Energy Levels in Hydrogen: Calculating Photon Energy & Wavelength

[Ponderer]

This school page goes over the basic math of calculating the photon energy and wavelength emitted by an electron in a hydrogen atom. It comes to one photon near 490nm. Is one photon always emitted by atoms? Why can't it be two or more photons at lower energy? Has a fraction of photons ever been detected such as 1.2 photons? Thanks

http://www.schoolphysics.co.uk/age1...ons/text/Energy_levels_in_hydrogen/index.html

 

[BiGyElLoWhAt]

Google spontaneous parametric down conversion.

Just out of curiosity, how would you interpret 1.2 photons? What would .2 photons mean?

 

[Ponderer]

What would .2 photons mean?

It would mean h*f*0.2

 

[Ponderer]

Google spontaneous parametric down conversion.

SPDC is the only exception?

 

[Physicist97]

Well the point of the photon being quantized is that you can only have an integer number of photons (1, 2, 3... etc). You can't have 1.3 or 1.7 photons. The formula h*f tells you the energy of the photon, so h*f*0.2 could at best be interpreted as a photon with an energy that is 0.2 of some other measured photon, but it is still a whole photon.

 

[BiGyElLoWhAt]

I would interpret that as a photon with one fifth the frequency. h*(0.2*f)

We don't really have a good idea of what a photon is, so to actually give physical meaning to a fraction of a photon (outside of an average) would be really hard to do.

 

[BiGyElLoWhAt]

SPDC is the only exception?

Not the only, but it is one example, of which there are many reliable sources to read.

 

[Ponderer]

Not the only, but it is one example, of which there are many reliable sources to read.

What about thermal energy from say a hot glowing piece of iron? IOW, would an electron in the hot iron that emits two or more simultaneous photons be a rare event?

 

[BiGyElLoWhAt]

What about thermal energy from say a hot glowing piece of iron? IOW, would an electron in the hot iron that emits two or more simultaneous photons be a rare event?

I would venture to say so. What's different about this case, is that the energy is stored in kinetic energy of the atom, versus with SPDC, it's stored in potential energy of the electron jumping to an outer shell. When the electron jumps out a layer (from say s to d [I think that's the right order, my chem sucks]) it isn't stable, so it collapses back to the previous layer, emitting energy. If the crystal is oriented properly (i.e. non linear) it can emit 2 photons which are entangled. My college uses BBO for this.

As far as why kinetic energy doesn't seem to release 2 photons when it's emitted, I'm not sure, honestly.

 

[bhobba]

Just out of curiosity, how would you interpret 1.2 photons? What would .2 photons mean?

They never occur in our theories.

Thanks
Bill

 

[bhobba]

We don't really have a good idea of what a photon is,

And exactly in what way is QED lacking in giving us a 'good idea'?

QED is the most accurately verified physical theory of all time.

Thanks
Bill

 

[bhobba]

When the electron jumps out a layer (from say s to d [I think that's the right order, my chem sucks]) it isn't stable, so it collapses back to the previous layer, emitting energy.

I an not sure 'jump' is the best language to use here - transition is probably better. What's going on really requires QED:
https://en.wikipedia.org/wiki/Spontaneous_emission

Thanks
Bill

 

[Ponderer]

And exactly in what way is QED lacking in giving us a 'good idea'?

But if one formulates equations to predict how a ball bounces, does that explain what's inside the ball or what any possible fields around the ball are made of?

 

[Ponderer]

QED is the most accurately verified physical theory of all time.

What about the NIST experiment?

