1. I have read that they have now electron pumps that can shoot single electrons, so the following is a thought experiment that could really take place, can you imagine what would happen:

suppose we shoot single electrons in a sequence in a vacuum, like in a cathotic tube.
We know from TV that the uncertainty is by far less than a pixel, now after we have localized the trajectory , we put in between a screen with a hole whith its center bang on that trajectory. How narrow can that hole get, so that most electrons pass through the hole? If we then vary the speed of the electrons would that influence the result? And what if the screen is made of wood or iron, would that change the results?
Of course I do not expect precision, just would like to get a rough idea
Thanks, folks

2.

3. Originally Posted by whizkid
I have read that they have now electron pumps that can shoot single electrons, so the following is a thought experiment that could really take place, can you imagine what would happen:

suppose we shoot single electrons in a sequence in a vacuum, like in a cathotic tube.
We know from TV that the uncertainty is by far less than a pixel, now after we have localized the trajectory , we put in between a screen with a hole whith its center bang on that trajectory. How narrow can that hole get, so that most electrons pass through the hole? If we then vary the speed of the electrons would that influence the result? And what if the screen is made of wood or iron, would that change the results?
Of course I do not expect precision, just would like to get a rough idea
Thanks, folks
Ha. This is a challenge - what I say below is open to correction by a proper physicist.

What I think will happen with successively smaller holes is that, once the hole becomes comparable in dimensions with the wavelength of the electron, you will start to see diffraction, just as you do with a pinhole and light.

The wavelength of the electron is given by de Broglie's relation: momentum,p = h,Planck's constant/lambda, wavelength. p=h/λ.

So the slower the electrons the longer the wavelength and the greater the size of the hole at which diffraction might be observed.

The mystery of QM is that even individual electrons, shot one by one, can interfere with themselves. What you will see on the screen, eventually, is a pattern of diffraction rings, but this will progressively be built up, dot by dot, as each electron arrives. It's very weird.

4. Thanks, is thickness of the hole relevant? and what about wood vs iron? can there be magnetic or other interference?

5. Originally Posted by whizkid
Thanks, is thickness of the hole relevant? and what about wood vs iron? can there be magnetic or other interference?
I imagine the thickness would be relevant as you could get diffraction from both "upstream" and "downstream" edges. For a clean experiment you would probably want to "sharpen" the edges of the hole to a blade type edge all the way round (i.e. looking like the point of a needle in cross section). Not sure what effect the material would have.

6. Originally Posted by whizkid
I have read that they have now electron pumps that can shoot single electrons, so the following is a thought experiment that could really take place, can you imagine what would happen:

suppose we shoot single electrons in a sequence in a vacuum, like in a cathotic tube.
We know from TV that the uncertainty is by far less than a pixel, now after we have localized the trajectory , we put in between a screen with a hole whith its center bang on that trajectory. How narrow can that hole get, so that most electrons pass through the hole? If we then vary the speed of the electrons would that influence the result? And what if the screen is made of wood or iron, would that change the results?
Of course I do not expect precision, just would like to get a rough idea
Thanks, folks
Cathode ray tubes already have a "shadow mask" or an "aperture grille" that focuses the electrons emitted by the electron gun onto the pixels on the screen. The mask is simply a sheet of perforated steel. There is no limit as to how small the holes can get since the electrons are point-like particles. There is no "difraction".

8. Originally Posted by xyzt
Cathode ray tubes already have a "shadow mask" or an "aperture grille" that focuses the electrons emitted by the electron gun onto the pixels on the screen. The mask is simply a sheet of perforated steel.
Yes, but the apertures are of the order of size of the phosphor dots/lines on the screen. That's much, much larger than the wavelength of the electron.

