Question 26.1: Antiproton Creation Two protons moving in opposite direction...
Antiproton Creation
Two protons moving in opposite directions collide, causing the reaction p+p \rightarrow p+p+p+\bar{p}. What’s the minimum kinetic energy for each proton?
ORGANIZE AND PLAN Figure 26.2 shows the situation before and after the collision, where we’ve defined the x-axis to be along the colliding protons’ line of motion. With the minimum initial energy, there’s no energy left over as kinetic energy after the reaction, so the products are at rest. Momentum conservation then requires that the incoming protons have equal speed, and hence equal kinetic energy. The energy needed to create a proton and antiproton, each with mass m_{p} is E=m_{ total } c^{2}=2 m_{p} c^{2}.
\text { Known: Proton mass } m_{p}=1.67 \times 10^{-27} kg ; c=3.00 \times 10^{8} m / s .
Using the proton mass, the energy required is
E=2 m_{p} c^{2}=2\left(1.67 \times 10^{-27} kg \right)\left(3.00 \times 10^{8} m / s \right)^{2}.
=3.006 \times 10^{-10} J.
The incident protons share this energy equally, so each has kinetic energy K=1.503 \times 10^{-10} J =938 MeV.
REFLECT The kinetic energy of each incident proton is equal to the rest energy of a proton (or antiproton). You could skip this calculation and just look up the proton s rest energy about 938 MeV (see Chapter 25), equivalent to the value computed here. That s substantial kinetic energy, requiring a particle accelerator capable of nearly 1 GeV.