Decay of an element

  • Thread starter siddharth
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siddharth
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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?
 

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Gokul43201
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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]
 

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