The half-life of strontium-90 is 28 years. How long will it take a 44 mg sample to decay to a mass of 11 mg?
A radioactive isotope's nuclear half-life tells you how much time must pass until an initial sample is halved.
In your case, strontium-90 is known to have a half-life of
#A_0 * 1/2 ->#after one half-life passes;
#A_0/2 * 1/2 = A_0/4 ->#after two half-lives pass;
#A_0/4 * 1/2 = A_0/8 ->#after three half-lives pass;
#A_0/8 * 1/2 = A_0/16 ->#after four half-lives pass;
and so on.
Notice that you can write the remaining amount of an initial sample by using the number of half-lives that pass
#"remaining amount" = "initial amount"/2^n" "#, where
Now, you initial sample has a mass of
#"11 mg" = "44 mg"/4 = "44 mg"/2^2#
This means that two half-lives must pass in order for the strontium-90 sample to decay to a quarter of its initial mass.
This implies that you have
#2color(red)(cancel(color(black)("half-lives"))) * "28 years"/(1color(red)(cancel(color(black)("half-life")))) = color(green)("56 years")#