"The most energetic photons from electron transitions in helium have energies of around 39 electron volts.The photon energy scales as Z2, so analogous photons observed in the helium-like atoms witha nuclear charge of Z=22, should have energies that are (22/2)2=121 times higher.The most energetic photons from the helium-like atoms, studied with high precision bent-crystal spectroscopy, have energies around 4,750 electron volts, which is in the soft x-ray region.The energy vs. Z of the most energetic photons from these studies of helium-like atoms were compared with the predictions of quantum electrodynamics, a part of the Standard Model that, up to now, has had an essentially unblemished record in predicting the results of experimental measurements.It was found that the data are systematically larger in energy than the 3-body QED predictions by about 0.1 to 0.6 electron-volts, depending on the value of Z.Further, the deviations in the heavier high-Z helium-like atoms appear to grow as Z3.The reported discrepancy with QED has a statistical significance of about 5 standard deviations. Thus, QED, a central and highly trusted component of the Standard Model, seems to be failing in a very fundamental and consistent way."

http://www.npl.washington.edu/AV/altvw167.html

http://www.nist.gov/pml/div684/ebit-112712.cfm

 

[BiGyElLoWhAt]

@ bhobba how does QED define a photon? Just out of curiosity. Specificly, please.

 

[bhobba]

But if one formulates equations to predict how a ball bounces, does that explain what's inside the ball or what any possible fields around the ball are made of?

I think you need to cognate on what explain means.

Our theories depend on assumptions that explain the predictions of the theory.

In your example classical mechanics explains how the ball bounces and doesn't require the other stuff you mentioned.

QED explains the behaviour of photons.

Thanks
Bill

 

[bhobba]

@ bhobba how does QED define a photon? Just out of curiosity. Specificly, please.

The quantum of the quantised EM field.

Further detail requires studying the theory, but loosely its analogous to the creation and annihilation operators of the quantum harmonic oscillator:
https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

If you want to know more here is the book to get:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

What about the NIST experiment?

Don't know that one.

But if true it would be Earth shattering news comparable to the paradigm shift that occurred early last century. Since that hasn't happened its likely, at the most controversial, and probably wrong.

I suggest you do a separate post about it where people up on that sort of thing can comment.

Thanks
Bill

 

[Derek Potter]

They never occur in our theories.
Thanks
Bill

Ah yes, but "our" theories don't believe in virtual particles - do you? :)

 

[bhobba]

Ah yes, but "our" theories don't believe in virtual particles - do you? :)

And its relevance to actual photons or the question asked is?

Virtual particles are part of the theory. They are in the Dyson series and pictorially represented in Feynman diagrams:
http://bolvan.ph.utexas.edu/~vadim/classes/11f/dyson.pdf

Thanks
Bill

 

[BiGyElLoWhAt]

I already have that book, thanks.

In my (and many others') opinions, a quantum of the electric field, or a comparison to a mathematical construct isn't a good definition of a physical entity.

 

[bhobba]

In my (and many others') opinions, a quantum of the electric field, or a comparison to a mathematical construct isn't a good definition of a physical entity.

I think you will find most physicists accept the mathematics as the description of reality. But what else would you use? English - it can't be physical reality either.

Thanks
Bill

 

[newjerseyrunner]

If you are interested in why mathematical models and physical reality can sometimes be so far apart from each other, I recommend watching this:
About half way through, he starts talking about how the affects of gravity can be written in three very different ways and be completely equivalent.

Mathematical algorithms can be manipulated so far from their starting point that they don't even look anything like the original anymore, but because of certain mathematical laws, they're still completely equivalent. Someone who needs to use those laws will use the most mathematically simple way.

 

[bhobba]

If you are interested in why mathematical models and physical reality can sometimes be so far apart from each other,

I think you will find that Feynman is in the mathematics describing reality camp. It's been a while since I watched that clip, but if I recall correctly Feynman was making the point the laws are written in mathematical language - as all current physical theories are.

Thanks
Bill

 

[BiGyElLoWhAt]

I think you will find that Feynman is in the mathematics describing reality camp. It's been a while since I watched that clip, but if I recall correctly Feynman was making the point the laws are written in mathematical language - as all current physical theories are.

Of course they are. Physics is about making quantitative predictions, so you need a mathematical model to be able to get said quantitative predictions. This does not mean that the math is the same as the physical entities.

I think you will find most physicists accept the mathematics as the description of reality. But what else would you use? English - it can't be physical reality either.

That very well may be, but not in my personal experience. I am, however an undergrad, but even my professors would disagree, the chair in particular. I know these aren't really "credible sources" on this forum, but once again, in my personal experience.
English is not what the "stuff" that we're talking about is, whatever it may be (photons in this case). English is what we use to describe it. Math is the same way. It's not what the "stuff" is, it's what we use to describe it.

 

[bhobba]

Of course they are. Physics is about making quantitative predictions, so you need a mathematical model to be able to get said quantitative predictions. This does not mean that the math is the same as the physical entities.

The map is not the territory. So?

Thanks
Bill

 

[BiGyElLoWhAt]

That's the point. We have a good idea what the map looks like, but it looks a lot like the first maps of North America, you know:

 

[bhobba]

And that's my point.

Its a trivially obvious statement that applies to any description of anything. Its basically vacuous because it means you can never know anything - photons, fields, the big bang - anything.

Thanks
Bill

 

[BiGyElLoWhAt]

Perhaps we should just agree to disagree on this point.

 

[newjerseyrunner]

I'm curious, what's the difference both physically and mathematically of a photon and a virtual photon?

 

[bhobba]

I'm curious, what's the difference both physically and mathematically of a photon and a virtual photon?

A virtual photon is just a diagrammatic representation of something called a Dyson series - it doesn't exist - but because of an unfortunate name people who don't know the technicalities get confused. A real photon will register on things like a photomultiplier.

You will find many threads on this forum discussing it - so please don't pursue it here. It is unfortunately one of those things that leads to long threads that go nowhere.

Thanks
Bill

 

[newjerseyrunner]

A virtual photon is just a diagrammatic representation of something called a Dyson series - it doesn't exist - but because of an unfortunate name people who don't know the technicalities get confused. A real photon will register on things like a photomultiplier.

You will find many threads on this forum discussing it - so please don't pursue it here. It is unfortunately one of those things that leads to long threads that go nowhere.

Thanks
Bill

I'll look into that, but my mention of it here was simply to illustrate that mathematical entities may not always correspond to actual stuff. I asked it as a question because I wasn't totally sure I was correct. I should have phrased it to make that more obvious.

 

[Ponderer]

Let's not forget that math alone is incomplete without an interpretation. How are you going to use real life experiments without an interpretation? What interpretations are you most interested in? I find MWI to be particularly interesting.

 

[bhobba]

I'll look into that, but my mention of it here was simply to illustrate that mathematical entities may not always correspond to actual stuff.

That's true. Mathematical models can and often do contain things there are no correspondence rules for in the model. An obvious example is, say, minus numbers. You can't have a minus number of ducks for example. But you can owe someone some ducks so it can be given meaning.

The whole area of mathematical modelling in general, and physics is a mathematical model, is full of that. It's so basic its almost, but not quite because novices of a philosophical bent, in an understanding sense, can get confused by it, trivial.

Also, and this is another point those that don't have experience in mathematical modelling and applied math in general, is they read articles from pure mathematics where objects are abstract. The axioms of applied math are not like that - they can, and do, have explicit or implied correspondences with actual things. For example in QM axiomatically it mentions things like observations. Observations are a primitive and actually exist. One can develop QM in a pure math way but the resultant math is - HARD - and is not recommended for the beginner. But just for completeness here is a book that does it:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

Let's not forget that math alone is incomplete without an interpretation. How are you going to use real life experiments without an interpretation? What interpretations are you most interested in? I find MWI to be particularly interesting.

The axioms of applied math explicitly or implicitly contain that correspondence. See Euclids geometric axioms compared to Hilbert's as an example. You will find a good discussion on this in Fellers classic on probability:
https://www.amazon.com/dp/0471257087/?tag=pfamazon01-20

Thanks
Bill