Electron vs Photon question? Significance of momentum?

[curiousmind04]

Homework Statement

, 2. Homework Equations , 3. The Attempt at a Solution :
[/B]
If an electron and photon have the same energy, the electron will have a shorter wavelength, and a larger momentum. The shorter wavelength makes it useful for electron microscopes, outperforming optical microscopes because optical microscopes use light with wavelengths in the visible light range (cant see things as small with optical). My question is, what is the significance of the larger momentum of the electron for microscopes? And what is the significance of the larger momentum of the electron for other applications? I can't find this info anywhere. And one last question, why can't there be a microscope that uses wavelengths of light that are not in the visible light range? Like, if an electron microscope uses a plate to imprint the image, why can't a light microscope, then you will not need to view it with your eye.. Is this where the significance of electron momentum comes into play?? Thanks.

 

[Let'sthink]

Your assumption,"
If an electron and photon have the same energy, the electron will have a shorter wavelength, and a larger momentum. " is wrong I think. It turns out to be exactly opposite. electron wavelength comes out as (hc/E)*(c/v), where E is the energy and v is the velocity of electron. The wavelength of photon of energy E = [(hc)/E]!

 

[ehild]

Your assumption,"
If an electron and photon have the same energy, the electron will have a shorter wavelength, and a larger momentum. " is wrong I think. It turns out to be exactly opposite. electron wavelength comes out as (hc/E)*(c/v), where E is the energy and v is the velocity of electron.

It is not right.

 

[ehild]

Homework Statement

, 2. Homework Equations , 3. The Attempt at a Solution :
[/B]
If an electron and photon have the same energy, the electron will have a shorter wavelength, and a larger momentum. The shorter wavelength makes it useful for electron microscopes, outperforming optical microscopes because optical microscopes use light with wavelengths in the visible light range (cant see things as small with optical). My question is, what is the significance of the larger momentum of the electron for microscopes? And what is the significance of the larger momentum of the electron for other applications? I can't find this info anywhere. And one last question, why can't there be a microscope that uses wavelengths of light that are not in the visible light range? Like, if an electron microscope uses a plate to imprint the image, why can't a light microscope, then you will not need to view it with your eye.. Is this where the significance of electron momentum comes into play?? Thanks.

It is the wavelength that counts. Think of diffraction. You get clear image of an object if its size is much bigger than the wavelength. The distance between the atoms in a crystal is less than 1 nm. The wavelength of visible light is about 400-700 nm. That of the X-rays is longer than 0.1 nm. Atoms can not be resolved with optical frequencies, and you can get information of the lattice parameter from the diffraction of X-rays, but can not see atoms. With high-resolution transmission electron microscopy it is possible to see the position of atoms or molecules in a crystal. http://motherboard.vice.com/read/this-microscope-can-see-down-to-individual-atoms

 

[curiousmind04]

It is the wavelength that counts. Think of diffraction. You get clear image of an object if its size is much bigger than the wavelength. The distance between the atoms in a crystal is less than 1 nm. The wavelength of visible light is about 400-700 nm. That of the X-rays is longer than 0.1 nm. Atoms can not be resolved with optical frequencies, and you can get information of the lattice parameter from the diffraction of X-rays, but can not see atoms. With high-resolution transmission electron microscopy it is possible to see the position of atoms or molecules in a crystal. http://motherboard.vice.com/read/this-microscope-can-see-down-to-individual-atoms

Awesome. So are you saying that the lowest wavelength of light is not short enough to compete with the resolution of an electron microscope? Also, When you said "it is not right" to the guy that replied first, did you mean that when I said, "If an electron and photon have the same energy, the electron will have a shorter wavelength, and a larger momentum," that i was incorrect?? And finally, you didnt mention the significance of the larger momentum for the electron, is there anything significant about that??

 

[ehild]

Awesome. So are you saying that the lowest wavelength of light is not short enough to compete with the resolution of an electron microscope? Also, When you said "it is not right" to the guy that replied first, did you mean that when I said, "If an electron and photon have the same energy, the electron will have a shorter wavelength, and a larger momentum," that i was incorrect??

You were correct, and the guy who said that you were not correct was not correct.

And finally, you didnt mention the significance of the larger momentum for the electron, is there anything significant about that??

