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Rate of reaction in detector?

  1. Jun 18, 2015 #1
    1. The problem statement, all variables and given/known data

    A reactor fires out ##10^{21}## neutrinos per second. A detector containing ##10m^3## of liquid which contains 30 carbon atoms every 60 hydrogen atoms. The detector-reactor distance is ##1000##. The cross section for the reaction is ##\sigma = 10^{-46} m^2##, and the density of the liquid is ##870 kg m^{-3}##. Find the expected rate of reactions.

    2. Relevant equations


    3. The attempt at a solution

    I know that the rate of reactions is ##W = \sigma J n \delta x## where ##J## is incoming particles per second and ##n## is number density and ##\delta x## is thickness.
    Number of carbon atoms per unit volume in the detector is ##\frac{60}{90} \frac{(870)(10.3)}{(1.67 \times 10^{-27}) (10.3)} = 3.5 \times 10^{29} m^{-3}##. Can I take ##J## to be ##10^{21}##? What is the thickness in this case?
     
  2. jcsd
  3. Jun 18, 2015 #2
    Or is it better to use ##W = \sigma \frac{J}{A} (nA\delta x) = \sigma \frac{J}{A} N## where I can find the flux from using ##\frac{J}{4\pi r^2}##?
     
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