Final answer:
Approximately 4.063 grams of the 8 gram sample of radium-223 would remain after 9 days.
Step-by-step explanation:
The half-life of radium-223 is approximately 11.43 days. To determine how much of an 8 gram sample of radium-223 would remain after 9 days, we can use the formula:
Final amount = Initial amount * (1/2)^(t/half-life)
where:
Final amount = remaining amount after time t
Initial amount = initial amount of the sample
t = time passed
half-life = half-life of the sample
Plugging in the values:
- Initial amount = 8 grams
- t = 9 days
- half-life = 11.43 days
Final amount = 8 * (1/2)^(9/11.43)
Final amount ≈ 4.063 grams
Approximately 4.063 grams of the 8 gram sample of radium-223 would remain after 9 days.