The Relationship Between Wavelength and Amplitude of Photons and Electrons

[bobie]

Is there a relation between the wavelength and the amplitude of a photon (or particle), or all frequencies have the same amplitude?
If the latter, why the wavelength affects the way a radiation passes through matter or slits?

Thanks.

 

[PhysicoRaj]

There is no dependence of amplitude on wavelength. And it is not necessary that all frequencies (equivalently wavelengths) must have same amplitudes.

 

[bobie]

Can you answer the second question, too?

 

[Larry Gopnik]

Indeed, Amplitude is not affected, it is merely a 'loudness' I do believe. (Or so I was taught at about 13, therefore it may be wrong).

As for depending on diffraction, longer wavelengths equal lower frequency. That means the wave has less energy, and therefore diffracts more. This is as it is more deeply effected by its environment. That's why wavelength affects awes going through slits more.

 

[bobie]

Thanks, but if we have a laser beam of polarized,collimated light passing throu a wooden slit, the photons are affected or not according to wavelength?

 

[PhysicoRaj]

Can you answer the second question, too?

I suggest these are very informative on that : http://hyperphysics.phy-astr.gsu.edu/hbase/mod3.html
http://resources.yesican-science.ca/trek/radiation/final/index_em_matter.html

 

[PhysicoRaj]

As for depending on diffraction, longer wavelengths equal lower frequency. That means the wave has less energy, and therefore diffracts more.

That I think is rather a misconception. The wavelength must be comparable to the slit width to get an effective diffraction.
See these in the wiki:
http://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Wavelength%3Dslitwidthspectrum.gif/220px-Wavelength%3Dslitwidthspectrum.gif

http://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/5wavelength%3Dslitwidthsprectrum.gif/220px-5wavelength%3Dslitwidthsprectrum.gif

 

[Nugatory]

Thanks, but if we have a laser beam of polarized,collimated light passing throu a wooden slit, the photons are affected or not according to wavelength?

Save yourself some grief and try to forget that you ever heard the word "photon" - you can rediscover it when you get to quantum electrodynamics.

Here you are describing a purely classical wave problem, and even thinking in terms of photons is pretty much guaranteed to confuse you if you can't describe and analyze it in classical terms.

 

[bobie]

Save yourself some grief and try to forget that you ever heard the word "photon"

Do your remark apply also to an electron passing through a slit or a hole?
Also, is there any clue to the amplitude of visible light wave?, or of an electron traveling say, at 10^7 cm/s ?

 

[Larry Gopnik]

That I think is rather a misconception. The wavelength must be comparable to the slit width to get an effective diffraction.

See these in the wiki:

http://upload.wikimedia.org/wikiped...um.gif/220px-Wavelength=slitwidthspectrum.gif
http://upload.wikimedia.org/wikiped....gif/220px-5wavelength=slitwidthsprectrum.gif

I do apologise. I was merely attempting a simple answer.

 

[bobie]

http://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Wavelength%3Dslitwidthspectrum.gif/220px-Wavelength%3Dslitwidthspectrum.gif

That is exactly the picture that made me start this thread, the width of the slit must be equal to the wavelength, that suggested the amplitude to me. What is the relation between the width and the wavelength?

 

[sophiecentaur]

Do your remark apply also to an electron passing through a slit or a hole?
Also, is there any clue to the amplitude of visible light wave?, or of an electron traveling say, at 10^7 cm/s ?

Amplitude of a 'light wave' (or any other EM wave) is a function of the total number of photons involved and not the energy in an individual photon.

Re your comments about electrons, you would hardly expect to get 'big or small' electrons, would you? So amplitude of an electron beam would have to refer to the number of them or the total energy.

Do not reject Nugatory's remark about photons. If you want to discuss wave phenomena then forget the particular nature of Photons or Electrons. You cannot have both views at the same time.

 

[sophiecentaur]

That is exactly the picture that made me start this thread, the width of the slit must be equal to the wavelength, that suggested the amplitude to me. What is the relation between the width and the wavelength?

