Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Decay of an element

  1. Dec 22, 2004 #1


    User Avatar
    Homework Helper
    Gold Member

    My school textbook says that "The decay of a radioactive element is a random process and does not depend on external factors such as temperature". But if the decay is a random process, how can we accuratley predict the amount of substance after t seconds using the rate law?? Did I miss something?
  2. jcsd
  3. Dec 22, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Actually, it's because radioactive decay is random that we can derive the rate law. The route is through probability.

    Given a radioactive nucleus, you can never tell when the next decay event is going to happen, because it is equally likely to happen any time. So, if you have a large enough radioactive sample, then in any small time interval [itex] \Delta t [/itex], the number of decay events expected will be proportional to the number of nucleii in the sample.

    Or, [tex]~~ lim_{\Delta t \rightarrow 0} (\frac {\Delta N}{\Delta t}) = \frac {dN}{dt}~~ \alpha ~~N [/tex]

    This is exactly what gives you the first-order rate law :

    [tex]N(t) = N(0)~e^{-kt} [/tex]
  4. Dec 22, 2004 #3


    User Avatar

    Staff: Mentor

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Decay of an element
  1. Charge decay (Replies: 9)

  2. Monoatomic elements (Replies: 8)

  3. Beta Minus Decay (Replies: 2)

  4. Rb Decay (Replies: 3)