Question

Particle physicists use particle track detectors to determine the lifetimeof short-lived particles. A muon has a mean lifetime of 2.2sand makes a track 9.5 cm long before decayinginto an electron and two neutrinos. What was the speed of the muon?

Answer 1

To calculate the speed of a muon before it decays, the distance the muon travels and the time it takes are used in the formula L = v x t. For a distance of 9.5 cm and a time of 2.20 microseconds, the speed is found to be approximately 43,182 meters per second.

Step-by-step explanation:

The question is seeking to calculate the speed of a muon before it decays. Assuming the mean lifetime of a muon is 2.20 microseconds (us) and the muon makes a track 9.5 cm long in this time, we can calculate the muon's speed. Let's consider the formula:

L = v x t

where L is the distance traveled, v is the velocity, and t is the time. Given L = 9.5 cm (or 0.095 m) and t = 2.20 x 10-6 s, we plug in the values:

v = L/t

v = 0.095 m / 2.20 x 10-6 s

v = 4.31818 x 104 m/s

The muon's speed was approximately 43,182 m/s.

Answer 2

v = 4.32 10⁴ m /s

Step-by-step explanation:

The speed of a particle is defined as the relationship between distance and time

v = d / t

In this case the particle goes at high speed, but the formula is the same, it has changes if you want to transform from a mobile reference system to a fixed one

v = 9.5 10⁻² / 2.2 10⁻⁶

v = 4.32 10⁴ m /s

This speed is much lower than the speed of light, so the relativistic effects are small