# If a substance has a half life of one million years, how much of its will be left after three million years? After four million years?

Nov 29, 2016

After 3 million years there will be 12.5% left. After 4 million, 6.25%.

#### Explanation:

The half-life of a substance is the amount of time it takes for half of that substance to decay. However, after two half-lives, half of the half remaining will decay, leaving you with one quarter of the original substance.

So, after 1 million years you will have 50% of the original substance remaining.

And, after 2 million years you will have 25% of the original substance remaining.

After 3 million years you will have 12.5% of the original substance remaining.

And after 4 million years you will have 6.25% of the original substance remaining.

You can generalize this to:

"Amount of substance" = "Initial amount" xx 1/(2^("number of half lives"))

So for 0 half-lives, you have $\text{Initial amount" xx 1/2^0 = "Initial amount} \times 1$

One half-life gets you $\text{Initial amount" xx 1/2^1 = "Initial amount} \times \frac{1}{2}$

For 3.323 half-lives: $\text{Initial amount" xx 1/2^3.323 = "Initial amount} \times \frac{1}{10}$