Final answer:
Approximately 47.15 grams of the sample will be remaining after 100 years.
Step-by-step explanation:
To calculate how much of the sample will be remaining after 100 years, we can use the half-life formula:
Remaining mass = Initial mass * (1/2)^(t/h)
where:
- Remaining mass is the mass of the sample after time t
- Initial mass is the mass of the sample at the beginning
- t is the time in years
- h is the half-life of the isotope in years
In this case, the initial mass is 50 grams, the time is 100 years, and the half-life is 1601 years. Plugging these values into the formula:
Remaining mass = 50 * (1/2)^(100/1601)
Calculating this expression gives us the remaining mass:
Remaining mass ≈ 50 * 0.943
Remaining mass ≈ 47.15 grams
Therefore, approximately 47.15 grams of the sample will be remaining after 100 years.