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

  1. Apr 1, 2012 #1
    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?

    I feel i am going about this wrong, any help is appreciated.
     
  2. jcsd
  3. Apr 1, 2012 #2

    tiny-tim

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    Hi JFuld! :smile:
    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 :wink:)
     
  4. Apr 1, 2012 #3
    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)
     
  5. Apr 2, 2012 #4

    tiny-tim

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    looks good! :smile:
     
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