# Matter & Antimatter

I am really stuck on setting up the problem & equations to solve, can someone please help me out with this beginning step?

The question is:
1) A plasma out in space containing protons and electrons meets up with another plasma containing anti-protons and positrons. At what rest wavelengths would you expect to observe the spectral signatures of this collision?

Will both plasmas annihilate completely or only half of each plasma will annihilate? I know that when protons and antiprotons collide, they annihilate completely. But in this case, say, the protons surely can collide with the positrons instead of colliding with the anti-protons, right?

I think I need the "mass" to do the calculations. How can I figure out the total mass the the two plasmas? I don't know how many protons, positrons, etc., there are...

And I don't even know the speed of the protons, positrons, etc., how can I calculate the energy without the speed of the particles?

How many photons will be released? One? Two? Three? How can I know?

Any help of any kind is greatly appreciated! Thank you!:)

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andrevdh
Homework Helper
A proton and antiproton will annihilate each other. Same with an electron and a positron. Each of these will result in its own set of photons with specific wavelengths. More matter will just result in more photons with the same wavelengths.

as far as i know protons shouldnt anihilate the positrons. whilst they have opposite charges they are not the matter/antimatter reflections of each other

i think

Should would the 2 plasmas annihilate completely?

Another trouble is that I don't know the mass and velocity of the plasmas...

Can anyone explain in greater detail? Thanks!

But another trouble is that I don't know the mass and velocity of the plasmas...

Can anyone explain in greater detail? Thanks!

Dick
Homework Helper
The problem says "at what REST wavelengths". While not very good english, I assume this would mean you can ignore the velocities. The total mass, whether annihilation is complete etc etc are irrelevant. Just take eg one e+/e- encounter. What happens?

But the protons, antiprotons, etc., have kinetic energy before they collide, if I am not given their velocities, how can I find the total energy (the quantity that is conserved)?

So we only need the mass of the protons, antiprotons, electron, and positron rather than the mass of the plasmas in doing this calculation?

Dick
Homework Helper
Yes. I think you can assume the KE is negligible compared with the annihilation energy. And, yes, the mass of the plasma would only affect the intensity and amount of radiation. Not the spectrum.

So
E=2mc^2=hc/(wavelength)
wvaelength=h/(2mc)

Substituting mass of proton and I get the first wavelength?
Substituing mass of electron and I get the second wavelength?

Am I right?

By the way, what is the meaning of REST wavelength? At rest relative to what (in which frame of reference?) ?

Dick
Homework Helper
I'm assuming 'rest wavelength' means the the annihilation is at rest relative to the observer. And yes, you are almost right. But does it seem ok that two particles can annihilate and produce a single photon and still conserve momentum?

So I guess there will be 2 photons, giving the following calculations:

E_final=2(E_photon)=2mc^2=E_initial (Conserivation of energy)
And 2*hc/(wavelength)=2(E_photon)=2mc^2
So wavelength=h/(mc)

But why 2 photons? not 3 or 4 photons?

Dick
Homework Helper
Excellent question!! I don't think 3 would workkinematically, though I could be wrong. 4 would. But this would be a rare process (it would involve more loops in a Feynmann diagram - are you working at this level or is it just a simple question?).

Dick
Homework Helper
One could also note that the annihilation in general can be a messy process. e+/e- is pretty clean but p+/p- is not. There could be other products. But I don't think that is what the question is after.

Excellent question!! I don't think 3 would workkinematically, though I could be wrong. 4 would. But this would be a rare process (it would involve more loops in a Feynmann diagram - are you working at this level or is it just a simple question?).
Just wondering...but nevermind...I don't think I am up to that level

So in most cases, 2 photons will be produced when 1 particle and 1 antiparticle collide?

Dick
Homework Helper
Likely there are other ways for protons to annihilate - but you probably don't care much about them since their products are unstable and more than a two body decay won't give you sharp spectral lines.