I sometimes wonder whether you actually read anything other than what people write on PF. Wiki and Hyperphysics are full of stuff about diffraction and interference. You can find such a lot of information about the basics of the diffraction of waves. I'm afraid it's very Maths based, but that goes with the territory and it does involve some effort on the part of the reader.

 

[bobie]

Amplitude of a 'light wave' (or any other EM wave) is a function of the total number of photons involved and not the energy in an individual photon.

2) Re your comments about electrons, you would hardly expect to get 'big or small' electrons, would you? So amplitude of an electron beam would have to refer to the number of them or the total energy.
.

What if the number of photons involved is 1?
I was referring to one single EMR light-wave or electron: if light is a wave, can there be a wave (of any kind, EM sound etc) without amplitude? I supposed not.
Probably I was wrong, but if a light wave must have an amplitude, I'm asking: what is it and, is it related to frequency?

2) I was told in another thread that now you have electron pumps that can shoot single electrons. Or, imagine an individual electron shot in a cathotic tube, I supposed both go straight like a bullet, else, we could never move it around with precision and get a TV-picture. Am I right so far?
Now imagine that, knowing the precise trajectory of the electron we put exacly in its path a screen (I said wooden to avoid magnetic or other interference) with a hole of varying diameter. There is certainly a point where it would pass throug the hole.
I do not know if this experiment can be made in practice or if it is just theoretical, my question is:
(whatever the real nature or size , if it is poinlike or a wave, or both) how big must the hole be for the particle to go through? and, would it vary with the speed of the electron?

Thanks for your help

 

[PhysicoRaj]

A photon is not a wave again. The wave is not a photon. They are both two ways of interpreting the same thing. The intensity of light in the wave sense refers to it's amplitude. In the particle sense it refers to the number of photons.

 

[PhysicoRaj]

the width of the slit must be equal to the wavelength, that suggested the amplitude to me.

Are you saying that the width has something to do with amplitude?

 

[Drakkith]

What if the number of photons involved is 1?
I was referring to one single EMR light-wave or electron: if light is a wave, can there be a wave (of any kind, EM sound etc) without amplitude? I supposed not.
Probably I was wrong, but if a light wave must have an amplitude, I'm asking: what is it and, is it related to frequency?

Classically, the amplitude of an EM wave is a measure of the strength of the electric and magnetic fields. You can imagine this as the amount of voltage and current induced in an antenna that detects the EM wave. A higher amplitude EM wave will cause more voltage and current in the antenna than a lower amplitude EM wave. Amplitude is not related to frequency.

2) I was told in another thread that now you have electron pumps that can shoot single electrons. Or, imagine an individual electron shot in a cathotic tube, I supposed both go straight like a bullet, else, we could never move it around with precision and get a TV-picture. Am I right so far?

The uncertainty in the position of an electron is very small. Many orders of magnitude smaller than the size of a single pixel on a CRT. So while we don't actually know the exact position of the electron, it turns out we don't need to.

Now imagine that, knowing the precise trajectory of the electron we put exacly in its path a screen (I said wooden to avoid magnetic or other interference) with a hole of varying diameter. There is certainly a point where it would pass throug the hole.
I do not know if this experiment can be made in practice or if it is just theoretical, my question is:
(whatever the real nature or size , if it is poinlike or a wave, or both) how big must the hole be for the particle to go through? and, would it vary with the speed of the electron?

Thanks for your help

No matter how small you make the hole the electron will always have at least a small probability of passing through. This even applies when there is no hole, since the electron can tunnel through a solid barrier and appear on the other side. The thicker the barrier, the smaller the chance is.

 

[bobie]

No matter how small you make the hole the electron will always have at least a small probability of passing through. This even applies when there is no hole, since the electron can tunnel through a solid barrier and appear on the other side. The thicker the barrier, the smaller the chance is.

