'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?

1 Answer
Simon M. · David G.
Nov 24, 2016

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.

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