Question

Carbon-14 is radioactive, and has a half-life of 5,730 years. It’s used for dating archaeological artifacts. Suppose one starts with 264 carbon-14 atoms. After 5,730 years, how many of these atoms will still be carbon-14 atoms? Write this number in standard scientific notation here. (Hint: remember that 264/2 isn’t 232, it’s 263.)

Answer 1

After a half-life of 5,730 years, half of the carbon-14 atoms will have decayed. Therefore, the number of carbon-14 atoms remaining would be:

264 / 2 = 132

After another half-life of 5,730 years, half of the remaining 132 carbon-14 atoms would decay:

132 / 2 = 66

Following this pattern, we can continue halving the number of atoms for each subsequent half-life:

66 / 2 = 33
33 / 2 = 16.5 (approximately)

At this point, we can no longer have half of an atom. Therefore, after 5,730 years, there will be approximately 16 carbon-14 atoms remaining.

Writing this number in standard scientific notation, it would be:

1.6 x 10^1