In a system of two particles with energies and momenta (E(1), p(1)) and (E(2), p

Question

In a system of two particles with energies and momenta (E(1), p(1)) and (E(2), p(2)), respectively, the quantity

s^2 = (E(1) +E(2))^2 - c^2 (p(1) +p(2))^2

is invariant; that is, it has the same numerical value in all inertial frames.

(a) Consider a center of mass collision of a proton and an antiproton (mc^2 =938.3 MeV). What is the minimum momentum required to produce a particle with mass Mc^2 =91.2e3 MeV?

(b) In a fixed target accelerator, an antiproton projectile collides with a proton target at rest. What is the minimum energy that the antiproton must have to create the new particle of part (a)?

Explanation / Answer

a)

2 * (p2 c2 + (mc2)^2) = 91.2e9 eV

2 * (p2 c2 + (938.3e6)^2) = 91.2e9

p c = 4.55903e10 eV

p c = 4.55903e10*1.6e-19 J

p = 4.55903e10*1.6e-19/3e8

p = 2.43e-17 Kg.m/s

b)

91.2e3 - 2*938.3 = 8.93e4 MeV

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.