[hamdani yusuf (OP)]

https://en.m.wikipedia.org/wiki/Rydberg_formula
As stressed by Niels Bohr,[2] expressing results in terms of wavenumber, not wavelength, was the key to Rydberg's discovery. The fundamental role of wavenumbers was also emphasized by the Rydberg-Ritz combination principle of 1908. The fundamental reason for this lies in quantum mechanics. Light's wavenumber is proportional to frequency
1/L=f/c, and therefore also proportional to light's quantum energy E. Thus,
1/L=E/hc (in this formula the h represents Planck's constant).

It can be interpreted that the amount of radiation energy is proportional to the number of waves, regardless of how much time is elapsed to radiate it. In effect, given the same number of oscillators, low frequency radiation took longer to radiate a specified amount of energy, compared to higher frequency.

[alancalverd]

So there's no voltage where the light suddenly "turns on".

Oh yes there is!

The I/V curve isn't definitive - the transiting electron must have sufficient energy to generate a photon of the appropriate color, so the emitted spectrum is related to the critical forward voltage of the diode. V_f increases with increasing current because the semiconductor process has a resistive component, but any particular LED behaves as a "conventional" (non-light-emitting) diode below V_fcrit. Above that value the intensity of emission increases with current, usually limited by heating which reduces efficiency, but the spectrum is relatively fixed.

[Bored chemist]

Oh yes there is!

No, there's not.
Thermal energy can make a contribution to promoting an electron into an excited state.  (which is also why the V/I curve is temperature dependent.)

What voltage do you calculate that you need to get, for example, a green LED to light up?
Something like this...
https://uk.farnell.com/multicomp/mcl053gd/led-5mm-36-green/dp/1581138?

[alancalverd]

If you look at the pdf data sheet you will see that there is "leakage only" current below about 1.65 V, and (obviously) no light emission at zero junction current. Since the lowest visible energy is about 1.2 eV, conservation laws suggest that even if we add a bit of thermal energy, you need at least a volt from somewhere to get any visible light from an LED. UV LEDs typically run at 4 - 8 volt V_f.

[alancalverd]

Returning to the original question, EMR is not necessarily quantised. Maxwell's propagation laws apply at any and all frequencies, so you can in principle generate radiation at any photon energy you want.

What Planck said was IF you have an ideal particle rattling about in a perfectly elastic box, it can only have discrete energy levels, and you can use this model to predict the UV spectrum etc. If the box does not have defined dimensions then the number of permissible states tends to infinity, hence the black body continuum with a continuous distribution of energy versus wavelength as predicted by the rigid box model for any particular wavelength.

[hamdani yusuf (OP)]

Above that value the intensity of emission increases with current, usually limited by heating which reduces efficiency, but the spectrum is relatively fixed.

The video shows that the spectrum is temperature dependent.

[hamdani yusuf (OP)]

Returning to the original question, EMR is not necessarily quantised. Maxwell's propagation laws apply at any and all frequencies, so you can in principle generate radiation at any photon energy you want.

Afaik, Maxwell's model for electromagnetic radiation has no concept of photon.

[Bored chemist]

Since the lowest visible energy is about 1.2 eV...

If you can see 1330nm.
For human, a better estimate is about 1.75eV  Or 708 nm.
So, no LED should produce visible light if driven with less than 1.75V; is that right?

And, if you take the "limit" down to 1.5V you get a cut-off wavelength of 826 nm- which is invisible.
If you are right, a single "1.5 v" dry cell couldn't produce visible light from an LED even if you allow that a new one might produce about 1.6V...

Regular viewers may be able to work out what happens next.
:-)

[alancalverd]

Afaik, Maxwell's model for electromagnetic radiation has no concept of photon.

But ours does. And Maxwell doesn't have a model - he derived a selfpropagating wave from the mathematics of known experimental electromagnetic phenomena.

[alancalverd]

OK, BC, I'm intrigued. Where does the photon energy come from if the device has no internal potential differences exceeding 1.5V?

[Bored chemist]

Where does the photon energy come from

It's still  because of this.

Thermal energy can make a contribution to promoting an electron into an excited state.  (which is also why the V/I curve is temperature dependent.)

This is sort-of related.
https://www.esa.int/gsp/ACT/projects/electroluminescent_cooling_using_LEDs/

[alancalverd]

I haven't found a credible estimate of the thermal energy of a semiconductor electron at room temperature. Classically it would be around 0.03 eV, scarcely significant, but one authoritative source calculates 5 eV, so the LED would be generating ultraviolet radiation spontaneously,which seems a bit unlikely too.

[hamdani yusuf (OP)]

Afaik, Maxwell's model for electromagnetic radiation has no concept of photon.

But ours does. And Maxwell doesn't have a model - he derived a selfpropagating wave from the mathematics of known experimental electromagnetic phenomena.

He built a mathematical model based on wave mechanics. In his model, light is propagating electromagnetic wave in a medium.

[Bored chemist]

one authoritative source calculates 5 eV

Define "authoritative"...

[alancalverd]

University of Michigan physics department lecture notes.

[alancalverd]

In his model, light is propagating electromagnetic wave in a medium.

No medium was required or specified. μ₀ and ε₀ are arbitrary constants that relate observation to common units of measurement.

[Bored chemist]

Not very plausible because 5eV is enough to tear apart most molecules.
https://en.wikipedia.org/wiki/Bond-dissociation_energy#Representative_bond_enthalpies

conservation laws suggest

Your appeal to the conservation laws is good, but you are applying them the wrong way round.

