Uranium-238 forms Thorium-234 after radioactive decay and has a half-life of 4.5 × 10^9 years. How many years will it take to decay 75% of the initial amount?

4.5 × 10^10

4.5 × 10^9

9 × 10^9 years

None of these

To find the time it takes to decay 75% of the initial amount, we need to find the time it takes for 25% of the initial amount to remain.

Since the half-life is 4.5 × 10^9 years, after one half-life, 50% of the initial amount remains.

After two half-lives, 25% of the initial amount remains (50% of 50%).

Therefore, the time it takes to decay 75% of the initial amount is:

2 × half-life = 2 × 4.5 × 10^9 years = 9 × 10^9 years