The momentum of a particle and its de Broglie wavelength are related by p=h/λ. Larger momentum means shorter wavelength.
https://en.wikipedia.org/wiki/Matter_wave

 

[curiousmind04]

You were correct, and the guy who said that you were not correct was not correct.

The momentum of a particle and its de Broglie wavelength are related by p=h/λ. Larger momentum means shorter wavelength.
https://en.wikipedia.org/wiki/Matter_wave

lol and I know it is inversely proportional, but, is there a benefit to having a larger momentum than the photon?

 

[curiousmind04]

You were correct, and the guy who said that you were not correct was not correct.

The momentum of a particle and its de Broglie wavelength are related by p=h/λ. Larger momentum means shorter wavelength.
https://en.wikipedia.org/wiki/Matter_wave

and also, this says:

5.5 trillionths of an inch! It sounds very infinitesimal, but gamma rays of the electromagnetic spectrum have wavelengths of that size and shorter. The lengths range from 10-10 meters to 10-15 meters or shorter. There is no absolute lower limit to the extent of the shortest wavelength because it has not yet been reached. These waves are generated by radioactive atoms and in nuclear explosions, such as supernova explosions or the destruction of atoms. Things like neutron stars and pulsars, and black holes are all sources of gamma rays in space. These rays have the most electromagnetic energy of any other rays in the spectrum. They have tremendous penetrating ability and have been reported to be able to pass through 3 meters of concrete. Also, as a medicinal advantage, gamma rays can be used to kill cancerous cells.

Unlike visible light and X-rays, gamma rays cannot be captured and reflected in mirrors. The high-energy photons would pass right through. Gamma-ray telescopes use a process called Compton scattering, where a gamma-ray strikes an electron and loses energy.

Today, there are bursts of gamma rays in deep space, which happen at least once a day. They last for fractions of a second to a minute. Gamma-ray bursts can release more energy in 10 seconds than the Sun will emit in its entire 10 billion-year lifetime!

If we had gamma-ray vision, we would be able to peer into the hearts of solar flares, supernovae, neutron stars, black holes, and galaxies. It is a wonder that such powerful energies are generated from such a tiny wavelength.

Elena Won -- 2001...::::::: so if light can have smaller wavelength than electron's used in electron microscope according to that, then how is electron better?

 

[Let'sthink]

I think I am right if E stands for total energy of electrons including its rest energy!

 

[Let'sthink]

Electron's momentum is decided by its velocity but that of photon by its frequency or energy as all photons have same velocity. So if at all you wish to compare their energy and momenta compare them on the same footing. Total energy and total momentum.

 

[Let'sthink]

While using the formula, λ = h/p for electron one has to use relativistic momentum and not not non-relativistic momentum. I had tried to relate this with total relativistic energy of electron. For photons there is not anything non-relativistic.

 

[ehild]

I think I am right if E stands for total energy of electrons including its rest energy!

Electron Microscopy uses the concept "energy of the electron" in the meaning "kinetic energy".

 

[ehild]

lol and I know it is inversely proportional, but, is there a benefit to having a larger momentum than the photon?

The benefit is that the electron has shorter wavelength than the photon.
Calculate what is the momentum and wavelength of a photon having 2 eV energy, and the same for an electron, having 2eV kinetic energy.

 

[Let'sthink]

If that is so then the ratio of photon momentum to electron momentum for the non-relativistic case comes out to be √[E/(2mc^2)] < 1 when E < 1 MeV, double the rest energy of electron. Obviously it is true for optical photon. But for photons of energy above 1 MeV this formula also shows that phton momentum will be larger than electron momentum but for that case this formula would be inaccurate and you will have to fall back on what I described earlier.

 

[ehild]

If that is so then the ratio of photon momentum to electron momentum for the non-relativistic case comes out to be √[E/(2mc^2)] < 1 when E < 1 MeV, double the rest energy of electron. Obviously it is true for optical photon. But for photons of energy above 1 MeV this formula also shows that phton momentum will be larger than electron momentum but for that case this formula would be inaccurate and you will have to fall back on what I described earlier.

You can not produce electron having equal total energy to that of an optical photon.
Using the relation between momentum p and total energy E of the electron, the wavelength of the electron is $$\lambda=\frac{hc}{E}\frac{1}{\sqrt{1-\frac{m_0^2c^4}{E^2}}}$$. The formula has sense only for energies above m₀c². The wavelength of the photon with that energy is about 0.02 nm, kind of X ray.
We can compare the wavelength of an electron having kinetic energy KE with the wavelength of photon with energy E=KE.
Than the wavelength of the electron is less than that of the photon.