Because the band gap corresponds to enough energy to produce a visible photon, it figures that ant electron crossing that gap causes the emission of one.
OK, in reality, the efficiency isn't 100% but the electrons falling down don't have much idea what other electrons are doing, so the yield is pretty nearly independent of current.
The light output is pretty much proportional to current.
So you need to look at the variation of current with voltage.
That's temperature dependent because an electron that has nearly enough energy to get over the barrier can be promoted thermally over it.
https://en.wikipedia.org/wiki/Shockley_diode_equation

[Eternal Student]

Hi.

    I've always thought that Quantisation is fairly odd and can only be used with caution.  Although we can use Quantum mechanics to establish that quantisation should be there,  we then quickly establish that we cannot observe a perfect example of it.   Instead what we will typically observe is a frequency that could fall anywhere within some continuous range, with just some statements we can make about the probability distribution or spread of what is typically a continuous random variable.

     An atom with an electron in an excited state, should eventually have that electron fall back to a lower energy orbit but we don't really know exactly when that will happen.  Although the transition from one orbit to another should be quantised, there is an uncertainty relation between the time the atom takes to transition (remains in the excited state before falling back to the lower energy state) and the energy of the photon released.
    See  https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle
   for some discussion  (especially the section around equation 7.3.2 and example 7.3.3).

   As a consequence, all atomic spectral emission / absorption lines have some non-zero width rather than being perfect spikes at precisely one frequency.   There is another theoretical limitation that can be considered:  We also have a position - momentum uncertainty relation.   The atom which emitted the photon along with the detector that captured and identified it can be moving relative to the lab frame and a Doppler-shift in frequency is inevitable.   
    In practice there are also limitations on the accuracy of the equipment and random experimental errors that appear.   Even if you overlook those experimental limitations, the theoretical limitations from uncertainty relations cannot be avoided.   Overall, there should be some precise quantisation BUT you can't observe it in any single measurement.   Theoretically, we can only assert that the expected frequency of a photon emitted by an excited atom should correspond to the difference in the energy between the two states of the atom.   There is nothing we can do to remove all of the randomness and spread of the actual frequency that is really detected from any one atom and one emission.

Best Wishes.

[paul cotter]

Hi, ES. This is not my area but i'll hazard a guess with respect to the width of emission spectra. There must be effects from adjacent atomic fields( electrons and nuclei ) similar to the subtle shifts that enable nmr to be used to determine part or all of a molecular structure. I am guessing( again! ) that if a single hydrogen atom in isolation could be cycled through an energy transition the emission spectrum would be singular. Take all above with a pinch of salt.

[hamdani yusuf (OP)]

Returning to the original question, EMR is not necessarily quantised. Maxwell's propagation laws apply at any and all frequencies, so you can in principle generate radiation at any photon energy you want.

What Planck said was IF you have an ideal particle rattling about in a perfectly elastic box, it can only have discrete energy levels, and you can use this model to predict the UV spectrum etc. If the box does not have defined dimensions then the number of permissible states tends to infinity, hence the black body continuum with a continuous distribution of energy versus wavelength as predicted by the rigid box model for any particular wavelength.

The reason why we ended up with quantum mechanics was because Maxwell's electromagnetic theory doesn't give accurate predictions against experimental results.

https://en.wikipedia.org/wiki/History_of_quantum_mechanics#Founding_experiments
Founding experiments

Thomas Young's double-slit experiment demonstrating the wave nature of light. (c. 1801)
Henri Becquerel discovers radioactivity. (1896)
J. J. Thomson's cathode ray tube experiments (discovers the electron and its negative charge). (1897)
The study of black-body radiation between 1850 and 1900, which could not be explained without quantum concepts.
The photoelectric effect: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy.
Robert Millikan's oil-drop experiment, which showed that electric charge occurs as quanta (whole units). (1909)
Ernest Rutherford's gold foil experiment disproved the plum pudding model of the atom which suggested that the mass and positive charge of the atom are almost uniformly distributed. This led to the planetary model of the atom (1911).
James Franck and Gustav Hertz's electron collision experiment shows that energy absorption by mercury atoms is quantized. (1914)
Otto Stern and Walther Gerlach conduct the Stern?Gerlach experiment, which demonstrates the quantized nature of particle spin. (1920)
Arthur Compton with Compton scattering experiment (1923)
Clinton Davisson and Lester Germer demonstrate the wave nature of the electron[27] in the electron diffraction experiment. (1927)
Carl David Anderson with the discovery positron (1932), validated Paul Dirac's theoretical prediction of this particle (1928)
Lamb?Retherford experiment discovered Lamb shift (1947), which led to the development of quantum electrodynamics.
Clyde L. Cowan and Frederick Reines confirm the existence of the neutrino in the neutrino experiment. (1955)
Clauss J?nsson's double-slit experiment with electrons. (1961)
The quantum Hall effect, discovered in 1980 by Klaus von Klitzing. The quantized version of the Hall effect has allowed for the definition of a new practical standard for electrical resistance and for an extremely precise independent determination of the fine-structure constant.
The experimental verification of quantum entanglement by John Clauser and Stuart Freedman. (1972)
The Mach?Zehnder interferometer experiment conducted by Paul Kwiat, Harold Wienfurter, Thomas Herzog, Anton Zeilinger, and Mark Kasevich, providing experimental verification of the Elitzur?Vaidman bomb tester, proving interaction-free measurement is possible. (1994)

What does Maxwellian electromagnetism actually predict in each of those experiments? What were the assumptions made in making those predictions? Is it possible to change some of those assumptions which would change the predictions and reconcile with the experiments?