# Uranium-238 decays very slowly with a half life of 4.5 billion years. what percentage of a sample of uranium-238 would remain after 13.5 billion years?

Apr 25, 2018

$\left(\frac{1}{8}\right)$ or 12.5% of the mass left.

#### Explanation:

The mass of Uranium halves every 4.5 billion years, so 13.5 billion years= 3 half-lives.

$M = {M}_{0} \times {\left(\frac{1}{2}\right)}^{n}$

Is the equation that describes the decay, where ${M}_{0}$ is the initial mass and $n$ is the number of half-lives passed.

So if 3 half-lives have passed:

$M = {M}_{0} \times {\left(\frac{1}{2}\right)}^{3}$

$M = {M}_{0} \times \left(\frac{1}{8}\right)$

$M = \left(\frac{1}{8}\right) {M}_{0}$

So there will be $\left(\frac{1}{8}\right)$ of the original mass left after 13.5 billion years, or 12.5% of the mass left