Thanks, drakkith, did you mean small, or big?
is the material of the barrier relevant?
does conductive material make any difference?
What I am really trying to understand is on what exactly probability is dependent:
suppose we could reach such a precision in adjusting the pump and that we succeed in getting an electron through a hole of, say, 1mm, if we keep shooting do all electrons pass through the hole?

One last question, in water we can concretely measure the amplitude of a wave, is there a physical amplitude in sound waves and light waves, too?

 

[PhysicoRaj]

Thanks, drakkith, did you mean small, or big?
is the material of the barrier relevant?
does conductive material make any difference?

He meant small. The material does count on the electron being able to tunnel through.

What I am really trying to understand is on what exactly probability is dependent:
suppose we could reach such a precision in adjusting the pump and that we succeed in getting an electron through a hole of, say, 1mm, if we keep shooting do all electrons pass through the hole?

It really depends on a lot of factors. See this:http://en.wikipedia.org/wiki/Quantum_tunnelling

One last question, in water we can concretely measure the amplitude of a wave, is there a physical amplitude in sound waves and light waves, too?

Yes in the case of sound wave. Amplitude in case of light is basically the maximum value of electric and magnetic fields.

 

[bobie]

http://en.wikipedia.org/wiki/Quantum_tunnelling

I was not referring to quantum effects but to macroscopic world.
it is more probable that the electron passes through a hole with r= 1 cm or 1 mm?
and through a hole in wood or iron?

 

[PhysicoRaj]

I was not referring to quantum effects but to macroscopic world.
it is more probable that the electron passes through a hole with r= 1 cm or 1 mm?
and through a hole in wood or iron?

You can't deal with everything based on classical macroscopic mechanics. An electron is macroscopic? Obviously the probability increases with the aperture but for dependence on the material you need to ask quantum mechs for that. You MUST see this: http://en.wikipedia.org/wiki/Introduction_to_the_concept

 

[sophiecentaur]

@bobie
Your technique for 'finding things out' seems to be the scattergun approach. When a reply to one question is not what you can accept, you go off in another direction and ask a set of other random questions. What you are doing is the equivalent of trying to navigate down a road with your eyes closed and no map, relying on impacts with the various objects you encounter in order to find your goal.
Random Q and A is a hideously inefficient way to get an understanding of anything difficult. You need to read a textbook (or equivalent on-line), which will direct your learning along a path that will actual allow you to progress. If you are not prepared to do that then I can't see how you will ever get this stuff. It is not possible to jump into this topic half way through. You need to start with the basics and learn them thoroughly.

 

[Drakkith]

I was not referring to quantum effects but to macroscopic world.
it is more probable that the electron passes through a hole with r= 1 cm or 1 mm?
and through a hole in wood or iron?

Electrons are not classical objects and classical physics does not do an adequate job of describing them. An electron has virtually the same chance to pass through a 1cm hole as it does a 1mm hole. It is only when you get down to sub-nanometer scales that you start to see a noticeable difference.

 

[Khashishi]

What if the number of photons involved is 1?
I was referring to one single EMR light-wave or electron: if light is a wave, can there be a wave (of any kind, EM sound etc) without amplitude? I supposed not.
Probably I was wrong, but if a light wave must have an amplitude, I'm asking: what is it and, is it related to frequency?

Amplitude and frequency are two independent parameters for a wave. Knowing one doesn't tell you anything about the other.

The amplitude is only used to describe the wave nature of light. It cannot be used to describe the particle nature. Amplitude is NOT quantized, and there is no minimum. You can have an amplitude of less than one photon per second. For low intensities, the amplitude tells you the probability of detecting a photon over a short time.

A photon doesn't have an amplitude. That's going in the wrong direction.

As an analogy, consider a pipe that carries water. The minimum amount of water that can be carried is one molecule, but the RATE of water flow has no minimum. It could be one molecule per century, or 10^30 molecules per minute.

 

[bobie]

Amplitude and frequency are two independent parameters for a wave.

The amplitude is only used to describe the wave nature of light..

