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Author Topic: How much energy is in a photon?  (Read 14259 times)

Geezer

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How much energy is in a photon?
« on: 15/08/2011 08:07:45 »
We talk about photons a lot, and they seem to be able to convey energy from one place to another place, so how much energy does a photon contain?

Soul Surfer

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How much energy is in a photon?
« Reply #1 on: 15/08/2011 08:47:59 »
The energy in a photon is not a fixed value and depends on its frequency the higher the frequency is the more energy they contain.  The actual amount of energy has been measured and determines the famous Planck's constant h.

So E (nergy) = h (Planck's constant)  x  ν (pronounced nu the greek letter normally used to describe frequency)

It is vital to understand this relationship.  Low frequency photons like radio waves contain absolutely tiny amounts of energy and cannot be detected individually.  Medium frequency photons like light quanta contain moderate amounts of energy and can knock electrons out of atoms.  Very high frequency photons called gamma rays can smash up atomic nuclei and even individual subatomic particles.
« Last Edit: 15/08/2011 08:56:40 by Soul Surfer »

graham.d

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How much energy is in a photon?
« Reply #2 on: 15/08/2011 09:04:49 »
I am sure you knew this, Geezer (should I say "nu" this?). So I'm guessing there must be something else behind the question. Or are you being a sort of Agent Provocateur?

Geezer

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How much energy is in a photon?
« Reply #3 on: 15/08/2011 09:18:40 »
I am sure you knew this, Geezer (should I say "nu" this?). So I'm guessing there must be something else behind the question. Or are you being a sort of Agent Provocateur?

Rats! I am undone.

I was only trying to point out that there is no such thing as "a photon" per se.

graham.d

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How much energy is in a photon?
« Reply #4 on: 15/08/2011 09:51:48 »
Do you mean because it's energy is a variable that you can't call it by a single name??

Geezer

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How much energy is in a photon?
« Reply #5 on: 15/08/2011 10:03:47 »
Do you mean because it's energy is a variable that you can't call it by a single name??

Not my call.

Photons are quantized (I think). If they are quantized, how can they vary?

graham.d

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How much energy is in a photon?
« Reply #6 on: 15/08/2011 10:36:50 »
I guess calling a photon a particle (because it sometimes behaves like a particle) or a wave (because it sometimes behaves as a wave) is a matter of convention and it is now referred to as a wave-particle because we needed a new word to describe behaviour outside normal experience. I don't think it is known (proven) whether a photon's energy is quantised in the sense that all photons' energies must have a number of discrete values rather than being a continuous range. It seems likely but I have not heard of any proof of this. It would mean that there are discrete frequencies only allowed. I guess this may be related to the Planck length and te velocity of light.

In any case why do you think, whatever the scenario, that defining the energy is any different from E=hν?

BTW, are you up very early or up very late?!!

lightarrow

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How much energy is in a photon?
« Reply #7 on: 15/08/2011 13:44:47 »
I was only trying to point out that there is no such thing as "a photon" per se.
What do you mean?

simplified

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How much energy is in a photon?
« Reply #8 on: 15/08/2011 15:37:56 »
I am sure you knew this, Geezer (should I say "nu" this?). So I'm guessing there must be something else behind the question. Or are you being a sort of Agent Provocateur?

Rats! I am undone.

I was only trying to point out that there is no such thing as "a photon" per se.

Is photon just a traveling knot of some connection?

graham.d

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How much energy is in a photon?
« Reply #9 on: 15/08/2011 16:06:09 »
Are you thinking string theory here, simplified?

Anyway, whatever the underlying structure, it certainly exists and has specific properties. You see, Geezer poses these questions then goes to bed :-)

Soul Surfer

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How much energy is in a photon?
« Reply #10 on: 15/08/2011 17:03:15 »
The quantisation in photons comes in the process by which they are created or absorbed.  For example It requires a specific amount of energy to remove an electron from or change orbitals in an atom.  This may come from various sources for example collisions with higher energy atoms, electrons, subatomic particles and photons.  Conversely if an electron joins an atom it releases this energy as a photon (in this case this is the only sort of thing that can be released because of the low energy release).  The frequency of this photon is defined precisely by the energy released and the equation described above.

JP

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How much energy is in a photon?
« Reply #11 on: 15/08/2011 20:55:23 »
Photons are quantized (I think). If they are quantized, how can they vary?

There are many examples of things that are quantized, but can also vary.  Here's an advanced device producing sound waves of this type:

When the slide is in a fixed position, only a certain set of quantized modes of sound waves are allowed in the trombone because of the length of the tube.  But when you move the slide, you change to a new set of quantized modes.  At every slide position, you have a quantized set of sound waves, but you can continuously vary this set by moving the slide.

An easier to visualize example would be a string, fixed at both ends.  It's easy to calculate the modes of this string, because a half-integer number of waves have to fit on the string.  For a given length of string, you allow only a quantized set of modes, but if you change the length of the string, you can change the quantized set of modes to cover all possible frequencies.

