Determine the time required for an original 24.0-gram sample of sr-94 to decay until only 1.5 grams of the sample remains unchanged.

For the answer to the question above,

24 - - > 12 - - > 6 - - > 3 - - > 1.5

... 1 ... 2 ... 3 ... 4 ... four half-lives

The time is 4 (t½) ... where t½ is the half-life.

There are two types of problems dealing with half-life. One is the "super-simple" which is what you have here and the solution is also simple. It involves counting half-lives.

A more realistic problem wouldn't work out so nicely and would involve this equation or a variation since radioactive decay is a first-order process.

A = Ao e^ (-kt) ... where A is the activity (or amount) after some time (t), Ao is the original activity (or amount) at t=0, k is the decay constant and t is the elapsed time. The decay constant is related to the half-life. t½=ln2/k or k=ln2 / (t½).

A = Ao e^ (-kt)

ln A = - kt + lnAo

ln (A/Ao) = - kt

t = (ln (A/Ao)) / - k

t = ln (1.5/24) / - k

t = ln (0.0625) / - k

t = - 2.773 / - k

t = - 2.773 / - ln2 / (t½)

t = - 2.773 / (-0.693 / (t½))

t = 4 (t½)