Thanks, Khashishi, that is what I was asking :the wave nature: since the wave is a perturbation it must have amplitude, the 'intensity' of perturbation, right?.
I was wandering if the perturbation of EM field, has or can have a physical dimension.
Also , considering the nature wave of the electron, what is its "perturbation" and if its amplitude depends on anything or is related to its wavelength (which is related to its speed).

I am sorry if I give the impression of blundering or random questioning, but I follow my logical scheme following what I do not understand and what I cannot find in any book;
to get a clear picture I proposed a simple thought experiment : to shoot an electron through a hole of varying diameter and see what happens when we vary the diameter (or the speed) or the material. When I was told that the uncertainty is much smaller than a pixel, with my logic,I expected to hear that a hole a lot smaller than the size of a pixel (as long as it's larger than the wavelength) would be OK, and if I was wrong I expected to learn why.
I did not ask about quantum effects, tunnelling, thickness of the barrier or other, I specified (whatever the real nature or size). Probably I cannot make myself clear, or I'm just thick.

Thank you , anyway for your help

 

[sophiecentaur]

You want to discuss this without involving QM?
Can't be done. Read about it.

 

[Drakkith]

Thanks, Khashishi, that is what I was asking :the wave nature: since the wave is a perturbation it must have amplitude, the 'intensity' of perturbation, right?.
I was wandering if the perturbation of EM field, has or can have a physical dimension.
Also , considering the nature wave of the electron, what is its "perturbation" and if its amplitude depends on anything or is related to its wavelength (which is related to its speed).

The "wave nature" of QM has no comparison. There is nothing that it physically represents, unlike waves such as EM, sound, and other classical waves. In an EM wave, the "perturbation" is how strong the electric and magnetic fields are. These fields and their associated properties are easy to demonstrate; you can simply separate a couple of charges and see the effects the EM field has on other charged particles and then compare that to what an EM wave will do. You cannot do the same with probability amplitudes in QM.

I am sorry if I give the impression of blundering or random questioning, but I follow my logical scheme following what I do not understand and what I cannot find in any book;
to get a clear picture I proposed a simple thought experiment : to shoot an electron through a hole of varying diameter and see what happens when we vary the diameter (or the speed) or the material. When I was told that the uncertainty is much smaller than a pixel, with my logic,I expected to hear that a hole a lot smaller than the size of a pixel (as long as it's larger than the wavelength) would be OK, and if I was wrong I expected to learn why.
I did not ask about quantum effects, tunnelling, thickness of the barrier or other, I specified (whatever the real nature or size). Probably I cannot make myself clear, or I'm just thick.

Thank you , anyway for your help

Sorry, but the answer is complicated. You cannot ask what happens to an individual electron without taking into account all the quantum effects, otherwise you wouldn't have the right answer!

 

[sophiecentaur]

Also , considering the nature wave of the electron, what is its "perturbation" and if its amplitude depends on anything or is related to its wavelength (which is related to its speed).

You want to talk about where you can find evidence of the wave nature of electrons when there is only one? One electron will not fly through a small hole and always turn up in the place you would expect if it were a bullet and a 10cm hole. You would get very little information from where just one electron turns up; nothing about any 'wavelength' that would be involved. If you send a lot of electrons, one at a time, the statistical pattern of their arrival sites will follow what you would expect with a diffracted (de Broglie) wave of wavelength h/P (P = momentum). The intensity of the beam would relate to the number of electrons arriving per second. This would correspond to your idea of 'amplitude'. (But that is amplitude of the wave and not the electron.)
Nowhere, in the above paragraph have I mentioned the amplitude of an electron wave; that is a meaningless idea - however many times you ask about it.

Of course, the nature of the material of the screen with the hole in, will affect what actually happens to the electron. It will interact with the atoms on the way through and, because its exact path through the hole is also subject to uncertainty, this will affect its 'classical' direction as it leaves. Also, a lot of electrons in a beam will deflect each other and cause the beam to spread. But these are different issues.

Sort out one thing at a time. And READ about it, rather than just asking questions. (What have you actually read, independently? We could discuss that, if you give a reference.)