How many half-lives will it take for a 50 gram sample of carbon-14 to decay to 6.25 grams?

To determine how many half-lives it will take for a 50 gram sample of carbon-14 to decay to 6.25 grams, you can follow this process:

Each half-life is the period over which half of the material decays. If you start with 50 grams, after one half-life, you will have 25 grams remaining, as half of the sample has decayed.

After a second half-life, the 25 grams will reduce to 12.5 grams.

Then, after a third half-life, the 12.5 grams will decay to 6.25 grams.

Therefore, it takes three half-lives for the original 50-gram sample to reduce to 6.25 grams. Each half-life you consider results in the remaining amount being halved, which leads you from 50 grams to 25 grams, then to 12.5 grams, and finally achieving the desired 6.25 grams after three intervals.

This logical deduction clarifies that the answer is indeed three half-lives.