Question

Particle track detectors are used to measure the speed of particles if the lifetime of the...

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 10.4 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?

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Answer #1

The lifetime is 256.2ps in a frame of reference where the particle is at rest.

Due to time dilation the observed lifetime is =

The observed speed, v = distance / (observed lifetimes)

here distance = 10.4cm 0r 0.104 m

by putting this in above equation, we get

by taking both sides squares, we get

bu putting the value of speed of light

by taking both sides square root, we get

now the avg speed in terms of light of speed is

speed of light

Therefore the average speed of the particle in terms of the speed of light is (0.80 times the speed of light)

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