Radon-222 has a half-life of 3.8 days. How many half-lives will it take for an 11 g sample to be reduced to 2.

Question

Radon-222 has a half-life of 3.8 days. How many half-lives will it take for an 11 g sample to be reduced to 2.75 g?

Answer 1

11 * 0.5^n = 2.75, when n = number of half-lives.

Rewrite this as 0.5^n = (2.75/11) and take the log of both sides.

n * ln(0.5) = ln(2.75/11) -->n = ln(2.75/11)/ln(0.5).