# The half-life of Iodine-131 is 8 days. What mass of I-131 remains from an 8.0g sample after 2 half-lives?

##### 1 Answer

#### Explanation:

The key to this problem lies with how the **nuclear half-life** of a radioactive isotope was defined.

For a given sample of a radioactive isotope, the time needed for **half** of the sample to undergo decay will give you that isotope's **nuclear half-life**.

This means that **every passing of a half-life** will leave you with **half** of the sample you started with.

Let's say that you start with a sample

#A_0 * 1/2 = color(purple)(A_0/2) -># afterone half-life

What about after the passing of **another** half-life?

#color(purple)(A_0/2) * 1/2 = color(orange)(A_0/4) -># aftertwo half-lives

What about after the passing of **another** half-life?

#color(orange)(A_0/4) * 1/2 = color(brown)(A_0/8) -># afterthree half-lives

and so on. With every half-life that passes, your sample will be **halved**.

Mathematically, you can express this as

#color(blue)(A = A_0 * 1/2^n)" "# , where

**number of half-lives** that pass in that period of time

You know that your sample of iodine-131 has a half-life of *undecayed* after the passing of

This means that here

#A = A_0 * 1/2^2 = A_0/4#

Since you started with an

#A = "8 g" * 1/4 = color(green)("2 g")#