Question

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?

Answer 1

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.