Final answer:
The half-life of the sample is 12 years.
Step-by-step explanation:
The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the activity of the sample decreases from 10,000 Bq to 1250 Bq in 12 years, so the half of the original activity is 5,000 Bq. Therefore, the half-life of the sample can be calculated by finding the time it takes for the activity to decrease to half of the original value.
To find the half-life, we can use the formula:
T1/2 = t * log2(N0/Nt)
Where T1/2 is the half-life, t is the time taken (12 years), N0 is the initial activity (10,000 Bq), and Nt is the final activity (5,000 Bq).
Plugging in the values, we get:
T1/2 = 12 * log2(10,000/5,000) = 12 * log2(2) = 12 * 1 = 12 years
Therefore, the half-life of the sample is 12 years.