To determine the time required for 504 grams of plutonium-239 to decay down to 63 grams, we can use the concept of half-lives.
The half-life of plutonium-239 is 24,100 years. The amount of plutonium-239 is reduced by half with each half-life.
Starting with 504 grams, let's find out how many half-lives it takes to reduce it to 63 grams:
- Half-life 1: 504 grams → 252 grams (after 24,100 years)
- Half-life 2: 252 grams → 126 grams (after 48,200 years)
- Half-life 3: 126 grams → 63 grams (after 72,300 years)
It takes 3 half-lives to decay from 504 grams to 63 grams.
Now, to find the total time:
3 half-lives × 24,100 years/half-life = 72,300 years
Therefore, the time required for 504 grams of plutonium-239 to decay to 63 grams is 72,300 years.