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Law of radioactive decay

  • 13-05-2008 7:23pm
    #1
    IrishKnight
    Registered Users, Registered Users 2 Posts: 922 ✭✭✭


    Can anyone point me to a website/tell me how to derive, from first principles, an expression for the law of radioactive decay?


Comments

  • #2
    ZorbaTehZ
    Registered Users, Registered Users 2 Posts: 2,149 ✭✭✭ZorbaTehZ


    Dunno a site but I can do it heer using calculus, tis simple enough.
    Rate of decay is proportional to amount of nuclei N.(Δ = change, t = time)
    So: ΔN/Δt = -λN , λ is a constant of proportionality called the decay constant.
    So if you integrate both sides:
    ⌠dN/N = -λ⌠dt
    lnN = -λt + C

    To get C, we say that initially (ie t=0) the amount of nuclei is N_0
    So: lnN = -λt + lnN_0
    lnN - lnN_0 = -λt
    N/N_0 = e^(-λt)*
    -> N=N_0[e^(-λt)]

    So if you look at *, we say that after 1 half-life N/N_0 will be 1/2 (definition of half-life), sO;
    1/2 = e^(-λT)...T is half life
    ln1/2 = -λT
    And then: T = -ln2/λ
    So the formula above becomes:
    N=N_0[2^(-t/T)]


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