# How long will it take for 3/4 of the sample of 131 iodine that has half-life of 8.1 days?

##### 1 Answer

Since you didn't specify whether **3/4** of the sample remains or undergoes decay, I'll show you both cases.

Here's the equation for exponential decay used in nuclear half-life calculations

**t** years;

*First case* - **3/4** *of the sample undergoes radioactive decay*.

If **3/4** of the sample undergoes radioactive decay, you wil be left with **1/4** of the original sample. This means that

This implies that

Therefore,

It will take 16.2 days for **3/4** of your sample to undergo radioactive decay.

*Second case* - **3/4** *of the sample remains, i.e. does not undergo radioactive decay*.

The same principle applies in this case as well, only this time **1/4** of the sample will decay and **3/4** will remain. This means that

As a result,

It will take 3.36 days for **1/4** of the sample to undergo radioactive decay.