I know this problem has to do with half-life but I do not know how to do this problem. Thanks for any help. It is gratly appreciated.
a) Find the activity of a sample of 3 x 1016 nuclei of 226Ra which has a half-life of 1600 years.
b) How long will it take for the number of nuclei to be reduced by 10%?
c) What will be the activity at this time?
The decay constant lambda of a radioactive isotope is equal to 0.693 divided by the half lifeT1/2:
[The decay constant is the probability that any particular radioactive atom will decay in the given time period.
The activity Ao of a radioactive sample is equal to the product of the number of atoms present No multiplied by the decay constant lambda.
The activity A of a sample at any future time t is equal to:
In this case the new activity A is 90% of the initial activity Ao:
Take the natural log of both sides of,the equation:
Therefore, the time t when the activity A, and therefore the number of atoms present is 90% of the number initially present becomes:
While the activity will be 90% of the initial activity: