Question

The half-life of Radium-226 is 1590 years. If a sample contains 500mg, how many mg will remain after 4000 years? Give your answer accurate to at least 2 decimal places.

Answer 1

4000 / 1590 = 2.52 half lives

500 mg * 1/2^2.52 = x where x is the amount left after 2.52 half-lives

(1/2)^2.52 = y where y is the needed fraction

2.52 ln 1/2 = ln y

2.52 * -.693 = -1.746 = ln y

y = .174

And 500 * .174 = 87 mg left after 2.52 half-lives

Check:

.5^2.52 = .174