Question

The half-life of tritium (hydrogen-3) is 12.3 years. If 56.2 mg of tritium is released from a nuclear power plan during the course of an accident, what mass of the nuclide will remain after 100. years?

Answer 1

To find the mass of tritium remaining after 100 years, we calculate the number of half-lives in that period and use the decay formula. With a half-life of 12.3 years, there are about 8.13 half-lives in 100 years, which leaves approximately 0.22 mg of tritium from the initial 56.2 mg.

Step-by-step explanation:

To determine the mass of tritium (hydrogen-3) that will remain after 100 years given its half-life of 12.3 years, we can use the concept of radioactive decay. The question asks how much of the original 56.2 mg of tritium will remain after 100 years. To solve this, we calculate the number of half-lives that occur in 100 years, which is 100 years ÷ 12.3 years/half-life = approximately 8.13 half-lives.

Now, for each half-life, the amount of the nuclide remaining is halved. Therefore, the remaining mass can be determined using the formula:

Remaining mass = Initial mass × (1/2)Number of half-lives.

Plugging in the values:

Remaining mass = 56.2 mg × (1/2)8.13

By calculating this, we find the mass of tritium remaining after 100 years is approximately 0.22 mg.