JR0011 : Wave-Particle Duality

Guru Vishnu

Mar 12, 2020 07:07

@JohnRennie: Hi sir. Good morning :-)

John Rennie

@GuruVishnu hi :-)

Guru Vishnu

I've seen that photon is said to have zero mass. But if we use $p=mv$ and $p=h/\lambda$, I get an expression for $m=h/c\lambda$. So is it wrong to the equation $p=mv$ in this way? If yes, is that because it's an equation of classical mechanics which can't hold true for tiny particles?

John Rennie

Yes, you can't use $p=mv$ for massless partices.

However the expression $p = h/\lambda$ always works for both massless and massive particles. For massive particles $\lambda$ is the de Broglie wavelength.

Guru Vishnu

Ok sir. For massless particles, is $\lambda$ not the de Broglie wavelength?

Or in other words, is it not right to say de Broglie wavelength of a photon?

John Rennie

For massless particles like photons the de Broglie wavelength is equal to the classical wavelength.

So for light the de Broglie wavelength of the photon is the same as the wavelength of the light wave.

Guru Vishnu

Mar 12, 2020 07:18

Ok sir. Thank you.

If find the following question to be confusing. If possible could you give some hints? :
A hot body is placed in a closed room maintained at a lower temperature. Is the number of photons in the room increasing?

John Rennie

It's a rather vague question.

I assume the question refers to the black body radiation emitted by the hot body.

Guru Vishnu

My guess is: The photon count initially increases and then attains a constant value when the object attains thermal equilibrium with the surroundings. Thermal energy is electro magnetic in nature and I think it has something to do with the electro magnetic nature of light or photons.

@JohnRennie Ok sir. Then shall we treat the question as per my guess?

John Rennie

The intensity of the radiation is given by Stefan-Boltzmann law, and to find the number of photons per second you need to divide the intensity by the energy per photon $hf$.

Guru Vishnu

Ok sir.

John Rennie

Where the peak wavelength will be given by Wien's law.

Guru Vishnu

Mar 12, 2020 07:25

Ok sir. I understand your method. I think here it's more than enough to treat the question qualitatively. We have no values for the absolute temperature.

For both the object and the surroundings.

John Rennie

Well the intensity is proportional to $T^4$ and the peak frequency, and therefore the energy per photon, is proportional to $T$.

So the number of photons emitted per second is going to be proportional to $T^3$

Guru Vishnu

Ok sir. Shall we move to a different question? I think it would take some more time for me to understand this one completely.

John Rennie

OK

Guru Vishnu

Should the energy of a photon be called its kinetic energy or its internal energy?
(not my question. It's from my book and I'm puzzled why he is asking so)

John Rennie

For relativistic particles, and photons are relativistic because they move at the speed of light, we normally only ever talk about the total energy given by:

$$ E^2 = p^2c^2 + m^2c^4 $$

For a photon $m=0$ so this simplifies to:

$$ E = pc $$

Asking whether this is kinetic energy or internal energy is not meaningful.

Guru Vishnu

Mar 12, 2020 07:32

I think you added the square of $E=mc^2$ and $E=pc$. First one is a familiar formula. What does the second one mean - Momentum X Speed?

John Rennie

$p$ is the relativistic momentum $p = \gamma m v$

Where $\gamma = 1/\sqrt{1-v^2/c^2}$

Guru Vishnu

Ok sir. I haven't learnt about that yet. I'll cover it and its derivation after my exams.

John Rennie

Or for photons $p = h/\lambda$

Guru Vishnu

@JohnRennie Yes. I have seen this equation :)

@JohnRennie Ok sir. Thank you.

John Rennie

@GuruVishnu the equation comes from special relativity and it isn't easy to explain with getting deeper into SR than is probably appropriate. It comes from the magnitude of the energy-momentum four vector.

Guru Vishnu

Mar 12, 2020 07:37

@JohnRennie Ok sir. I didn't understand this message completely (particularly "magnitude of the energy-momentum four vector"). However, I've realised that this is something I must learn after my exams.

John Rennie

@GuruVishnu you won't need to learn this unless you do a physics degree.

It's quite advanced stuff.

Guru Vishnu

Ok sir :-)

John Rennie

Four-momentum

In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with relativistic energy E and three-momentum p = (px, py, pz) = γmv, where v is the particle's three-velocity and γ the Lorentz factor, is p = ( p 0 , p 1...

That's the energy-momentum four vector. Also known as the four-momentum.

Guru Vishnu

@JohnRennie The diagram is at least familiar to me :-) I've seen that in mathematics > Conic sections.

John Rennie

The diagram shows a light cone.

Guru Vishnu

Mar 12, 2020 07:41

Ok sir. It looks interesting - past, future cones and I guess the present is the plane cutting it at the vertex. I guess we're all on the plane. And only time travellers could use the top and bottom cones.

Light is related to time? Cool.

@John Sir, is the law of conservation of momentum valid for photon-electron collision in a photo electric experiment?

I understand law of conservation of number of photons is not valid as a photon might get absorbed or released. What about this basic law of classical mechanics?

I also understand law of conservation of energy must hold true as it's an universal law.

John Rennie

@GuruVishnu Momentum is always conserved, including for photons.

Guru Vishnu

Ok sir. Thank you.

John Rennie

That's why light exerts a force. When a photon hit an object and is absorbed its momentum is passed on to the object.

Guru Vishnu

@JohnRennie Do you mean propulsion using solar sails?

John Rennie

Yes, that is an example of light exerting a force.

Guru Vishnu

Mar 12, 2020 07:53

Aha! Great. Another big example of particle nature of light.

.
It seems the de Broglie wavelength of electrons is roughly in the X-Ray region. Is this some kind of coincidence? If so do all materials around us emit X-Rays? I don't think so.

