# 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
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 $\frac{x}{2}$.

After 2 half-life, the amount of C-14 left is $\frac{x}{4}$.

After 3 half-life, the amount of C-14 left is $\frac{x}{8}$.

After $n$ half-life, the amount of C-14 left is $\frac{x}{{2}^{n}}$.

Notice that the amount of C-14 left ($x \text{/} {2}^{n}$) 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.