# How do you calculate nuclear half life?

##### 1 Answer

You calculate the half-life from the amount of material that disappears in a given time.

Half-life (

Radioactive nuclei decay according to the equation:

*Equation 1*:

*decay constant*. Each nucleus has its own decay constant.

The equation for half-life is

*Equation 2*:

We can combine these two equations to get

*Equation 3*:

*EXAMPLE*:

A 50 g sample of radium–226 decays to 5.7 g after 5000 years. What is the half-life of radium–226?

*Solution*:

Let’s use Equation 3:

Take the natural logarithm of each side

The half-life of radium–226 is 1600 yr.