How can I calculate the rate of decay of a radioactive element?

The decay of a radioactive element is a random process which is governed by the laws of chance.

The rate of decay only depends on the number of undecayed atoms.

This means that the more atoms of a radioactive element you have in your sample, the more chance a decay event will occur in that sample.

This is a 1st order process (which you may have met if you have studied chemical kinetics) for which:

#-RatepropN#

The minus sign shows N is decreasing with time

We can write this as:

#-Rate=lambdaN#

Where #lambda# is the decay constant, which is a constant for a particular isotope.

A process like this follows exponential decay which means that the time taken for half the original sample to decay is a constant.

This is termed the half - life or #t_(1/2)#.

Here is an example for the decay of carbon - 14:

It can be shown that #t_(1/2)=(0.693)/(lambda)#

Let's see how we can use this to calculate the rate of decay from this example:

"What is the rate of decay of 1.00g of radon - 224 which has a half - life of 55s?"

Rearranging we get:

#lambda=(0.693)/(t_(1/2)#

#lambda=0.693/55=0.0126s^(-1)#

#R=-lamdaN#

#R=-0.0126xx1.00=-0.0126"g/s"#

(I have used grams and not atoms as these are proportional and is reflected in the answer's units.)