This is the type of decay associated with nuclear decay and capacitor discharge. In nuclear decay, each atom has a set probability of decaying over a given time period. In a capacitor, the rate of flow of current is dependant on the charge on the plates. In both cases, a simple differential equation can be derived:

dx/dt = -kx

This, in English, means that the rate of disappearance of x will depend of the amount of x you have left, with k as a rate constant. We can solve this differential equation by inspection, simply by the thought process:

"What, differentiated, gives minus k times itself?"
The answer is, of course Ae-kt, thus we recieve the equation x=Ae-kt giving us values of x for varying t.

For values of the constants, we can put t=0, ie when the system begins. For the radioactive decay, at t=0, x is equal to however many atoms you begin with, or x0. k is the decay constant, given in s-1 (This is frequently written as a lambda). T1/2 (the half life of your sample) can be found by the equation T1/2=ln(2)/k.

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