Photons are a lot more complicated, but the same basic idea can apply.  The classical frequency of your light determines the quantization of the photons (as packets of h*nu energy). But just like the instruments above, you can vary the classical frequency of your light continuously, and for every value it takes, you get a different quantized energy for your photons.

Geezer

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How much energy is in a photon?
« Reply #12 on: 16/08/2011 08:33:21 »
Nice analogy JP. Of course, like all analogies, it's only valid in certain respects  As far as I know, the energy of any particular photon cannot vary, so its "slider" is fixed in a particular position.

When we talk of photons as particles, I think we should point out that photons come in a lot of different energy levels (is there a limit to the number?), so "a photon" is a rather incomplete description. That was the point of my sneaky question. It's more about helping people with less experience understand than anything.

graham.d

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How much energy is in a photon?
« Reply #13 on: 16/08/2011 09:20:49 »
Nice analogy JP. Of course, like all analogies, it's only valid in certain respects  As far as I know, the energy of any particular photon cannot vary, so its "slider" is fixed in a particular position.

When we talk of photons as particles, I think we should point out that photons come in a lot of different energy levels (is there a limit to the number?) [...]

It is certainly possible that photon energies only appear in distinct increments but I don't know if anyone has proposed a theory which would put any quantitative value on the size of such an increment. If space itself is quantised (as some recent theories propose) then it seems distictly possible that so are photon energies.

Anyway Geezer, at what time were you typing away the other night or are/were you on vacation in the UK?

imatfaal

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How much energy is in a photon?
« Reply #14 on: 16/08/2011 11:38:25 »
Nice analogy JP. Of course, like all analogies, it's only valid in certain respects  As far as I know, the energy of any particular photon cannot vary, so its "slider" is fixed in a particular position.

Not sure that photons can never vary in energy - as a well worn example; the photons that were emitted by hot hydrogen at around 380000 years after BB were ultra-violet - since then they have been travelling in an expanding universe for 13.6ish billion years and are now cold microwave.  All red shifting and blue shifting is a variation in energy within the frame of reference of measurement; to increase a photon's energy just run towards it.
« Last Edit: 16/08/2011 11:40:16 by imatfaal »

Soul Surfer

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How much energy is in a photon?
« Reply #15 on: 16/08/2011 13:00:05 »
In principle it is possible to predict the energy levels of electrons in atoms and therefore the photons that they emit when electrons change level but for complex atoms and compounds this can get very difficult.  For the hydrogen atom it is possible to do this classically.  However as you introduce more electrons they all affect each other's motions and adjusting for these effects is what makes it difficult.  Its a bit like predicting the path of one ball on a billiard table compared with doing it for one hundred on the same table all moving in different directions and colliding.

Energy levels inside nuclei are much more difficult because motions there are all relativistic and the constraints only poorly understood but approximate solutions exist

JP

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How much energy is in a photon?
« Reply #16 on: 16/08/2011 14:31:02 »
Nice analogy JP. Of course, like all analogies, it's only valid in certain respects  As far as I know, the energy of any particular photon cannot vary, so its "slider" is fixed in a particular position.

Not sure that photons can never vary in energy - as a well worn example; the photons that were emitted by hot hydrogen at around 380000 years after BB were ultra-violet - since then they have been travelling in an expanding universe for 13.6ish billion years and are now cold microwave.  All red shifting and blue shifting is a variation in energy within the frame of reference of measurement; to increase a photon's energy just run towards it.

You could also chop the trombone waveform up into small chunks.  Each chunk isn't changing as it propagates, but by moving the slider you can make consecutive chunks vary.  Similarly, if you have a tuneable laser, you can vary the frequency of emitted photons over time, even if each individual photon can't change as it propagates.

This analogy will break down if you push it much further, though, since the trombone sound wave is a classical wave form, much like the classical EM wave coming out of a laser.  Photons are obtained by quantizing this classical EM wave, which is considerably more complex than chopping it up into chunks over time.

Still, it gets at what I think is the main point here: that you can have a system that is quantized, i.e. it can only take on a certain discrete set of values, but it is possible for those values to change over time as you tweak some parameter of the system.  Quantization in this case just refers to the fact that at any instant in time, you have only a discrete set of values.  It doesn't really care if you can scan over other values given enough time.
« Last Edit: 16/08/2011 14:34:25 by JP »

Geezer

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How much energy is in a photon?
« Reply #17 on: 16/08/2011 18:42:02 »
Anyway Geezer, at what time were you typing away the other night or are/were you on vacation in the UK?

Yes - it was a bit late! I was unwinding after a Peter Frampton concert that was just down the road from here.

Geezer

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How much energy is in a photon?
« Reply #18 on: 16/08/2011 18:46:12 »
Nice analogy JP. Of course, like all analogies, it's only valid in certain respects  As far as I know, the energy of any particular photon cannot vary, so its "slider" is fixed in a particular position.