There is no limit as to how small the holes can get since the electrons are point-like particles. There is no "difraction".
That's not quite right. Exchemist gave the correct answer -- the de Broglie wavelength is the relevant dimension to compare with the would-be diffracting element's dimensions. It is true that deep-inelastic scattering experiments show the electron to be a point particle (to within the resolution of experiment). But thanks to QM, that point-particle has a wavefunction whose wavelength is nonzero, meaning that the probability of finding it at a location is not given by a delta "function". Hence, diffraction is very much possible by nonzero-sized apertures, and in fact has been observed experimentally. CJ Davisson won the first Nobel for Bell Labs around 1927 for his experimental demonstration of electron diffraction. More recently, various groups have demonstrated diffraction patterns built up by single electrons successively traversing a double slit: Single electron double slit wave experiment - YouTube

9. Originally Posted by tk421
Originally Posted by xyzt
Cathode ray tubes already have a "shadow mask" or an "aperture grille" that focuses the electrons emitted by the electron gun onto the pixels on the screen. The mask is simply a sheet of perforated steel.
Yes, but the apertures are of the order of size of the phosphor dots/lines on the screen. That's much, much larger than the wavelength of the electron.

There is no limit as to how small the holes can get since the electrons are point-like particles. There is no "difraction".
That's not quite right. Exchemist gave the correct answer -- the de Broglie wavelength is the relevant dimension to compare with the would-be diffracting element's dimensions. It is true that deep-inelastic scattering experiments show the electron to be a point particle (to within the resolution of experiment). But thanks to QM, that point-particle has a wavefunction whose wavelength is nonzero, meaning that the probability of finding it at a location is not given by a delta "function". Hence, diffraction is very much possible by nonzero-sized apertures, and in fact has been observed experimentally. CJ Davisson won the first Nobel for Bell Labs around 1927 for his experimental demonstration of electron diffraction. More recently, various groups have demonstrated diffraction patterns built up by single electrons successively traversing a double slit: Single electron double slit wave experiment - YouTube
I think you are referring to the Davisson-Germer experiment, right? The diffraction observed has nothing to do with a mechanically generated grating (i.e. drilled holes) but with a much , much finer (crystalline) lattice. whizkid asked about holes drilled (by using the electron flux).

10. Originally Posted by xyzt
I think you are referring to the Davisson-Germer experiment, right? The diffraction observed has nothing to do with a mechanically generated grating (i.e. drilled holes) but with a much , much finer (crystalline) lattice. whizkid asked about holes drilled (by using the electron flux).
There is a quantitative difference, but not a qualitative one. You'll get diffraction in both cases.

Upon re-reading the OP, I don't actually see where he said that the holes are drilled by the electrons. But, in any case, if one uses an e-beam to mill a hole, one can indeed observe diffraction effects with that hole. The youtube video uses a double-slit arrangement with dimensions that are accessible with e-beam milling (although I do not know if that was the actual method used).

By the way, Davisson and Germer weren't looking for electron diffraction; their observation was actually an accident. They broke vacuum, the nickel target oxidized and crystallized in the process. They were smart enough to understand what they observed, and won a Nobel. But the crystal-as-grating was, as I say, an accident, not a necessity. A 1eV electron has a de Broglie wavelength of a bit over 1nm, so practical gratings for demonstrating electron diffraction aren't limited to crystalline solids.

11. Originally Posted by tk421

By the way, Davisson and Germer weren't looking for electron diffraction; their observation was actually an accident. They broke vacuum, the nickel target oxidized and crystallized in the process. They were smart enough to understand what they observed, and won a Nobel. But the crystal-as-grating was, as I say, an accident, not a necessity. A 1eV electron has a de Broglie wavelength of a bit over 1nm, so practical gratings for demonstrating electron diffraction aren't limited to crystalline solids.
Yes, I am aware of that, I studied the experiment in school. I wasn't aware that one can drill holes of 1nm diameter.

12. Originally Posted by xyzt
I wasn't aware that one can drill holes of 1nm diameter.
We are not too far from features of this scale in semiconductor manufacturing.
Quantum optical lithography proven at 1nm resolution - Electronics Eetimes

13. Originally Posted by xyzt
Originally Posted by tk421

By the way, Davisson and Germer weren't looking for electron diffraction; their observation was actually an accident. They broke vacuum, the nickel target oxidized and crystallized in the process. They were smart enough to understand what they observed, and won a Nobel. But the crystal-as-grating was, as I say, an accident, not a necessity. A 1eV electron has a de Broglie wavelength of a bit over 1nm, so practical gratings for demonstrating electron diffraction aren't limited to crystalline solids.
Yes, I am aware of that, I studied the experiment in school. I wasn't aware that one can drill holes of 1nm diameter.
Gosh, it's like London buses: you wait ages for a physicist and then 2 arrive at once.

