Please help me find the half life of radon.?

Question

The half-life of radon-222 is 3.8 days. If a sample currently has 3.1 grams of radon-222, how much radon-222 did this sample have 15.2 days ago?

Answer 1

There is a formula for half-life problem, but since you don't have it here, you can manually calculate half-life.

For ever 3.8 days, R-222 reduced by half. So whatever you have now, you would have double that 3.8 days ago. Therefore,

For t = 0 to - 3.7 days ago, R-222 = 3.1 * 2 = 6.2 grams

for t = -3.8 to 7.5 days ago, R-222 = 6.2 * 2 = 12.4 gr

for t = - 7.5 to -11.4 days ago, R-222 = 12.4 * 2 = 24.8 gr

for t = 11.4 to 15.2 days ago, R-222 = 24.8 *2 = 49.6 grams :Ans.

Answer 2

The concentration halves in 3.8 days. There a 4 x 3.8 days in 15.2 days, therefore the answer is 2^4 x 3.1 = 16 x 3.1 = 49.6g.