Question

If one starts with 264 carbon-14 atoms, how many years will pass before there will be only one carbon-14 atom? Write this number here, and don’t use scientific notation. (Hint: it’s 63 half-lives of carbon-14.)

Answer 1

Carbon-14 has a half-life of approximately 5730 years. If we start with 264 carbon-14 atoms, we can calculate the number of half-lives it would take for the number of atoms to reduce to 1.

63 half-lives would mean that the original number of atoms is divided by 2 for each half-life.

So, the number of atoms remaining after 63 half-lives would be:

264 / (2^63)

Calculating this value, we find that it is approximately:

0.00000000000005684345

Since we are looking for the number of years until there is only one carbon-14 atom remaining, and each half-life is approximately 5730 years, we can multiply the number of half-lives by the length of each half-life:

63 * 5730 = 361,110 years.

Therefore, it would take approximately 361,110 years for the number of carbon-14 atoms to reduce to one.