Question

Radium-226 has a half-life of 1660 years. How many years does it take a radium sample to decay to 55% of the original amount? Round your answer to the nearest year.

Answer 1

1432 years

Explanation:

A(t) = I(0.5)^t/t1/2

Where t1/2 = half life = 1660

Final amount, A(t) = 0.55 of its original amount =. 0.55I

Hence, we have

0.55I = I(0.5)^t/1660

Take the log of both sides

Log(0.55) = log(0.5)^t/1660

t/1660 = log(0.55) / log(0.5)

t/1660 = 0.8624964

t = 0.8624964 * 1660

t = 1431.7441

t = 1432(nearest whole number)