How much mass of thorium-234 would remain after 96 days if the initial mass was 25 g?

To determine how much mass of thorium-234 remains after 96 days, it's essential to understand its half-life, which is about 24 days. The half-life is the time required for half of a given amount of a radioactive substance to decay.

Starting with an initial mass of 25 g, we can calculate how many half-lives fit into the 96-day period. By dividing 96 days by the half-life of 24 days, we find:

96 days ÷ 24 days/half-life = 4 half-lives

After each half-life, the mass of the substance is halved. Therefore, we can compute how much mass remains after 4 half-lives:

1. After the first half-life (24 days): 25 g → 12.5 g

2. After the second half-life (48 days): 12.5 g → 6.25 g

3. After the third half-life (72 days): 6.25 g → 3.125 g

4. After the fourth half-life (96 days): 3.125 g → 1.5625 g

Rounding 1.5625 g gives us