Plutonium-239 is used as a fuel for some nuclear reactors and also as the fissionable material in atomic bombs. It has a half-life of 24,400 years. How long will it take 14 grams of plutonium-239 to decay to 1 grams? Select the correct answer rounded to the nearest integer.
A)23,250 years
B)93,000 years
C)92,900 years
D)185,800 years
E)46,500 years

Question

Quizplus · Accepted Answer

To solve this problem we use the formula for radioactive decay: 
N(t) = N0 * (1/2)^(t/T) 
Where N(t) is the amount remaining after time t, N0 is the initial amount, T is the half-life, and (1/2)^(t/T) is the fraction remaining after time t. 
We are given N0 = 14 grams, N(t) = 1 gram, and T = 24,400 years. 
Substituting these values we get: 
1 = 14 * (1/2)^(t/24,400) 
(1/2)^(t/24,400) = 1/14 
Taking the natural logarithm of both sides: 
ln[(1/2)^(t/24,400)] = ln(1/14) 
(t/24,400) * ln(1/2) = ln(1/14) 
t = 24,400 * ln(1/14) / ln(1/2) 
Using a calculator we get t ≈ 92,900 years. 
Therefore, the best choice is C, rounded to the nearest integer.

Plutonium-239 Is Used as a Fuel for Some Nuclear Reactors