**The Radioactive Decay Equation**

### N=N_{o}e^{-(0.693t/T½)}

Use this equation to find out how much of a radioactive material is left after a given period of time.

__To use the equation:__

The information required by the equation is the initial activity (N_{o}), the time elapsed since the initial activity was measured (t), and the half-life of the isotope (T_{½}).

- Select the isotope from the list at the top of the page; this provides the equation with the isotope's half-life. If your isotope is not on the list, you can still use the equation if you manually enter the half-life in the
**Half-life** textbox at the top of the page. You can get half-life values **here**.
- Next enter the initial activity, N
_{o}. It is not necessary to worry about units here, just keep in mind that the units for the final activity will be the same as for the initial activity.
- Enter the time elapsed, t, since the initial activity was measured.
- Select the correct time unit. If the time unit is not available, you will have to convert the time elapsed to a unit that is available.
- Click the
**Calculate** button and the final activity is displayed.

**An example:**

You purchase 9.25 µCi of P-32, but it sits for 9 days before you get a chance to use it. How much of the original 9.25 µCi is left?

- Select
**Phosphorus 32 **from the isotope list. **14.26** and **d** show up in the **Half-life** and **Half-life time unit** textboxes.
- Enter
**9.25** in the **Initial activity (N**_{o}) textbox.
- Enter
**9 **in the **Decay time (t)** textbox and select the **d** radio button.
- Click the
**Calculate** button and the answer **5.97** is received in the **Final activity (N)** textbox.

__Advanced:__

You can use the equation in reverse to find out the initial activity if you know the current activity. For example, you have 5.97 µCi of P-32 now and you want to know how much was there 9 days ago. Enter **5.97** in the **Initial activity (N**_{o}) textbox and **-9** in the **Decay time (t)** textbox. **Calculate**shows that you had **9.25** µCi 9 days ago.