How long will Uranium-235 need to be stored to be considered safe at 0.10 percent of the original level?

To determine how long Uranium-235 (U-235) must be stored to reach 0.10 percent of its original level, we need to use the concept of half-life, which is the time it takes for half of the radioactive isotope to decay. The half-life of U-235 is approximately 703.8 million years.

To find the time required for the activity to drop to 0.10 percent of its original level, we can use the formula which relates remaining quantity to the number of half-lives elapsed:

Remaining quantity = Initial quantity × (1/2)^(n)

where n is the number of half-lives. In this case, we need to set up the equation:

0.001 × Initial quantity = Initial quantity × (1/2)^(n)

This simplifies to:

0.001 = (1/2)^(n)

Taking the logarithm of both sides can help us solve for n:

n = log(0.001) / log(0.5)

Calculating this gives us approximately n ≈ 9.9658, meaning around 10 half-lives are required to reach 0.10 percent of the original U-235 quantity.

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