# Decay of a muon-probability of decay

## Homework Statement

An energetic muon is created by the interaction of a cosmic ray 20 km away from the surface of the earth. How energetic does the muon have to be to be detected on earth before it decays with a 10% probability?
For a single muon, what is the probability that it will not have decayed after time Δt?

Show that, assuming the muon would be detected if it doesn’t decay, the length of time since creation of the muon Δt where 10% of the muons will be detected is given by Δt = [ln(10)= ln(2)]τ ' 3:3τ .

## Homework Equations

For a decay half-life τ, the fractional proportion of a large population of N0 muons remaining after a time Δt is N=N0 = exp(- ln(2)Δt=τ ). How can relate this to a singe muon without having t and λ?

## The Attempt at a Solution

I set up the decay equation but not sure what to do next.