I Why is the EM spectrum contiguous instead of gapped

[bluestar]

I understand the EM spectrum is made up of photons at different energy levels (wavelengths); where, the higher the energy level the shorter the wavelength. What I do not understand is how collectively photons are created at a range of energy levels that produce a contiguous EM spectrum. (When I use the word gapped I do not mean absorption gaps; I mean the lack of a photons at that wavelength).I understand when an electron drops to a lower orbital shell it releases a photon at a specific wavelength; likewise, I understand there are multiple orbital shells each producing photons at their respective energy levels. I even understand electrons can drop down more than one level thus producing a photon of a different wavelength. However, the EM spectrum appears to be continuous even at infinitely small increments. Thus, it would appear there are more EM spectrum increments than electron shell combinations.Hopefully, someone can shed some light J on this question.

 

[blue_leaf77]

It's true that the emission and absorption spectra of individual atoms or molecules are discrete, but it's of different story when these atoms or molecules form bonds with one another to form solid or liquids whose absorption and emission spectra are continuous. When atoms or molecules form bonding, the resulting material will have each of its energy levels consisting of the total number of levels of all the constituent atoms but they are modified such that each atomic level is infinitely adjacent to another atomic level, hence forming the so-called energy bands of the resulting material.

 

[bluestar]

when these atoms or molecules form bonds with one another to form solid or liquids whose absorption and emission spectra are continuous.

Great Info, I did not know this. Hummm, during the bonding process is that when the photon is released? This bonding is between two or more atoms and in some cases when an electron is shared, is that when the photon it released? If so, is the change in the electron energy what releases the photon?

 

[blue_leaf77]

When atoms form a molecule, usually the process is accompanied by photon emission process, this is a quantum mechanical process due to the change in electronic energy. But my point in my previous post to make you aware that the reason why light frequencies are continuous instead of "gapped" is that because we have got solid and liquid material aside from individual atoms and molecules.

 

[sophiecentaur]

This bonding is between two or more atoms and in some cases when an electron is shared,

All electrons in a solid or liquid are 'shared' to some extent. The idea of Covalent bonding is a simplification which applies to some molecules but still each valence electron is in a more complicated electric field than just the field due to the nuclear protons. Every extra nearby atom will split the possible levels that an electron can take and once you get to the vast numbers in even a tiny sample of a solid, the splitting fills in all the gaps. At that point we no longer talk about orbits or discrete energy levels and changes in energy can take a continuum of values and the theory changes to include Statistics.

 

[SlowThinker]

I believe that thermal spectrum is continuous, even if it comes from pure helium or whatever.

 

[bluestar]

Terrific answers! Now I understand how the EM spectrum is contiguous. Your comments are much appreciated.

 

[sophiecentaur]

contiguous

This word needs amending. Contiguous doesn't mean what you want to say. It means all in one line - as with a computer file that's not fragmented. In that context, the structure is segmented into individual bits / bytes / words. "Continuous" is preferable and implies an uninterrupted sequence or Continuum.

 

[bluestar]

Define: Contiguous
Source:
https://www.merriam-webster.com/dictionary/contiguous
touching or connected throughout in an unbroken sequence

Define: Continuous
https://www.merriam-webster.com/dictionary/continuous
having the property that the absolute value of the numerical difference between the value at a given point and the value at any point in a neighborhood of the given point can be made as close to zero as desired by choosing the neighborhood small enough

From Merriam-Webster's definition of both words it would appear both would be applicable; although, from a mathematical perspective I understand your preference. If the physics institution prefers the word continuous over contiguous I have no issue what that.

 

[sophiecentaur]

Define: Contiguous
Source:
https://www.merriam-webster.com/dictionary/contiguous
touching or connected throughout in an unbroken sequence

Define: Continuous
https://www.merriam-webster.com/dictionary/continuous
having the property that the absolute value of the numerical difference between the value at a given point and the value at any point in a neighborhood of the given point can be made as close to zero as desired by choosing the neighborhood small enough

From Merriam-Webster's definition of both words it would appear both would be applicable; although, from a mathematical perspective I understand your preference. If the physics institution prefers the word continuous over contiguous I have no issue what that.

Actually, from your two quotes, Webster makes it quite clear that the two words mean very different things. An 'unbroken sequence' doesn't imply 'as close to zero as required'. The difference between discrete and continuous variables is very significant. 1,2,3,4,5,6,7,8 is contiguous but 1,2,3,6,7,8 is not contiguous. One cannot write down a similar example of 'continuousness'.
I think that, as we're discussing Physics, it's the Physics rules that must apply.

 

[SlowThinker]

Actually, from your two quotes, Webster makes it quite clear that the two words mean very different things.

2 fun facts:
1. I am not sure whether you conclude that continuous or contiguous spectrum is the correct one.
2. It seems that rational numbers are continuous by that definition.

 

[sophiecentaur]

Basically, I have never come across the word "contiguous" used in the context of any continuous variable. That gives me more than a little confidence in bringing this up. Mr Webster has only managed to confirm my view.
The spectrum of black body radiation is continuous because the random nature of its generation means that any value is possible. The named notes on a piano, in my opinion, are contiguous because there are discrete keys that you can press. But, of course, one can bend or mis-tune notes over a continuous range around those defined frequencies.
Even a notionally single frequency from an oscillator (however much you pay for it) will vary in value over a continuous range of possibilities.
My Maths is pretty bad - by the standards of the people with who I worked for years and by the standards of many PF members. But I had an excellent Analysis course at University (mid 1960s) and the finer points of that Maths are always in the back of my mind because of that course. 'Proper' Maths is very precise and the meanings of terms are totally inflexible - necessarily - if you want to rely on it to deliver the goods.
Rational numbers can be regarded as continuous (I think) because you can get arbitrarily close to the next one -i.e. reduce the step size as much as you want). You can introduce irrational and transcendental numbers, I know, but you can sandwich π between two rational numbers and they can be as close as you want. That makes continuity.
1,2,3,4 will always have gaps between them and you are 'not allowed' to make the gap smaller. They are contiguous.

 

[bluestar]

Getting back to the topic question, what is the photon emission mechanism at picometer and fentometer wavelengths?

 

[Khashishi]

Atomic and molecular lines have a certain width (called line broadening). For this reason, if the lines are closely spaced, as in a large molecule, they will overlap, giving a continuous spectrum. You should look into natural line broadening and Doppler broadening. Molecules can have rotational and vibrational energy states which are more closely spaced in energy than electron energy states.

 

[bluestar]

Hey Khashishi,

Very interesting reply. Good, I shall look into natural line broadening. Hummm, I knew molecules have rotational and vibrational states but are photons released from these states and if so what is the mechanism of their release/absorption? Is it that a change in the associated electric field from “shared” electrons, as mentioned by sophiecentaur above, causes the photon release or absorption?

 

[sophiecentaur]

You can explain the continuum / line broadening in terms of the Pauli Exclusion Principle, which tells you Fermions (the stuff that atoms are made of) cannot share Energy states. A large number, together will fill up all the available possible values so that the transitions can take any value within a given band.

 

[bluestar]

Hey sophiecentaur
Very good reply! This I understand.
THANKS!