Is v discrete in E=hv equation?

[SamRoss]

h is a constant in Planck's equation but I have not seen anything written saying that the frequency cannot be arbitrarily small, thus making E arbitrarily small. Is it that v is only allowed to be integral (after all, when we're measuring a frequency we're essentially counting how many times something happens) and if it happens to be a fractional frequency we would just change the unit of time to make it integral again?

 

[Simon Bridge]

There is nothing intrinsic to $\nu$ to make it take specific values.

i.e. a harmonic oscilator will have discrete energy states, with a non-zero minimum energy - however, the frequency is a characteristic of the oscillator, so there is only one possible value for it. Even so, an oscillator can be built to any arbitrary value for frequency.

 

[SamRoss]

There is nothing intrinsic to $\nu$ to make it take specific values.

i.e. a harmonic oscilator will have discrete energy states, with a non-zero minimum energy - however, the frequency is a characteristic of the oscillator, so there is only one possible value for it. Even so, an oscillator can be built to any arbitrary value for frequency.

If v can have any arbitrary value then why do people say that the equation E=hv shows that E is discrete?

 

[Simon Bridge]

If v can have any arbitrary value then why do people say that the equation E=hv shows that E is discrete?

Who says that?
Can you provide a reference?

- in (Plank model) cavity radiation (i.e. a blackbody) the cavity walls are modeled as harmonic oscillators which can only absorb or release energy in lumps of $\small h\nu$ where $\small \nu$ is a characteristic of the oscillator. [edit] hmmm... this is a bit over simplistic, don't take that description too far.
- in (Einstein model) photoelectric effect, light can only deliver energy in lumps of $\small h\nu$ where $\nu$ is the characteristic frequency of the light, in the wave model.

There is nothing in $\small E=h\nu$, by itself, to indicate that energy is always discrete.

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Aside: frequency is given by the Greek letter nu ... written \nu between double-hash's or itex tags to give "$\nu$" or, smaller version, "$\small \nu$". It looks a lot like the Latin "v" which is why you start out by using "f" for frequency.

The tex tags are very useful for writing out equations like \omega=2\pi\nu.

 

[Nugatory]

If v can have any arbitrary value then why do people say that the equation E=hv shows that E is discrete?

They don't. There are physical systems in which E is constrained to be discrete, and if you plug those discrete values of E into the equation you'll get discrete values. Many of these systems are very important ones (electrons in atoms, harmonic oscillators) so they get a lot of press and we spend a lot of time studying and talking about them - so it's easy to get the impression that it's always that way.

 

[tom.stoer]

If v can have any arbitrary value then why do people say that the equation E=hv shows that E is discrete?

I think that's a misinterpretation.

The energy $E = nE_\nu,\;n=0,1,2,\ldots$ of an electromagnetic field is quantized in terms of individual photons each carrying a discrete amount of energy $E_\nu = h\nu$.

The frequency of the photon is quantized only in cases when the system emitting the photons has discrete energy levels $E_k$ such that $\Delta E_{kl} = E_k - E_l$ corresponds to the energy of a single photon, i.e. $E_\nu = \Delta E_{kl}$.

So energy of the el.-mag. field is intrinsically quantized in terms of individual photons, but the frequency of a single photon is not intrinsically quantized.

 

[San K]

They don't. There are physical systems in which E is constrained to be discrete, and if you plug those discrete values of E into the equation you'll get discrete values. Many of these systems are very important ones (electrons in atoms, harmonic oscillators) so they get a lot of press and we spend a lot of time studying and talking about them - so it's easy to get the impression that it's always that way.

I think that's a misinterpretation.

So energy of the el.-mag. field is intrinsically quantized in terms of individual photons, but the frequency of a single photon is not intrinsically quantized.

This clears the confusion among a lot of people. Good posts.

hope this is in the pf faq somewhere.

 

[tom.stoer]

This clears the confusion among a lot of people. Good posts./QUOTE]
thanks

hope this is in the pf faq somewhere.

don't know

 

[SamRoss]

- in (Einstein model) photoelectric effect, light can only deliver energy in lumps of $\small h\nu$ where $\nu$ is the characteristic frequency of the light, in the wave model.

Ok. This is starting to come together for me a bit more now. Is it correct to say that before E=h\nu , people thought that even when the frequency was specified the energy could take on any value because it also depended on the intensity of the light, but after E=h\nu , they knew that specifying the frequency determined the energy?

 

[Nugatory]

Ok. This is starting to come together for me a bit more now. Is it correct to say that before E=h\nu , people thought that even when the frequency was specified the energy could take on any value because it also depended on the intensity of the light, but after E=h\nu , they knew that specifying the frequency determined the energy?

The frequency gives you the energy content of a single photon; the intensity is the total amount of energy delivered by all the photons arriving per unit time.

 

[SamRoss]

The frequency gives you the energy content of a single photon; the intensity is the total amount of energy delivered by all the photons arriving per unit time.

And before the idea of the photon, the intensity was thought to be continuous, i.e. it could take any arbitrarily small value, regardless of the frequency of the light?

 

[Avodyne]

Yes.