Pions and protons, both with kinetic energy 1 GeV/c 2 , travel between two scint
ID: 1894707 • Letter: P
Question
Pions and protons, both with kinetic energy 1 GeV/c2, travel between two scintillation counters distance 1 meter apart. Calculate the time (time-of-flight, TOF) that it takes for each particle to travel the distance
between the counters in relativistic kinematics and compare the results. Masses of pions and protons are 0.14 GeV/c2 and 0.94 GeV/c2, respectively.
Explanation / Answer
mass initial: 938.272 MeV/c2 mass final: 938.272MeV/c2 + 135 MeV/c2 (a) energy conservation is violated by (mass final - massinitial)c2 =135MeV (b) uncertainty principle: ?E?t > h/(2p) h is Planck's constant So, ?t > h/(2p?E) is the minimum uncertainty inthe measurements. Therefore the pion must be absorbed within thisuncertainty.