Not sure that photons can never vary in energy - as a well worn example; the photons that were emitted by hot hydrogen at around 380000 years after BB were ultra-violet - since then they have been travelling in an expanding universe for 13.6ish billion years and are now cold microwave.  All red shifting and blue shifting is a variation in energy within the frame of reference of measurement; to increase a photon's energy just run towards it.

You could also chop the trombone waveform up into small chunks.  Each chunk isn't changing as it propagates, but by moving the slider you can make consecutive chunks vary.  Similarly, if you have a tuneable laser, you can vary the frequency of emitted photons over time, even if each individual photon can't change as it propagates.

This analogy will break down if you push it much further, though, since the trombone sound wave is a classical wave form, much like the classical EM wave coming out of a laser.  Photons are obtained by quantizing this classical EM wave, which is considerably more complex than chopping it up into chunks over time.

Still, it gets at what I think is the main point here: that you can have a system that is quantized, i.e. it can only take on a certain discrete set of values, but it is possible for those values to change over time as you tweak some parameter of the system.  Quantization in this case just refers to the fact that at any instant in time, you have only a discrete set of values.  It doesn't really care if you can scan over other values given enough time.

I think I understand

Do two photons with the same frequency always have identical amounts of energy?

JP

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How much energy is in a photon?
« Reply #19 on: 16/08/2011 19:43:52 »
Yes, Geezer.  The simplest way to understand photons is to think of a single frequency plane wave.  If you ask how energy can be extracted from the wave by quantum interactions, you find that it has to be in multiples of h*nu, where nu is the frequency of the wave and h is a constant.  We can check this in a lab, since a well-conditioned laser can be a good approximation to a plane wave of this type.

A field that's more complicated than a single-frequency plane wave can be written as a bunch of single-frequency plane waves superimposed, and so the photons present are those from all these plane waves. However, you can only extract energy corresponding to the photons that are present.  If you have no "blue" photons present, you can't cause effects that rely on "blue" photons.

lightarrow

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How much energy is in a photon?
« Reply #20 on: 17/08/2011 15:29:09 »
It must be added that a photon has not an exactly defined frequency (and so energy): it would imply it was emitted in infinite time.
The half life of an atom's excited state is inversely proportional to the emitted photon's energy indeterminacy (Hesenberg principle).

JP

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How much energy is in a photon?
« Reply #21 on: 17/08/2011 20:22:11 »
It must be added that a photon has not an exactly defined frequency (and so energy): it would imply it was emitted in infinite time.
The half life of an atom's excited state is inversely proportional to the emitted photon's energy indeterminacy (Hesenberg principle).

Wait a minute, I'm not so sure that's true.  I thought photon was defined to be one specific frequency and that a finite duration light wave contains photons of many frequencies much in the same way a classical pulse contains plane waves of many frequencies.  I could be wrong, but that's how I've understood them...

lightarrow

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How much energy is in a photon?
« Reply #22 on: 18/08/2011 00:56:14 »
Wait a minute, I'm not so sure that's true.  I thought photon was defined to be one specific frequency and that a finite duration light wave contains photons of many frequencies much in the same way a classical pulse contains plane waves of many frequencies.  I could be wrong, but that's how I've understood them...
Ah, yes, it's because there are at least two different definitions of the word "photon": the one you are referring to comes from QED and it's essentially a mathematical concept; the other is more physical and is, e.g., the single electromagnetic pulse emitted by an atom's de-excitation. According to the first definition, the single em pulse emitted by an atom is an overlapping of an infinite number of photons of different energy. Physically this "sounds" bad. Anyway I intended the second kind.
Don't know which of the two is more preferred in the physics community.
« Last Edit: 18/08/2011 00:58:05 by lightarrow »

JP

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How much energy is in a photon?
« Reply #23 on: 18/08/2011 01:04:25 »
Wait a minute, I'm not so sure that's true.  I thought photon was defined to be one specific frequency and that a finite duration light wave contains photons of many frequencies much in the same way a classical pulse contains plane waves of many frequencies.  I could be wrong, but that's how I've understood them...
Ah, yes, it's because there are at least two different definitions of the word "photon": the one you are referring to comes from QED and it's essentially a mathematical concept; the other is more physical and is, e.g., the single electromagnetic pulse emitted by an atom's de-excitation. According to the first definition, the single em pulse emitted by an atom is an overlapping of an infinite number of photons of different energy. Physically this "sounds" bad. Anyway I intended the second kind.
Don't know which of the two is more preferred in the physics community.

Ah, got it.  I think both are used loosely in the broader physics community.  I've even heard of optical rays being described as photons, which seems to be pushing it a bit.  I think within quantum optics, they're very picky about what they call photons and stick to the QED definition.

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How much energy is in a photon?
« Reply #23 on: 18/08/2011 01:04:25 »