Practice Problem 7

Calculate the fraction of ¹⁴C that remains in a sample after eight half-lives.

Solution

Half of the ¹⁴C  present initially decays during the first half-life, half of what is left decays during the second half-life, and so on.  The ¹⁴C   left after eight half-lives is equal to one-half raised to the eighth power:

(1/2)⁸ = 0.00391

Less than 0.4% of the original  is left after eight half-lives.