Plutonium-239, a radioactive isotope often used as fuel in nuclear reactors, has a half-life of 24,100 years. Approximately how long would it take for 504 grams of plutonium-239 to decay to just 63 grams?(1 point)

Question

Responses

48,200 years
48,200 years

72,300 years
72,300 years

96,400 years
96,400 years

24,100 years

Answer 1

To determine how long it would take for 504 grams of plutonium-239 to decay to 63 grams, we can use the concept of half-lives.

1. Calculate the number of half-lives needed:

   • The starting amount is 504 grams.
   • We want to know how many half-lives it takes to reduce that to 63 grams.

   The decay can be analyzed as follows:

   • After 1 half-life: $504\text{ grams}\to 252\text{ grams}$
   • After 2 half-lives: $252\text{ grams}\to 126\text{ grams}$
   • After 3 half-lives: $126\text{ grams}\to 63\text{ grams}$

   Thus, it takes 3 half-lives to go from 504 grams to 63 grams.

2. Calculate the total time:

   • Each half-life of plutonium-239 is 24,100 years.
   • Therefore, for 3 half-lives, the total time is: $$3\times 24,100\text{ years}=72,300\text{ years}$$

So, the answer is 72,300 years.