# 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?

##### 1 Answer

#### Explanation:

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 -># afterone half-lifepasses;#A_0/2 * 1/2 = A_0/4 -># aftertwo half-livespass;#A_0/4 * 1/2 = A_0/8 -># afterthree half-livespass;#A_0/8 * 1/2 = A_0/16 -># afterfour half-livespass;

#vdots#

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")#