# Half life of potassium-40,is approximately 1.25 billion years.what will be the fraction of radioactivity left after 5 billion years?

Apr 20, 2018

$\frac{1}{16} {P}_{0}$

#### Explanation:

${P}_{0}$ initial value of potassium

The half-life of potassium is 1.25 billion years. How many times does 1.25 go in 5 billion years?

$\frac{5}{1.25} = 4$

There are $4$ half-lives.

1) $\frac{1}{2} {P}_{0}$

2) $\frac{1}{2} \left(\frac{1}{2} {P}_{0}\right)$

3) $\frac{1}{2} \left(\frac{1}{2} \cdot \frac{1}{2} {P}_{0}\right)$

4) $\frac{1}{2} \left(\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} {P}_{0}\right)$

So after five billion years, it will be $\frac{1}{16} {P}_{0}$.