Thanks to TK421 for doing what I should also have done and actually work out what wavelength a 1eV electron would have. This certainly puts it into perspective.

Evidently, from what you both say, one is not going to see the electron diffraction effects I described unless one resorts to pretty exotic methods for making a hole that is only one order of magnitude larger than typical interatomic distances. But, amazingly, this is not beyond today's technology.

Interesting.

14. Originally Posted by Strange
Originally Posted by xyzt
I wasn't aware that one can drill holes of 1nm diameter.
We are not too far from features of this scale in semiconductor manufacturing.
Quantum optical lithography proven at 1nm resolution - Electronics Eetimes
Chip lithography deals with traces, I was curious to see if there is a technology capable of drilling holes of the order of 1nm diameter.

15. Originally Posted by tk421
Upon re-reading the OP, I don't actually see where he said that the holes are drilled by the electrons. .
Thank you all for your invaluable help. I did not think of holes drilled by electron, as I thought that problems might already arise with holes bigger than that.
What is not clear to me is why the wavelength which is longitudinal is influenced by diameter, which is transversal. It seems like the electron is wiggling its way in space, sort of swaying its hips. I always thought of electrons as males .
Any ideas?

16. Originally Posted by whizkid
Originally Posted by tk421
Upon re-reading the OP, I don't actually see where he said that the holes are drilled by the electrons. .
Thank you all for your invaluable help. I did not think of holes drilled by electron, as I thought that problems might already arise with holes bigger than that.
What is not clear to me is why the wavelength which is longitudinal is influenced by diameter, which is transversal. It seems like the electron i wiggling its way in space, sort of swaying its hips. I always thought of electrons as males .
Any ideas?
It's a WAVE. So yes it does wiggle its hips. Look up diffraction and you will see the sort of thing that happens.

17. Originally Posted by exchemist
It's a WAVE. So yes it does wiggle its hips. Look up diffraction and you will see the sort of thing that happens.
When we say the wavelength of an electron is 1 cm, does it mean that the oscillation takes place in the direction of motion or in all directions?

18. Originally Posted by whizkid
Originally Posted by exchemist
It's a WAVE. So yes it does wiggle its hips. Look up diffraction and you will see the sort of thing that happens.
When we say the wavelength of an electron is 1 cm,
It is NOT 1 cm, it is of the order of 1 nm. Pay attention.

19. Originally Posted by xyzt
Chip lithography deals with traces
Much more than that nowadays. It includes complex 3D structures including vias through the entire die so they can be stacked with interconnections right through the stack. We are not (yet) at 1nm holes, though.

20. Originally Posted by xyzt

It is NOT 1 cm, it is of the order of 1 nm. Pay attention.
thanks, but I was thinking of an electron going at a cm/sec to make it macroscopic

21. Originally Posted by Strange
Originally Posted by xyzt
Chip lithography deals with traces
Much more than that nowadays. It includes complex 3D structures including vias through the entire die so they can be stacked with interconnections right through the stack. We are not (yet) at 1nm holes, though.
Via is not a hole, it is technically a vertical trace.

22. Originally Posted by xyzt
Via is not a hole, it is technically a vertical trace.
A hole is etched, and then filled with metal (or polysilicon).

23. Originally Posted by Strange
Originally Posted by xyzt
Via is not a hole, it is technically a vertical trace.
A hole is etched, and then filled with metal (or polysilicon).
I don't think that at this geometry they use etching, they use deposition, so the via is a "column" , not a (filled) hole anymore.

24. Originally Posted by xyzt
I don't think that at this geometry they use etching, they use deposition, so the via is a "column" , not a (filled) hole anymore.
Many structures are grown by a combination of etching and deposition. It is possible that, in future, instead of vias through the silicon substrate, all of the structure (including 3D interconnect) will be grown and then the original substrate removed. But that introduces a whole new set of problems.

On the other hand, by the time we get close to 1nm feature size, I expect that standard CMOS devices will have been largely replaced with alternatives. It will be interesting to see how Moore's Law fares in the next decade or two.

But we are getting off topic. Maybe we need an "advanced semiconductor fabbing" thread...

