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 .
