Answer to Question #312032 in Mechanics | Relativity for line

Question

2. The half-life of muons provides you with a muon clock. Plot a graph of the number of muons versus time. Use 500 muons as the size of the sample. This graph will become your clock.

a. If 125 muons remain, how much time has elapsed?

b. If 31 muons remain, how much time has elapsed?

c. If 300 muons remain, how much time has elapsed?

d. If 400 muons remain, how much time has elapsed?

Answer 1

$T=1.56~\mu s,$

$N=N_02^{-\frac tT},$

$t=T\log_2{\frac{N_0}N},$

a)

$t=3.12~\mu s,$

b)

$t=6.24~\mu s,$

c)

$t=1.15~\mu s,$

d)

$t=0.50~\mu s.$