# Phosphorus-32 has a half-life of 14.0 days. Starting with 8.00g of 32P, how many grams will remain after 70.0days ?

##### 1 Answer

You'll be left with **0.25 g** of phosphorus-32.

The nuclear half-life of a radioactive isotope expresses the time needed for a sample of that isotope to reach **half of its initial value**.

In your case, regardless with how much phosphorus-32 you start with, you'll be left with **half** of that initial mass after **14.0 days**. After *another* **14 days**, you'll be left with **half** of what you had after the *first* **14 days**, which is equivalent to **a quarter of the initial mass**.

The original mass of the isotope will be **halved** *for each* passing of a half-life. In your case, you'll be left with

*50% of the initial mass*#-># after**1**half-life has passed;*25% of the initial mass*#-># after**2**half-lives have passed;*12.5% of the initial mass*#-># after**3**half-lives have passed;*6.25% of the initial mass*#-># after**4**half-lives have passed;*3.125% of the initial mass*#-># after**5**half-lives have passed.

and so on.

When the numbers allow it, such as you have in your problem, you can easily figure out how many half-lives have passed by dividing the total time passed by the half-life of the isotope

This means that you need to divide the initial mass **by 2** for *every half-life that passed*, which is equivalent to having

In your case, you'll be left with