Final answer:
It will take approximately 106.6 million years for 10% of a 1000-gram sample of uranium-235 to decay, calculated using the radioactive decay formula and the half-life of uranium-235.
Step-by-step explanation:
The question asks how long it will take for 10% of a 1000-gram sample of uranium-235 to decay, given that the half-life of uranium-235 is 703,800,000 years. Using the decay formula A(t) = A0e-(ln(2)t/T), where A(t) is the amount of substance remaining after time t, A0 is the initial amount, T is the half-life, and ln is the natural logarithm:
- First, determine the remaining amount of uranium-235 after decay: A(t) = 1000 g * (1 - 0.10) = 900 g.
- Use the decay formula to solve for time t:
900 = 1000 * e-(ln(2)t/703800000)
ln(900/1000) = -(ln(2)t/703800000)
t = (ln(1000/900) * 703800000) / ln(2) - Calculate t: t ≈ (0.10536 * 703800000) / 0.69315 ≈ 106,594,859.6 years.
It will take approximately 106.6 million years for 10% of a 1000-gram sample of uranium-235 to decay.