Chapter 37, problem 001 the mean lifetime of certain subatomic particles is measured to be 2.7196 μs when they are stationary. however, the mean lifetime of fast-moving particles of the same kind observed in a burst of cosmic rays is measured to be 17.258 μs. what is the speed parameter β of these cosmic-ray particles relative to earth?

 v = 0.9875 c

Explanation:

This is an exercise of time dilation in special relativity, which is described by the equation

      t =  γ

      γ = 1 / √ (1 — v² / c²)

The most important is to find respect for which system the measurement is performed.

Since the particle is still, the measured time is the proper time = 2.7196 10-6 s, in the system where the particles move t = 17,258 10-6 s

Let's clear dam

     γ = t /

     γ = 17,258 10-6 / 2.7196 10-6

     γ = 6.345

     γ = 1 / √ (1-β²)

     1-β² = 1 /γ²

    β = √ (1- 1 / γ²)

    β = √ (1 - 1 / 6,345²)

    β = 0.9875

    v / c = 0.9875

    v = 0.9875 c

1 a

2 b

3 b

4 d

5 d

6 d

explanation: