# How can I calculate the half life of an element?

##### 1 Answer

Nuclear half-life expresses the time required for half of a sample to undergo radioactive decay. Exponential decay can be expressed mathematically like this:

**(1)**, where

**t** years;

So, if a problem asks you to calculate an element's half-life, it must provide information about the initial mass, the quantity left after radioactive decay, and the time it took that sample to reach its post-decay value.

Let's say you have a radioactive isotope that undergoes radioactive decay. It started from a mass of **67.0 g** and it took **98** years for it to reach **0.01 g**. Here's how you would determine its half-life:

Starting from **(1)**, we know that

Therefore, its half-life is

So, the initial mass gets halved every **7.72** years.

Sometimes, if the numbers allow it, you can work backwards to determine an element's half-life. Let's say you started with **100 g** and ended up with **25 g** after 1,000 years.

In this case, since 25 represents **1/4th** of 100, two hal-life cycles must have passed in 1,000 years, since

**another**

So,