 

[curiousmind04]

The benefit is that the electron has shorter wavelength than the photon.
Calculate what is the momentum and wavelength of a photon having 2 eV energy, and the same for an electron, having 2eV kinetic energy.

I have already done that for a 2.2eV electron and photon. I think i have found the answer though can you confirm please?

I said this to someone after asking them questions: "Are you telling me that electron microscopes are preferred because if they both were using the same wavelength (electromagnetic radiation microscope(photons) vs electron microscope(electrons)):

1) electrons will have same wavelength but less energy 2) electrons will have less energy but same momentum 3)combination of less energy, but same momentum, at this small wavelength produces better microscope because the energy of the photon would be too great and blast away the image or pass right through."

So i think it is a combination of less energy, but same momentum, for the same wavelength. (a photon of the same wavelength would have too much energy)

 

[ehild]

I said this to someone after asking them questions: "Are you telling me that electron microscopes are preferred because if they both were using the same wavelength (electromagnetic radiation microscope(photons) vs electron microscope(electrons)):So i think it is a combination of less energy, but same momentum, for the same wavelength. (a photon of the same wavelength would have too much energy)

If the resolution of an optical microscope is enough, we would not use electron microscope. The electron microscopes provide higher resolution because of the smaller wavelengths they use. And the electron is easy to accelerate to that speed and momentum, that corresponds to the short wavelength. And the electron beam can be focused and image can be formed. For the resolution of an electron microscope, too high energy of the photon would be necessary.

 

[curiousmind04]

If the resolution of an optical microscope is enough, we would not use electron microscope. The electron microscopes provide higher resolution because of the smaller wavelengths they use. And the electron is easy to accelerate to that speed and momentum, that corresponds to the short wavelength. And the electron beam can be focused and image can be formed. For the resolution of an electron microscope, too high energy of the photon would be necessary.

yes but optical telescopes aside, a photon can have the same wavelength as the electrons, from your answer you are implying that electrons have shorter wavelengths so they are better but i am saying that light can have that small of a wavelength too. So what makes the electron better?

 

[ehild]

yes but optical telescopes aside, a photon can have the same wavelength as the electrons, from your answer you are implying that electrons have shorter wavelengths so they are better but i am saying that light can have that small of a wavelength too. So what makes the electron better?

Electromagnetic waves of very short wavelength can not be handled by optical instruments. You can not make a microscope for gamma rays...

 

[curiousmind04]

Electromagnetic waves of very short wavelength can not be handled by optical instruments. You can not make a microscope for gamma rays...

ok, but an electron microscope isn't optical. So, what if the light microscope wasn't optical as well, would it work then? And i think the wavelength of an electron in an electron microscope is comparable to mostly xray photons not gamma rays, i think?

 

[ehild]

ok, but an electron microscope isn't optical. So, what if the light microscope wasn't optical as well, would it work then? And i think the wavelength of an electron in an electron microscope is comparable to mostly xray photons not gamma rays, i think?

Yes, they belong mostly to hard X rays.
How would you make a light microscope that it is not optical?
You need focusing elements. If you have hard x-ray photons, with wavelength about 10 pm, what principle and what materials would you use to focus radiation?

 

[curiousmind04]

Yes, they belong mostly to hard X rays.
How would you make a light microscope that it is not optical?
You need focusing elements. If you have hard x-ray photons, with wavelength about 10 pm, what principle and what materials would you use to focus radiation?

That is what I don't know, I figured if you could imprint an image on a plate of some sort with an electron microscope, you could do the same with a light microscope, without viewing it with the eye directly, but instead on a plate of some sort like an electron microscope.

 

[curiousmind04]

Yes, they belong mostly to hard X rays.
How would you make a light microscope that it is not optical?
You need focusing elements. If you have hard x-ray photons, with wavelength about 10 pm, what principle and what materials would you use to focus radiation?

If you can imprint photons on a plate in the double slit experiment, why can't you do it in a microscope? Isn't it the same concept as an electron microscope? (to imprint an image on a plate?)