25. Originally Posted by Strange
Originally Posted by xyzt
I don't think that at this geometry they use etching, they use deposition, so the via is a "column" , not a (filled) hole anymore.
Many structures are grown by a combination of etching and deposition. It is possible that, in future, instead of vias through the silicon substrate, all of the structure (including 3D interconnect) will be grown and then the original substrate removed. But that introduces a whole new set of problems.

On the other hand, by the time we get close to 1nm feature size, I expect that standard CMOS devices will have been largely replaced with alternatives. It will be interesting to see how Moore's Law fares in the next decade or two.

But we are getting off topic. Maybe we need an "advanced semiconductor fabbing" thread...
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.

26. Originally Posted by whizkid
Originally Posted by xyzt

It is NOT 1 cm, it is of the order of 1 nm. Pay attention.
thanks, but I was thinking of an electron going at a cm/sec to make it macroscopic
Whizkid, it's been fun discussing with you, but I really think you need to tighten up your thought a bit. You are now mixing up the units of speed (cm/sec) with units of length (cm, nm). Meanwhile in the other thread, you seem to be mixing up force with energy. What is going on? It will help us all if you can try to show the sort of rigour in thought and expression that is a prerequisite for understanding physics.

27. Originally Posted by xyzt
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.
To get back to the topic at hand, it's important not to obsess too much over the particular (and revealingly round) numbers. The 1eV/~1nm figures I cited were not intended to describe anyone's actual experiment; the purpose was to provide a calibration to show that the orders of magnitude are such that electron diffraction is indeed observable, and without the use of crystalline solids. The point is to emphasize that the conditions prevailing in the Davisson-Germer experiment are not absolute requirements.

To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength; they don't have to be equal. So, although we can drill -- slowly (too slowly to be used in semiconductor manufacture, but fast enough for grad students trying to get a PhD) -- holes of the order of 1nm, that's not needed to demonstrate electron diffraction in manufactured structures. There is a beautiful (and quite recent) direct demonstration of electron diffraction here: Feynman's double-slit experiment gets a makeover - physicsworld.com. There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.

There's an accompanying video clip showing the building-up of the pattern over time. It's a lot more edifying than youtube cat videos.

28. Originally Posted by tk421
Originally Posted by xyzt
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.
To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength; they don't have to be equal. So, although we can drill -- slowly (too slowly to be used in semiconductor manufacture, but fast enough for grad students trying to get a PhD) -- holes of the order of 1nm, that's not needed to demonstrate electron diffraction in manufactured structures. There is a beautiful (and quite recent) direct demonstration of electron diffraction here: Feynman's double-slit experiment gets a makeover - physicsworld.com. There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
The slit in this experiment is 62 nm, nowhere close to 1 nm (and nowhere close to the 50 pm wavelength you mention):

"The team created a double slit in a gold-coated silicon membrane, in which each slit is 62 nm wide and 4 μm long with a slit separation of 272 nm. To block one slit at a time, a tiny mask controlled by a piezoelectric actuator was slide back and forth across the double slits"

Nevertheless, it appears that it is possible to create mechanical structures fine enough to run the experiment, without the need to resort to crystals as difraction grates.

29. Originally Posted by xyzt
Originally Posted by tk421
Originally Posted by xyzt
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.
To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength; they don't have to be equal. So, although we can drill -- slowly (too slowly to be used in semiconductor manufacture, but fast enough for grad students trying to get a PhD) -- holes of the order of 1nm, that's not needed to demonstrate electron diffraction in manufactured structures. There is a beautiful (and quite recent) direct demonstration of electron diffraction here: Feynman's double-slit experiment gets a makeover - physicsworld.com. There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
The slit in this experiment is 62 nm, nowhere close to 1 nm (and nowhere close to the 50 pm wavelength you mention):

"The team created a double slit in a gold-coated silicon membrane, in which each slit is 62 nm wide and 4 μm long with a slit separation of 272 nm. To block one slit at a time, a tiny mask controlled by a piezoelectric actuator was slide back and forth across the double slits"

Nevertheless, it appears that it is possible to create mechanical structures fine enough to run the experiment, without the need to resort to crystals as difraction grates.
Of course, one can get diffraction from a single edge…….

