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Math Help - Nuclear Chain Reaction and Atoms

  1. #1
    Junior Member Dragon's Avatar
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    Nuclear Chain Reaction and Atoms

    In a particular nuclear chain reaction, an atom ejects a neutron which causes an average of 1.3 atoms to do the same thing. What is the total number of atoms involved in the chain reaction after 30 generations?

    A.) 8,730
    B.)14,556
    C.)8,729
    D.)11,350
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Dragon View Post
    In a particular nuclear chain reaction, an atom ejects a neutron which causes an average of 1.3 atoms to do the same thing. What is the total number of atoms involved in the chain reaction after 30 generations?

    A.) 8,730
    B.)14,556
    C.)8,729
    D.)11,350

    If at generation k you have N_{k-1} atoms ejecting a neutron then in generation k we have:

    N_{k}=1.3N_{k-1}=1.3^{k+1}N_0

    So the total number to have emited a nutron in 30 generations is:

    NN_{30}=N_0(1+1.3+1.3^2+ ... + 1.3^{30})

    Assume we start with N_0=1, then we have a geometric series that you should be able to sum.

    (this is counting the first decay as generation zero, if you want it to be generation 1 then adjust the above accordingly)

    CB
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