Question

'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?

Answer 1

The amount of `""^14 C` will be reduced to `1/32` (which is `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.