Strontium-90 is radioactive and has a half life of 28.8 years. Calculate the activity of a 8.8mg sample of strontium-90. Give your answer in becquerels and in curies. Be sure your answer has the correct number of significant digits.

To solve this problem, we need to know a few key pieces of information:

1. The half-life of Strontium-90, which is given as 28.8 years.
2. The mass of the sample, which is given as 8.8 mg.
3. The atomic mass of Strontium-90, which is approximately 89.907 g/mol.
4. Avogadro's number, which is 6.022 x 10^23 atoms/mol.
5. The definition of a Becquerel (Bq), which is one decay per second.
6. The definition of a Curie (Ci), which is 3.7 x 10^10 decays per second.

Step 1: Convert the mass of the sample to moles. 8.8 mg = 0.0088 g 0.0088 g / 89.907 g/mol = 9.79 x 10^-5 mol

Step 2: Convert moles to number of atoms using Avogadro's number. 9.79 x 10^-5 mol x 6.022 x 10^23 atoms/mol = 5.89 x 10^19 atoms

Step 3: Use the half-life to calculate the decay constant (λ). λ = ln(2) / half-life = 0.693 / 28.8 years = 0.024 yr^-1 We need to convert this to seconds because a Becquerel is defined as one decay per second. λ = 0.024 yr^-1 x (1 year / 3.154 x 10^7 seconds) = 7.61 x 10^-10 s^-1

Step 4: Calculate the activity in Becquerels. Activity = λ x number of atoms = 7.61 x 10^-10 s^-1 x 5.89 x 10^19 atoms = 4.48 x 10^10 Bq

Step 5: Convert the activity to Curies. 1 Ci = 3.7 x 10^10 Bq Activity = 4.48 x 10^10 Bq x (1 Ci / 3.7 x 10^10 Bq) = 1.21 Ci

So, the activity of an 8.8 mg sample of Strontium-90 is approximately 4.48 x 10^10 Bq or 1.21 Ci.