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 12 grams of plutonium-239 to decay to 2 grams ?
Round your answer to the nearest hundreds.

A)31,600 years
B) 15,800 years
C) 126,200 years
D) 63,100 years
E) 63,200 years

Question

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 12 grams of plutonium-239 to decay to 2 grams  ?
Round your answer to the nearest hundreds.
 
A)31,600 years
B) 15,800 years
C) 126,200 years
D) 63,100 years
E) 63,200 years

Quizplus · Accepted Answer

Using the formula for exponential decay, we can set up the following equation:
N(t) = N0 (1/2)^(t/T)
where N0 is the initial amount (12 grams), N(t) is the final amount (2 grams), t is the time elapsed (in years), and T is the half-life (24,400 years).

Substituting the values given, we get:

2 = 12 (1/2)^(t/24,400)

Taking the natural logarithm of both sides, we can solve for t:

ln(2) = ln(12) - (t/24,400)ln(1/2)

t = -24,400 ln(2) / ln(1/2) + 24,400 ln(12) / ln(1/2)

t ≈ 63,104 years

Rounding to the nearest hundreds, we get 63,100 years, which is answer choice D.

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