Question

The amount of a sample remaining after t days is given by the equation mc005-1.jpg, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
1.5 days
2.5 days
9.4 days
21.1 days

Answer 1

Use A/A0 = (1/2)^{t/h}. So 0.18 = (1/2)^{t/3.8}. Take logs:
t = 3.8 * ln(0.18)/ln(0.5) ≈ 3.8 * (−1.7148)/(−0.6931) ≈ 9.4 days.
Answer: 9.4 days.