Particle track detectors are used to measure the speed of pa

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 15.2 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?

Solution

>> According to theory of relativity,

t = to/[1-(v/c)²]^1/2 ,

Here, to = Lifetime = 256.2 ps

c = Speed of Light = 3*10⁸ m/s

v = Required Velocity = ?

Also, t = d/v

d = distance = 15.2 cm = 0.152 m

Putting all the values here,

=> d/v = to/[1-(v/c)²]^1/2

The observed lifetime,t = (256.2x10^-12)/sqrt[1-(v/c)²]

=> v = d*[1-(v/c)²]^1/2 /to
v = 0.152 * sqrt[1-(v/c)²] / (256.2x10^-12)

v = 5.933 * 10⁸ * sqrt[1-(v/c)²]

v² = 35.20 * 10¹⁶ * [1 - (v/c)²]

v² = 35.20 * 10¹⁶ - 3.911*v²

4.911*v² = 35.20 * 10¹⁶

v = 2.677 * 10⁸ = 0.892*c .......ANSWER.......