# Find the probability that a muon is passing through your body this instant

1. Apr 1, 2012

### JFuld

1. The problem statement, all variables and given/known data

the flux of muons on the earths surface is about 100 muons per square meter per second. Estimate the probability that a muon is passing
through your body this instant to within a factor of three

attempt:

let F = flux of muons on earths surface = 100/m^2/s

let the average person occupy an area A on the earths surface.

then F*A =# of muons penetrating person every second

I dont really know where to go from here. if there are N "instants" in a second then FA/N gives the average # of muons passing through you in an instant?

2. Apr 1, 2012

### tiny-tim

Hi JFuld!
no, an instant is zero time,

it means how many are likely to be inside your body at any fixed time

(so you'll need an estimate of their speed )

3. Apr 1, 2012

### JFuld

ahh thank you, I knew I had no idea what I was doing haha. Well here is what I did in sight of your comment:

Im still using F*A =# of muons penetrating person every second, and im letting v=vertical velocity of muons. Also, I am picturing the incident muons as a steady stream.

v*(1 second) = d, the distance traveled by muons in one second. So a vertical segment of length d contains 100 muons/m^2.

and A*d corresponds to the # of muons contained in segment d over an area A.

then taking A to equal .25m^2, the volume d*A contains 25 muons at an instant.

and 25/d =# muons per area A, then h*25/d = N = the # of muons occupying a person at an instant

also, my estimate for the muon velocity is: 1*10^8 m/s < v < c

then the range for d is: 1*10^8 m < d < 3*10^8 m

this give the range for N: 4.5*10^-7 < N < 1.5*10^-7 (i aproximate h to be 1.8 m)

4. Apr 2, 2012

looks good!