The half-life of an element is #5.8 x 10^11#. How long does it take a sample of the element to decay to #2/5# its original mass?
The expression for the first-order decay of a population is
where the rate constant
In the question, the half-life should have units of time. Let's assume that the half-life is
In this case, the value of the rate constant is
Using the first equation, we can find the time,
(or about 24,300 years)