The half-life of carbon-14 is 5730 years. How long does it take for 3.6 grams of carbon-14 to be reduced to 0?

1 Answer
Bio
Mar 31, 2016

It takes an indefinitely long time.

Explanation:

For every half-life that passes, the mass of the carbon-14 is reduced by half. Suppose there were x amount of C-14 initially.

After 1 half-life, the amount of C-14 left is x/2.

After 2 half-life, the amount of C-14 left is x/4.

After 3 half-life, the amount of C-14 left is x/8.

After n half-life, the amount of C-14 left is x/(2^n).

Notice that the amount of C-14 left (x"/"2^n) can be brought as close as we like to zero, by letting n be a sufficiently large number. However, it will never reach zero no matter what n we use.

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