30. Originally Posted by xyzt
The slit in this experiment is 62 nm, nowhere close to 1 nm (and nowhere close to the 50 pm wavelength you mention):

"The team created a double slit in a gold-coated silicon membrane, in which each slit is 62 nm wide and 4 μm long with a slit separation of 272 nm. To block one slit at a time, a tiny mask controlled by a piezoelectric actuator was slide back and forth across the double slits"
I know this. I said as much in my post:

Originally Posted by tk421
To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength
and

Originally Posted by tk421
There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
Again, the point of my posts has merely been to emphasize that electron diffraction is observable, and without the use of crystalline solids. Your initial replies to the OP distinctly conveyed the opposite impression. That's all.

31. Originally Posted by exchemist
Originally Posted by xyzt
Originally Posted by tk421
Originally Posted by xyzt
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.
To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength; they don't have to be equal. So, although we can drill -- slowly (too slowly to be used in semiconductor manufacture, but fast enough for grad students trying to get a PhD) -- holes of the order of 1nm, that's not needed to demonstrate electron diffraction in manufactured structures. There is a beautiful (and quite recent) direct demonstration of electron diffraction here: Feynman's double-slit experiment gets a makeover - physicsworld.com. There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
The slit in this experiment is 62 nm, nowhere close to 1 nm (and nowhere close to the 50 pm wavelength you mention):

"The team created a double slit in a gold-coated silicon membrane, in which each slit is 62 nm wide and 4 μm long with a slit separation of 272 nm. To block one slit at a time, a tiny mask controlled by a piezoelectric actuator was slide back and forth across the double slits"

Nevertheless, it appears that it is possible to create mechanical structures fine enough to run the experiment, without the need to resort to crystals as difraction grates.
Of course, one can get diffraction from a single edge…….
Yes, yet I do not know of any experiment using electrons having achieved that. Do you?

32. Originally Posted by xyzt
Originally Posted by exchemist
Originally Posted by xyzt
Originally Posted by tk421
Originally Posted by xyzt
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.
To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength; they don't have to be equal. So, although we can drill -- slowly (too slowly to be used in semiconductor manufacture, but fast enough for grad students trying to get a PhD) -- holes of the order of 1nm, that's not needed to demonstrate electron diffraction in manufactured structures. There is a beautiful (and quite recent) direct demonstration of electron diffraction here: Feynman's double-slit experiment gets a makeover - physicsworld.com. There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
The slit in this experiment is 62 nm, nowhere close to 1 nm (and nowhere close to the 50 pm wavelength you mention):

"The team created a double slit in a gold-coated silicon membrane, in which each slit is 62 nm wide and 4 μm long with a slit separation of 272 nm. To block one slit at a time, a tiny mask controlled by a piezoelectric actuator was slide back and forth across the double slits"

Nevertheless, it appears that it is possible to create mechanical structures fine enough to run the experiment, without the need to resort to crystals as difraction grates.
Of course, one can get diffraction from a single edge…….
Yes, yet I do not know of any experiment using electrons having achieved that. Do you?
No, it was just a thought prompted by your observation that the slit was very wide compared to the wavelength, and yet diffraction was seen. I wondered if that was possibly the reason.

33. Originally Posted by tk421

Again, the point of my posts has merely been to emphasize that electron diffraction is observable, and without the use of crystalline solids. Your initial replies to the OP distinctly conveyed the opposite impression. That's all.
And I agreed, by pointing out that I wasn't aware that there were mechanical setups capable of mimicking the apertures of the crystaline arrays used by D-G.

34. Originally Posted by exchemist
Originally Posted by xyzt
Originally Posted by exchemist
Originally Posted by xyzt
Originally Posted by tk421
Originally Posted by xyzt
I agree. So, ~1nm holes cannot be drilled (yet). The technology is not there.
To observe diffraction, all we need is to create structures whose dimensions are roughly comparable to the wavelength; they don't have to be equal. So, although we can drill -- slowly (too slowly to be used in semiconductor manufacture, but fast enough for grad students trying to get a PhD) -- holes of the order of 1nm, that's not needed to demonstrate electron diffraction in manufactured structures. There is a beautiful (and quite recent) direct demonstration of electron diffraction here: Feynman's double-slit experiment gets a makeover - physicsworld.com. There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
The slit in this experiment is 62 nm, nowhere close to 1 nm (and nowhere close to the 50 pm wavelength you mention):

