How much Plutonium would have remained after 1 million years?

Question

The U.S. government spent nearly $10 billion planning and developing a nuclear waste facility at Yucca Mountain (Nevada), though the project was cancelled in 2011. The intent had been for the facility to store up to 77000 metric tons of nuclear waste safely for at least 1 million years. Suppose it had been successful and stored the maximum amount of waste in the form of plutonium-239 with a half-life of 24,000 years. how much plutonium would have remained after 1 million years?

Answer 1

F = 0.5n

F = fraction remaining

n = number of half lives that have elapsed = 1,000,000 yrs/24,000 yr/half life = 41.67 half lives elapsed

F = 0.5^41.67 = 2.8x10^-13

Amount remaining = 2.86x10^-13 x 7700 metric tons = 2.2x10^-8 metric tons remains