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Author Topic:   Photon's Energy to Kinetic Energy
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 1 of 9 (192336)
03-18-2005 2:40 PM


Melchoir asked in the "tired Light" forum:
quote:
What is the actual mechanism that allows the atomic nucleus to pick up and convert photons into kinetic energy?
How does this fit in with the mechanism used to explain light spectra, i.e., atoms can only absorb photons of a particular frequency and the rest are transmitted? Can any frequency be absorbed, but only frequencies that cause a jump in a quantum energy level are stable?
If this is accurate, how do the energy jumps which don't cause a quantum jump lose some of their energy to the kinetic energy of the atom?

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Message 2 of 9 (192460)
03-19-2005 9:15 AM


Thread moved here from the Proposed New Topics forum.

  
Eta_Carinae
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Posts: 547
From: US
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Message 3 of 9 (192546)
03-19-2005 2:55 PM
Reply to: Message 1 by JustinC
03-18-2005 2:40 PM


You are thinking only of .....
bound-bound transitions that cause spectral lines at specfic quanta.
Google Thomson or its relativistic counterpart Compton scattering.
Also energetic enough photons can cause transitions of the nucleons themselves which is a much more complex level structure than atomic electrons.

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JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 4 of 9 (192562)
03-19-2005 4:16 PM


I am aware of Compton Scattering and Line Spectra, but for some reason I can't reconcile the two.
Here is my reasoning. The theory I have learned behind spectral lines is that a atoms electrons can only absorb energy in with specific energies, i.e., specific wavelengths. The rest are transmitted and we are left with Fraunhofer lines.
Compton scattering seems to imply that an atom can absorb any frequency of energy, with a part of the energy raising the electron to a higher orbital and rest being converted to kinetic energy.
Or does Compton scattering only apply to free electrons, and a photon can increase the kinetic energy of the electron while reducing its own energy.
Can a photon, in general, increase an atoms kinetic energy?

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Eta_Carinae
Member (Idle past 4374 days)
Posts: 547
From: US
Joined: 11-15-2003


Message 5 of 9 (192565)
03-19-2005 4:41 PM
Reply to: Message 4 by JustinC
03-19-2005 4:16 PM


Compton scattering is usually referring to weakly bound valence electrons in a material. But in astrophysics it is usually referrring to free electron scattering at high energy.
Thomson scattering is the low energy scatttering with free electrons. Rayleigh scattering is the low energy scattering off bound electrons.

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Sylas
Member (Idle past 5259 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 6 of 9 (192576)
03-19-2005 5:51 PM
Reply to: Message 5 by Eta_Carinae
03-19-2005 4:41 PM


Can you please clarify just a bit on the difference between Compton and Thomson scattering in relation to photons interacting with plasma?
I've been trying some of the maths myself; and I've been simply using special relativistic dynamics where a photon interacts with a free electron, to exchange momentum and energy.
I gather that Compton scattering is a high energy case and Thomson scattering a low energy case. Can you expand on this a bit?

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Eta_Carinae
Member (Idle past 4374 days)
Posts: 547
From: US
Joined: 11-15-2003


Message 7 of 9 (192704)
03-20-2005 12:04 AM
Reply to: Message 6 by Sylas
03-19-2005 5:51 PM


Sylas
When dealing with scattering of free electrons in a plasma you can basically define two main regimes of interest.
i) Using the classical dipole treatment for the electron we get the Thomson scattering with a cross section of (8*Pi/3)*Re^2. Notice that the cross section is frequency independent.
ii) For more energetic radiation you have to use the Klein-Nishina formula for calculating the cross section. It's lengthy so Google it, I'm sure there are many web pages with it on.
We now have 2 regimes within this case:
a) Non-relativistic electrons doing the scattering.
Cross section is (8*Pi/3)*Re^2 *(1-2A+(26/5)A^2+....) where A is h*v/Me*c^2 where v is frequency.
b)Extreme relativistic regime where A>>1 which means the cross section is now (8*Pi/3)*Re^2*(3/8A)*(Ln(2A)+1/2).
For the in between regime then you use the full Klein-Nishina formula.
** Note that I remembered this out of my head so I might have an error above as I was too lazy to Google **
Also note that Thomson scattering, which is also when the recoil of the electron can be neglected is also called coherent scattering because the frequency of the incoming and outgoing photon is unchanged. Compton scattering is where the recoil has to be taken into account, thats what the Klein-Nishina formula does, is not coherent as the frequency is changed.
I remember in school having to derive the Klein-Nishina formula. A task I would not like to do tonight from memory!

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Gabe Webb
Inactive Member


Message 8 of 9 (199642)
04-15-2005 6:25 PM


Cool application of light and energy absorption by atoms:
(I don't have the foggiest what you two are talking about, but this seems related. Poke me if it isn't.)
Scientists have found a reaction between Metal That I Don't Know The Name and water that does a neat trick.
Putting a square 1"x1" sheet of Metal X on the back of a paper airplane and affixing a droplet of water to it, a focused microwave beam then makes the two act as a jet-propulsion unit.
The airplane will shoot out at speeds upwards of 25 mph, but fall short, however, when the neat little trick thingy runs out of water.
Oh and BTW: What exactly is Compton Scattering? You're talking to a High School Sophomore here, so slap me if I'm annoying and I'll go away.

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peaceharris
Member (Idle past 5596 days)
Posts: 128
Joined: 03-28-2005


Message 9 of 9 (200056)
04-18-2005 8:23 AM
Reply to: Message 8 by Gabe Webb
04-15-2005 6:25 PM


Amadameus writes:
What exactly is Compton Scattering?
You can easily use google to find out the answer. Here's my version:
If an energetic photon hits an electron bounded to an atom, the electron gets sufficient energy to escape. If the photon is not energetic enough, the electron may not escape, instead may just get excited to a higher energy level. Compton scattering happens when high energy photons (xrays) hit an electron.
To derive the Compton Scattering equation, you have to do the following:
1) Conserve energy.
2) Conserve momentum.
3) Assume that the photon has a momentum of h/L (L=wavelength)
4) Assume that the mass of the electron (m) is mo/sqrt(1-v2/c2)
5) Assume that the energy of the electron is mc2
6) Assume that the momentum of the electron is mv
The rest is mathematical jugglery.
This message has been edited by peaceharris, 04-18-2005 07:24 AM
This message has been edited by peaceharris, 04-18-2005 07:25 AM

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