If you start with 100.0 g of carbon-14, how much will remain after 4 half-lives?

To determine how much carbon-14 remains after four half-lives, it's essential to understand the concept of a half-life. A half-life is the time required for half of a sample of a radioactive substance to decay.

Starting with 100.0 g of carbon-14, after the first half-life, you would have half of the original amount remaining, which is 50.0 g. After the second half-life, you take half of that amount, resulting in 25.0 g remaining. Continuing this process, after the third half-life, you would have 12.5 g left. Finally, after the fourth half-life, you take half of the 12.5 g, yielding 6.25 g remaining.

Therefore, after four half-lives, the amount of carbon-14 left is 6.25 g. This step-by-step halving process illustrates the exponential decay characteristic of radioactive isotopes, allowing you to quantify remaining amounts accurately over successive half-lives.