, like in a laser, has the minimum possible standard deviation of photon number. Therefore, coherent light can be considered the "most classical form of light". Incoherent light sources have a much larger standard deviation in photon number. An incoherent light source can have a standard deviation in photon number larger than the average photon number. Thus, one can have a highly nonclassical situation with incoherent light.
You get the idea, though.
Quantum mechanics where the particle number is uncertain is called second quantization. First quantization is what is taught on an introductory level, because that is sufficient for most scientists outside of physics and engineering. However, the stochastic nature of the amplitude makes second quantization more complicated than first quantization.
Biologists do need quantum mechanics. However, they usually need only first quantization. Second quantization is a complication. A biologist is very likely to be interested in the energy of an electronic level. However, he is unlikely to be interested in the homogeneous band width of that electronic level. A biologist could be interested in the average number of photons, but he seldom would be interested in the standard deviation of the photon number.
This is one reason I am very leery of quantum biology. I have nothing fundamental against it. However, I don't think that the typical biologist knows enough about second quantization to develop plausible hypotheses. The effect of a biologist speculating about quantum mechanics is almost as bad as a physicist speculating about evolution. On the other hand, Alverez did all right.
To sum up: The amplitude of a wave is quantized. Furthermore, the amplitude is a stochastic quantity. Much of what we call noise is due to amplitude being a stochastic quantity.

16. Oct 9, 2012

### mraptor

If I think of a photon as a wave, could I then speculate that the amplitude of the EM field is consequence of "resonance" process happening with the wave-photons i.e. the more photons resonating at specific frequency the higher amplitude I will get because they interfere.. and uncertaincy comes from the time component i.e. amplitude goes up only when resonance happens at the same time ?

Just a thought, trying to get visual idea of how you can quantize the amplitude.

17. Oct 9, 2012

### Darwin123

I don't know what you mean by resonate or by wave-photons. I especially don't know what it means when a resonance happens at the same time. So it doesn't help me visualize quantized resonance.
My image of resonance is the like the classical picture of a child sitting on a swing, being pushed by the parents at the natural frequency of the swing. There is no concept of "same time" here.
Maybe the "traditional" Bohr atom is a better picture.
Imagine a classical electron in orbit around the nucleus. The average radius of an electrons orbit is the amplitude of the electrons oscillatory motion. Actual distance of the electron from the nucleus changes randomly. This is the stochastic noise on the amplitude. However, there are certain attractors in radius. There are discrete values of radius where the motion of the electron is relatively stable. Stable here means oscillatory as opposed to stochastic. These stable orbits are the Bohr radii.
You do know there is no way anyone can twist quantum mechanics into a fully Newtonian picture. Stochastic electrodynamics (SED) is as close as anyone has gotten, and even that doesn't work all the time. I think the OP question has been answered. Answer: Energy quantization really means amplitude quantization.
So there are values of instantaneous amplitude that are more stable than the values of the instantaneous amplitude at other values. That is a good as it gets unless you want me to discuss stochastic electrodynamics (SED). At that point, we need a bigger thread.