The half-life of radium is 1620 years. If a laboratory has 12 grams of radium, how long will it take before it has 8 grams of radium left?

Julius
Dec 22, 2017

#1**+2 **

OK....we can solve this :

8 = 12* (1/2)^{t/1620 } where t is the time (in years) we are looking for

Divide both sides by 12

8/12 = (1/2)^{t/1620}

2/3 = (1/2)^{t/1620} take the log of both sides

log (2/3) = log(1/2)^{t/1620} and we can write

log(2/3) = (t / 1620) * log (1/2) divide both sides by log(1/2)

log (2/3) / log (1/2) = t / 1620 multiply both sides by 1620

1620 * log (2/3) / log (1/2) = t ≈ 947.6 ≈ 948 years

CPhill
Dec 22, 2017