(doubling-time formula) if k < 0, then T = ln(.5)/k. The half-life of radium-226 is 1590 years. A certain sample has a weight of 2g. How much will this sample weigh in 5000 years? The half-life of radium-226 is 1590 years. A certain sample has a weight of 2g. How much will this sample weigh in 5000 years?