'Radiocarbon dating' is used to find the age of formerly-living things. The halflife of carbon-14 is 5730 years. By how much will the original amount of ""^14C decrease after 5 halflives?

Nov 24, 2016

The amount of ""^14 C will be reduced to $\frac{1}{32}$ (which is $\frac{1}{2} ^ 5$) of the original amount after 5 half lives.

Explanation:

Every half life period the amount of substance will reduce by half. For example after one half life of 5730 years the amount of ""^(14)C present within a sample will have halved.

If you start with $100$ $g$ of ""^(14)C, after one half life there will be $50$ $g$ left.
After 2 half lives (11460 years) there will be $25$ $g$ left.
After 3 half lives (17190 years) there will be $12.5$ $g$ left.
After 4 half lives (22920 years) there will be $6.25$ $g$ left
and after 5 half lives (28650 years) there will be $3.125$ $g$ left

This technique is only suitable for up to about 50 000 years as the quantities of ""^(14)C present in former living things is very small, and after ~8 half lives the quantity is too small.