The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the amount. An initial amount of 3 grams of radium would decay to 2 grams in approximately
A) 12200 years
B) 14200 years
C) 15200 years
D) 17200 years
E) 18200 years

Question

Quizplus · Accepted Answer

Using the formula for radioactive decay: A = A0*e^(-kt) where A is the final amount, A0 is the initial amount, k is the decay constant, and t is time, we can solve for t:

A/A0 = e^(-kt)
2/3 = e^(-k*24200)
ln(2/3) = -k*24200
k = 2.86x10^-5

Now we can solve for t when A=2:

2/3 = e^(-2.86x10^-5*t)
ln(2/3) = -2.86x10^-5*t
t = 14202 years (rounded to the nearest year)

Therefore, the answer is B) 14200 years.

The Half-Life of Plutonium 239 Is 24,200 Years