- #1
tnibbz
- 5
- 0
- Homework Statement
- A 2 GeV electron is incident on a proton with rest mass mpc^2 = .938 GeV at rest. Calculate the invariant mass of the electron proton pair in the center of mass, neglect the mass of the electron.
- Relevant Equations
- E^2 = p^2*c^2 + m^2*c^4
E = K + E0
So I know that since we are ignoring the mass of the electron, and the proton starts at rest, the proton has no KE and the electron has no rest energy.
So the initial total energy of the system would be
rest energy of proton + KE of electron = 2GeV + .938GeV = 2.938 GeV
and since energy is conserved this would also be the total energy of the final state as well correct?
Now with the equation
E2 = p2*c2 + m2*c4
I can subsitute in 2.938GeV for E, however from here I get confused, because I need both the resulting velocity of the system and the mass.
Or is the mass of the system in this case just the mass of the proton because we are neglecting the mass of electron? But in that case would the invariant mass of the system just be the mass of the proton?
So the initial total energy of the system would be
rest energy of proton + KE of electron = 2GeV + .938GeV = 2.938 GeV
and since energy is conserved this would also be the total energy of the final state as well correct?
Now with the equation
E2 = p2*c2 + m2*c4
I can subsitute in 2.938GeV for E, however from here I get confused, because I need both the resulting velocity of the system and the mass.
Or is the mass of the system in this case just the mass of the proton because we are neglecting the mass of electron? But in that case would the invariant mass of the system just be the mass of the proton?