Final answer:
After 10.5 years, which is 5 half-lives of Cesium-134 with a half-life of 2.1 years, a starting sample of 25.00 g will decay to approximately 0.78125 g. Therefore, the correct answer is D. 0.078 g, rounded to three decimal places.
Step-by-step explanation:
The decay of radioactive isotopes is governed by the concept of half-life, which specifies the time it takes for half of the original amount of the isotope to decay. To determine the remaining amount of Cesium-134 after a certain period, you can use the formula for exponential decay, taking into account the number of half-lives that have passed.
Calculating the Remaining Cesium-134
The half-life of Cesium-134 is 2.1 years. We are looking to find the remaining mass after 10.5 years, which is exactly 5 half-lives (since 10.5 divided by 2.1 equals 5). Using the concept of half-life:
- After 1 half-life (2.1 years), 12.50 g remains.
- After 2 half-lives (4.2 years), 6.25 g remains.
- After 3 half-lives (6.3 years), 3.125 g remains.
- After 4 half-lives (8.4 years), 1.5625 g remains.
- After 5 half-lives (10.5 years), we divide by 2 once more to get 0.78125 g.
Thus, the correct answer is D. 0.078 g (rounded to three decimal places).