John Rennie

The wavelength of electrons depends on their momentum. For the electrons in atoms the wavelength is around the ultraviolet rather than x-ray.

But the de Broglie wavelength of an electron doesn't mean the electron emits light of that wavelength so the electrons in matter around us aren't continually emitting photons.

Electron microscopes use electrons with a wavelength comparable to X-rays, but they accelerate the electrons to energies of tens of keV to decrease their wavelength.

Guru Vishnu

Ok sir. So the human eye cannot distinguish whether an UV light is made of photons or electrons? Or does the electron light cause any increase in mass inside our eyes with considerable usage? Photons don't have mass so no need to worry about mass build-up.

John Rennie

Electrons and photons aren't the same even if they have the same wavelength. Electrons with the same wavelength of light couldn't get into your eye because they'd be blocked by the cornea so you can't see them.

Guru Vishnu

Ok. Then how could we see the specimen in the electron microscope sir? Does the machine convert electrons to photons for us to see?

John Rennie

If you raised the energy to hundreds of keV then the electrons could get into your eye, but unfortunately such high energy ejectrons would vaporise it so I don't recommend trying the experiment.

Guru Vishnu

Mar 12, 2020 08:08

@JohnRennie "vaporise it" - does "it" refer to "eye"?

John Rennie

@GuruVishnu electron microscopes fire the electrons through an extremely thin sample and the electrons are detected by an electron detector. Your eye isn't involved anywhere in the process. It's not like a light microscope where your eye is the detector.

It's more like a light microscope using a camera to record the image except that the camera is specially designed to be sensitive to electrons.

And you have to operate the whole thing in ultrahigh vacuum.

@GuruVishnu yes

Guru Vishnu

Oh. Ok sir. Thank you for all the details. It's very interesting to learn about such applications.

I realise how different it's from classic compound microscope.

However it does have lenses.

John Rennie

The lenses are magnetic fields. They focus the electrons using the Lorentz force.

Guru Vishnu

Ok sir. At first I thought they were made of regular glass, but now it's totally different. I now see there's a completely different branch called "Electron optics". Sounds great and interesting to me.

It seems "Electron optics" is also used in particle accelerators.

John Rennie

I think it just means controlling the direction of electrons using electromagnetic fields.

So it would be used in accelerators to form the electron beam and guide it round the circle.

Guru Vishnu

Mar 12, 2020 08:21

Yes sir. I don't think any material medium is involved where it would have a different path length or so.

John Rennie

Electrons interact very strongly with matter so you cannot use any form of lens made from matter. The electrons would just be absorbed in the matter.

That's why only EM fields in a vacuum are used.

Guru Vishnu

@JohnRennie Yes. And I also think, they would use the fields in a proper way to make the two oppositely facing beams to collide at the exact location at the exact time. That's really great when handling such small particles travelling at very high speeds.

@JohnRennie Ok sir. Now understood it :-)

Sir, do you believe photosynthesis in plants is somehow related to photo-electric effect?

John Rennie

No.

Guru Vishnu

Ok sir.

John Rennie

In photosynthesis the light causes an electronic transition in the chlorophyll molecule and the higher energy form of the molecule then undergoes a redox reaction.

I don't know the details though I believe they are well understood.

Guru Vishnu

Mar 12, 2020 08:26

@JohnRennie Ok sir. Even I don't know that in detail. I think I studied it when I was it 9th or 10th grade. After that I haven't studied biology.

Just tried to relate physical phenomenon to something which happens everyday around us.

Compact Muon Solenoid

The Compact Muon Solenoid (CMS) experiment is one of two large general-purpose particle physics detectors built on the Large Hadron Collider (LHC) at CERN in Switzerland and France. The goal of CMS experiment is to investigate a wide range of physics, including the search for the Higgs boson, extra dimensions, and particles that could make up dark matter. CMS is 21 metres long, 15 m in diameter, and weighs about 14,000 tonnes. Over 4,000 people, representing 206 scientific institutes and 47 countries, form the CMS collaboration who built and now operate the detector. It is located in a cavern...

> CMS is 21 metres long, 15 m in diameter, and weighs about 14,000 tonnes.

Do you still believe it's still "Compact"?

:-)

John Rennie

:-)

Guru Vishnu

I know $p=E/c$ is valid for photons. Is it valid for electrons too?

where $E$ is the energy and $c$ is the speed of light.

John Rennie

No. The reason $E=pc$ is valid for photons is that their mass is zero so the equation:

$$ E^2 = p^2c^2 + m^2c^4 $$

simplifies to $E = pc$.

For massive particles we get:

$$ p^2 = \frac{E^2}{c^2} - m^2 c^2 $$

Or alternatively:

$$ p = \frac{mv}{\sqrt{1 - v^2/c^2}} $$

Guru Vishnu

@JohnRennie I think this formula is similar to the equation of rest mass and mobile mass (?).

I know only that formula and not it's origin.

John Rennie

@GuruVishnu it's the equation I posted earlier when I was talking about the energy-momentum four vector.

Guru Vishnu

Mar 12, 2020 08:42

@JohnRennie Yes sir. I remember that. Could you tell whether the $m$ above is known as rest mass of an electron and the mass on the LHS the mass of electron when it's not at rest?

John Rennie

In relativity we only ever use the rest mass, so whenever you see $m$ in an equation that is the rest mass.

Guru Vishnu

Ok sir.

John Rennie

The rest mass is a class of special properties known as scalar invariants so it is important in SR.

Guru Vishnu

Ok sir.

Thank you very much for making me understand many new interesting stuff :-)

John Rennie

More interesting than JEE revision anyway :-)

♦ Particle Accelerator

Participants