What Is the Minimum Photon Energy Needed to Produce a Proton-Antiproton Pair?

[PhyzicsOfHockey]

Homework Statement

How much photon energy would be required to produce a proton-antiproton pair? Give the answer in SI units.

Homework Equations

E^2=p^2c^2+m^2c^4
E=pc+pc
p=mc
E=2*m*c^2

The Attempt at a Solution

I seem to be confused I know the KE would be zero I also know this would not exist in real life but I need to find the min energy so KE of the photon pairs is 0. I am not sure if the equation has to do with the mass of a photon or the momentum of the photons. In either case I don't know what the mass of a photon would be. I read it was zero but can't figure out how to use this formula then.

 

[mjsd]

ok... mass of a photon is zero... I think we all know that. But its momentum is not... we can agree on that too I think. Now, your key equation is
[tex]E^2=p^2 c^2+m^2 c^4[\tex]
where m here is the rest mass of your particle, p is its momentum and E is its total energy. To do your question: remember 4-momentum is conserved...etc

 

[m2003]

The equation E=2*m*c^2 is the correct equation to use for pair production, where m is the mass of the particle being produced (in this case, the proton or antiproton). Since the mass of a photon is essentially zero, you can use this equation to solve for the minimum energy required.

First, we need to determine the mass of a proton and antiproton. In SI units, the mass of a proton is approximately 1.67 x 10^-27 kg. Using this value in the equation, we get:

E = 2 * (1.67 x 10^-27 kg) * (3 x 10^8 m/s)^2

Simplifying, we get:

E = 3.006 x 10^-10 J

Therefore, the minimum energy required to produce a proton-antiproton pair is approximately 3.006 x 10^-10 Joules.