Final answer:
To calculate the half-life of strontium-90, given a reduction in mass over 10 years, we use the formula for exponential decay and solve for the half-life. The calculation shows the half-life is approximately 28.8 years, which does not match any of the given options, suggesting a possible typo in the question or options.
Step-by-step explanation:
The student is asking to calculate the half-life of the isotope strontium-90 (9038Sr), given that a 0.500-g sample diminishes to 0.393 g in 10.0 years. We can use the half-life formula and the concept of exponential decay to solve this.
We know that the amount of a substance remaining after a certain number of half-lives can be expressed as:
(Remaining mass) = (Initial mass) × (1/2)(Time elapsed / Half-life)
So in the case of strontium-90, we have:
0.393 g = 0.500 g × (1/2)(10.0 years / Half-life)
When we solve for the half-life, we get:
Half-life = 10.0 years / (log(0.393/0.500) / log(0.5))
Plugging these values into a calculator, we find that the half-life of 9038Sr is approximately 28.8 years.
However, the options provided do not include this value. It might be a case where the problem has a typo or the given options are incorrect.
Based on the provided options, none of them are the correct calculation of half-life for 9038Sr as per the question's data. In such a case, it is suggested to double-check the problem statement or consult additional sources for the correct half-life value of 9038Sr if the provided answer options must be used.