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physics

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Radioactive nuclei are produced in an irradiated sample at the rate of 10 s-1. If the number in the sample builds up to a maximum of 1000, calculate the mean life and the half-life of the radioactive nuclei

Using dN / dt = P - λ N

dN / dt = 1000n /10/ 1 = 100
P - λ N = 10 – λ 1000N

Half life is -

(In2) / λ = (In2) / 1000) = 6.93x10^-4 seconds

Not sure of mean life any advice appreciated ...

  • physics - ,

    if none were added
    dN/dt = k N

    number produced per second = 10
    number lost per second = k n

    so
    dN/dt = 10 - k N
    N is maximum when dN/dt = 0
    0 = 10 - k (1000)
    k = .01

    so we know that for this fission reaction (without the inflow)
    dN/dt = -.01 N
    dN/N = -.01 dt
    ln N = -.01 t + C
    N = Ni e^-(.01 t)

    when is N/Ni = .5?
    ln .5 = -.01 t
    t = 69.3 seconds half life

    mean life = 1.443 * half life (see http://www.britannica.com/EBchecked/topic/371549/mean-life )

  • physics - ,

    THANK YOU .....

  • physics - ,

    You are welcome :)

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