Answer :
To determine the remaining quantity of Cs-137 after 8 years, the decay formula is used with the given half-life of 30.17 years. Approximately 6.69 kg of the initial 8.4 kg of Cs-137 will remain.
The question involves the concept of radioactive decay, focusing on calculating the remaining mass of a radioactive isotope, Cesium-137 (Cs-137), after a certain period based on its half-life. To find the remaining quantity of Cs-137 after 8.0 years, we can apply the exponential decay formula, where the amount remaining can be calculated using the initial mass and the number of half-lives that have passed.
The formula for radioactive decay is: A = [tex]A_0 \times (1/2)(t/t_{1/2})[/tex]
- A is the final activity
- A₀ is the initial activity
- t is the time elapsed
- Initial mass of Cs-137= 8.4 kg
- Half-life of Cs-137= 30.17 years
- Time elapsed, t = 8.0 years
Number of half-lives (n) = t / [tex]t_{1/2[/tex] = 8.0 years / 30.17 years = 0.2653 half-lives.
Mass remaining is thus: A = 8.4 kg * (1/2)0.2653
After calculations: A ≈ 6.69 kg
This means that after 8 years, there will be approximately 6.69 kg of Cs-137 remaining from the initial 8.4 kg released.
