Muons at speed 0.9994c are sent round and round a circular storage ring of radius 1500 m. If a muon at rest decays into other particles after an average T = 2.2*10 sup- ⁶ s, how many trips around the storage ring do we expect the 0.9994c muons to make before they decay? A) 2 B) 4 C) 0.2 D) 6

Question

Muons at speed 0.9994c are sent round and round a circular storage ring of radius 1500 m. If a muon at rest decays into other particles after an average T = 2.2*10 sup>- ⁶ s, how many trips around the storage ring do we expect the 0.9994c muons to make before they decay? A) 2 B) 4 C) 0.2 D) 6

Quizplus · Accepted Answer

The time dilation factor is:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} = \frac{1}{\sqrt{1 - 0.9994^2}} = 22.36$$So the muons will decay after:$$T' = \gamma T = 22.36 	imes 2.2 	imes 10^{-6} s = 4.9 	imes 10^{-5} s$$The muons will travel a distance of:$$d = vT' = 0.9994c 	imes 4.9 	imes 10^{-5} s = 299700 km$$The circumference of the storage ring is:$$C = 2\pi r = 2\pi 	imes 1500 m = 9425 m$$So the muons will make:$$n = \frac{d}{C} = \frac{299700 km}{9425 m} = 31.8$$trips around the storage ring before they decay.

Muons at Speed 0