"The team created a double slit in a gold-coated silicon membrane, in which each slit is 62 nm wide and 4 μm long with a slit separation of 272 nm. To block one slit at a time, a tiny mask controlled by a piezoelectric actuator was slide back and forth across the double slits"

Nevertheless, it appears that it is possible to create mechanical structures fine enough to run the experiment, without the need to resort to crystals as difraction grates.
Of course, one can get diffraction from a single edge…….
Yes, yet I do not know of any experiment using electrons having achieved that. Do you?
No, it was just a thought prompted by your observation that the slit was very wide compared to the wavelength, and yet diffraction was seen. I wondered if that was possibly the reason.
I very much doubt it.

35. Originally Posted by tk421
There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
This doesn't seem right, 600eV energy does not correspond to 50 pm wavelength , but to:

this might explain why the 62 nm aperture worked with the above wavelength. I do not see how 50 pm would have ever worked.

36. Originally Posted by xyzt
Originally Posted by tk421
There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
This doesn't seem right, 600eV energy does not correspond to 50 pm wavelength , but to:

this might explain why the 62 nm aperture worked with the above wavelength. I do not see how 50 pm would have ever worked.
Your calculation of wavelength is correct for a photon, but not for a massive particle like the electron. I'm too lazy to TeX it, but the correct equation is lambda = hc/pc, where pc for a massive particle (of energy well below its rest mass energy) is sqrt(2*KE*mc^2). When you plug in the corresponding values, you get the numbers I cited earlier. For a 1eV electron, the de Broglie wavelength works out to about 1.2nm. The wavelength goes inversely as the square-root of energy, so a 600eV electron will have a wavelength that is about 25x smaller, or about 50pm, as I cited earlier.

37. Originally Posted by tk421
Originally Posted by xyzt
Originally Posted by tk421
There, the team used 600eV electrons, whose 50pm wavelengths would seem to make things even harder. Yet, they fabricated slits with dimensions denominated in tens of nanometers, and were able to demonstrate diffraction quite clearly.
This doesn't seem right, 600eV energy does not correspond to 50 pm wavelength , but to:

this might explain why the 62 nm aperture worked with the above wavelength. I do not see how 50 pm would have ever worked.
Your calculation of wavelength is correct for a photon, but not for a massive particle like the electron. I'm too lazy to TeX it, but the correct equation is lambda = hc/pc, where pc for a massive particle (of energy well below its rest mass energy) is sqrt(2*KE*mc^2). When you plug in the corresponding values, you get the numbers I cited earlier. For a 1eV electron, the de Broglie wavelength works out to about 1.2nm. The wavelength goes inversely as the square-root of energy, so a 600eV electron will have a wavelength that is about 25x smaller, or about 50pm, as I cited earlier.
You are right, the correct formula for massive particles is :

which gives indeed 50 pm.
With an aperture of 62 nm, i.e 1200 times bigger than the wavelength, I cannot see how they observed any diffraction.

38. Originally Posted by exchemist
[ You are now mixing up the units of speed (cm/sec) with units of length (cm, nm).
Isn't the wavelength of the electron 2,42 cm when its speed is 1 cm/sec? or 1cm when 2.4 cm/sec?, we are in that range, aren't we?

39. Thank you for the excellent insight into the issue.

So the perforated screen was actually used in the range of mm, and not only it was not a problem , but helped focus the electrons.
Can I conclude that if the energy does not vary the trajectory of an electron is rather stable (if not 100%)?

If the hole gets near the size of the wavelength (in the range of nm at 1 eV, 10^7 cm/sec) we get diffraction; that means the electron still passes through the hole but the trajectory varies: does it depend on the phase of the wave or on chance?
Do you know if there is any experience of roughly when not all (or no) electron would pass through? The size of the electron was thought in the range of 10^-13 cm, but I read that it was changed to less then 10^-16, do you know what poinlike really means? Plancks length or what?

40. Originally Posted by whizkid
Originally Posted by exchemist
[ You are now mixing up the units of speed (cm/sec) with units of length (cm, nm).
Isn't the wavelength of the electron 2,42 cm when its speed is 1 cm/sec?
no,

41. Originally Posted by whizkid
Thank you for the excellent insight into the issue.

So the perforated screen was actually used in the range of mm, and not only it was not a problem , but helped focus the electrons.
Can I conclude that if the energy does not vary the trajectory of an electron is rather stable (if not 100%)?
The trajectory, in the absence of the activation of the deflection coils , is a straight line.

If the hole gets near the size of the wavelength (in the range of nm at 1 eV, 10^7 cm/sec) we get diffraction; that means the electron still passes through the hole but the trajectory varies: does it depend on the phase of the wave or on chance?
See here.

42. Originally Posted by xyzt
The trajectory, in the absence of the activation of the deflection coils , is a straight line..
I read that when travelling in a straight line, the electron has no spin, is it true?

43. Originally Posted by whizkid
When we say the wavelength of an electron is [whatever], does it mean that the oscillation takes place in the direction of motion or in all directions?
Consider an electron with a precise momentum in a precise direction. The wavefunction oscillation is over the entire space and time (position is completely uncertain). At a particular instant in time, a planar surface that is perpendicular to the direction motion has constant phase, and as this planar surface is moved forward (or backward) in the direction of motion (in space only, not in time), the phase changes such that the wavelength is inversely proportional to the momentum. Note that the constancy of the phase over the planar surface is simply the result of the momentum being zero in directions that are perpendicular to the direction of motion. At each point in space, the wavefunction oscillates over time at a frequency that is proportional to the energy.

44. Can we conclude that in order to pass through a hole the diameter must be slightly bigger than its wavelength?
Is there any difference between this model and the oscillation of a photon?

45. Originally Posted by whizkid
Can we conclude that in order to pass through a hole the diameter must be slightly bigger than its wavelength?
Not from what I wrote. I was only describing the wavefunction of particle (not specifically an electron) with definite momentum (in reply to another question you asked). To answer your latest question involves considering the diffraction.

Originally Posted by whizkid
Is there any difference between this model and the oscillation of a photon?
To the extent that what I described was a simplified version that doesn't account for the specific nature of the particle, then no. That doesn't mean that there aren't any differences, only that I didn't take such differences into account.

46. Originally Posted by whizkid
Originally Posted by xyzt
The trajectory, in the absence of the activation of the deflection coils , is a straight line..
I read that when travelling in a straight line, the electron has no spin, is it true?
No it most definitely is not. The electron is a fermion, which means it is a half integer spin particle. It has a spin of 1/2. This is intrinsic.

47. Originally Posted by exchemist
No it most definitely is not. The electron is a fermion, which means it is a half integer spin particle. It has a spin of 1/2. This is intrinsic.
I have read that if in the Stern-Gerlach experiment you run a beam of electrons instead of atoms of H there is no split observed, only deflection in one direction, have you any info to the contrary?

48. Originally Posted by whizkid
Originally Posted by exchemist
No it most definitely is not. The electron is a fermion, which means it is a half integer spin particle. It has a spin of 1/2. This is intrinsic.
I have read that if in the Stern-Gerlach experiment you run a beam of electrons instead of atoms of H there is no split observed, only deflection in one direction, have you any info to the contrary?
If you send charged particles through a Stern-Gerlach setup, surely the beam will be bent in a curve, due to its charge, which will obscure any other effect, won't it? So I'm afraid I don't understand how your question relates to the statement of mine that you quote. Can you elucidate?

In particular, are you attempting to challenge what I'm telling you about electrons having intrinsic spin of 1/2? If you are, please go and verify this for yourself. You will find it in about 10 seconds in a web search on "electron spin". It is really not something we can usefully argue about.

49. Originally Posted by exchemist
In particular, are you attempting to challenge what
Not at all, I am asking id the spin shows up in a stern-Gerlack machine, do they split in spin-up spin-down, I read somewhere they don't, but I may be wrong

50. Originally Posted by whizkid
Originally Posted by exchemist
In particular, are you attempting to challenge what
Not at all, I am asking id the spin shows up in a stern-Gerlack machine, do they split in spin-up spin-down, I read somewhere they don't, but I may be wrong
OK, I see. But I don't know the answer since, as I say, I'd have thought attempting this with a charged particle would be problematic, for the reasons I indicated.

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