Exponential decay question. fundamental

[rjsbass]

this is just something has been bugging me for the last few days. it seems like it has a very basic solution.

Muons decay randomly, but have a mean lifetime of about 2 us. If I plot the # of muons that decay vs. time (say the axis spans from 0 to 20 us), why is the plot exponential decay? shouldn't it be a gaussian distribution centered around the mean lifetime?

 

[rjsbass]

got it. textbooks ftw

 

[gneill]

Suppose you had a pile pile of newly minted muons. After 2 μs, how many would you expect to have left?

 

[rjsbass]

the majority of them will be gone but some will still remain?

 

[gneill]

You should be able to give a numerical answer from probability theory. Remember, the lifetime is a mean value.