 

[curiousmind04]

Yes, they belong mostly to hard X rays.
How would you make a light microscope that it is not optical?
You need focusing elements. If you have hard x-ray photons, with wavelength about 10 pm, what principle and what materials would you use to focus radiation?

and lasers focus light??

 

[ehild]

The problem is the formation of image of an object. When the image is formed on a screen, it can be made visible.
Lasers emit a narrow beam, as the photons form by stimulated emission, and only those survive which propagate parallel to the axis.of the laser. The beam of visible light lasers can be focused by lenses and mirrors.
The phenomenon in the double-slit experiment is diffraction and interference. The interference pattern is not image of the double slit.
In an electron microscope, the electron beam can be manipulated by electric and magnetic fields. For electromagnetic waves, you need some material with optical properties markedly different from that of air, but not absorbing. The refractive index of materials tend to 1 with increasing frequency. Metals become less and less reflecting, and even transparent.

 

[curiousmind04]

The problem is the formation of image of an object. When the image is formed on a screen, it can be made visible.
Lasers emit a narrow beam, as the photons form by stimulated emission, and only those survive which propagate parallel to the axis.of the laser. The beam of visible light lasers can be focused by lenses and mirrors.
The phenomenon in the double-slit experiment is diffraction and interference. The interference pattern is not image of the double slit.
In an electron microscope, the electron beam can be manipulated by electric and magnetic fields. For electromagnetic waves, you need some material with optical properties markedly different from that of air, but not absorbing. The refractive index of materials tend to 1 with increasing frequency. Metals become less and less reflecting, and even transparent.

That is interesting, I never knew refractive index tends towards one with increasing frequency

 

[ehild]

That is interesting, I never knew refractive index tends towards one with increasing frequency

see https://www.wired.com/2012/05/gamma-ray-lens/. It is interesting.

 

[curiousmind04]

see https://www.wired.com/2012/05/gamma-ray-lens/. It is interesting.

I am a little confused about lenses and mirrors. From my knowledge, lenses refract the light and cause diffraction (how can this produce an image, and does it produce a better image than mirror reflection?), and mirrors cause the light to be reflected (how does this produce an image, is there diffraction here as well? and does this produce a better image than lense refraction?) And finally, how is it difficult to use lenses and mirrors for gamma ray focusing, is it the same problem for both (refractive index tends towards one) or different issues for each method? Thanks

 

[curiousmind04]

see https://www.wired.com/2012/05/gamma-ray-lens/. It is interesting.

Do the mirrors have a reflective index that tends towards one with increasing frequency?

 

[ehild]

Do the mirrors have a reflective index that tends towards one with increasing frequency?

I am a little confused about lenses and mirrors. From my knowledge, lenses refract the light and cause diffraction (how can this produce an image, and does it produce a better image than mirror reflection?), and mirrors cause the light to be reflected (how does this produce an image, is there diffraction here as well? and does this produce a better image than lense refraction?) And finally, how is it difficult to use lenses and mirrors for gamma ray focusing, is it the same problem for both (refractive index tends towards one) or different issues for each method? Thanks

Do not mix refraction and reflection with diffraction.
You can use geometric optics to describe refraction and reflection, working with rays of light , ignoring wave nature. You can form image with mirrors and lenses.
Image formation means that the light rays originating from one point of the object intersect again in the image of that point.
Diffraction comes from the wave nature of light.

Read a book about principles of Optics or the Optics chapters of a Physics textbook.

 

[ehild]

Do the mirrors have a reflective index that tends towards one with increasing frequency?

Mirrors are made with highly reflecting materials, usually from metals, like gold or aluminium. Metals have high refractive index and high absorption, both changing with frequency, and above some frequency, they do not behave like metals any more.

 

[Let'sthink]

comparing wavelengths is one issue and comparing energies and momenta is another. comparison works fine for altogether different systems such as optical and electron microscopy instruments because mathematics is simpler and equivalent. Photons will not work in electron microscopy and electrons will not work in optical microscopy instruments.

Coming to the second issue, momentum and energy of two particles in non relativistic case and for particles with non-zero rest mass is simply:
P = √2mE and [E = (p^2)/2m]. The first equation tells us that the momentum of the heavier of the two particles having equal energy will be larger. and second equation tells us that the the energy of the heavier particle of the particles with same momentum will be smaller. I think such a comparison should not be made between photon and an electron.