Particle track detectors are used to measure the speed of particles if the lifet
ID: 2039807 • Letter: P
Question
Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle-X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 18.2 cm long tracks on average before they decay into other particles not observable by the detector.
1) What is the average speed of the particles in terms of the speed of light?
Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle-X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 18.2 cm long tracks on average before they decay into other particles not observable by the detector. What is the average speed of the particles in terms of the speed of light? Hints: The speed of the particle is the ratio of the track length and the lifetime. However the simple ratio of these two quantities gives unphýsically high speed: 2.368 c. The reason is that the length of the track is measured in the resting frame of the detector. On the other hand the lifetime of the particle is its life expectancy measured in the frame moving with the particle. Either transform the length tof the pare ros the sa ne referertcele r irne.ime to the detector's frame. You cán take the ratio of thetackenth and the lifetime only if they are from the same refèrence frame Submit Answer Incorrect. Tries 1/12 Previous TriesExplanation / Answer
The observed lifetime is = (256.2x10-12)/sqrt[1-(v/c)²]
The observed speed, v = distance / (observed lifetimes)
v = 0.182 * sqrt[1-(v/c)2] / (256.2x10-12)
v = 7.1 * 108 * sqrt[1-(v/c)2]
v2 = 5.04* 1017 * [1 - (v/c)2]
v2 = 5.04 * 1017 - 5.6*v2
6.6*v2 = 5.04 * 1017
v = 2.76 * 108 = 0.92*c