Answer
$25$ grams
Work Step by Step
Having a half-life of 3 hours means that the amount of radioactive element is reduced to one-half of its size after 3 hours.
Thus, if a nuclear reactor has an initial amount of $400$ grams of radioactive material, then the amount will be reduced to:
After 3 hours: $\dfrac{400}{2}$ grams = $200$ grams
After 6 hours: $\dfrac{200}{2}$ grams = $100$ grams
After 9 hours: $\dfrac{100}{2}$ grams = $50$ grams
After 12 hours: $\dfrac{50}{2}$ grams = $25$ grams
Therefore, there will be $25$ grams of radioactive material in the nuclear reactor after 12 hours.
