Cesium-137 is radioactive and has a half life of 30. years. Calculate the activity of a 9.5mg sample of cesium-137. Give your answer in becquerels and in curies. Be sure your answer has the correct number of significant digits.BqCi

To solve this problem, we need to know a few things:

1. The half-life of Cesium-137, which is given as 30 years.
2. The mass of the sample, which is given as 9.5 mg.
3. The atomic mass of Cesium-137, which is approximately 137 g/mol.
4. Avogadro's number, which is approximately 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. 9.5 mg is 0.0095 g. So, the number of moles is 0.0095 g / 137 g/mol = 6.934 x 10^-5 mol.

Step 2: Convert moles to number of atoms using Avogadro's number. 6.934 x 10^-5 mol x 6.022 x 10^23 atoms/mol = 4.17 x 10^19 atoms.

Step 3: Use the half-life to calculate the decay constant. The decay constant (λ) is ln(2) / half-life. Converting the half-life to seconds (since our activity units are in decays per second), we get 30 years x 365.25 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute = 9.46 x 10^8 seconds. So, λ = ln(2) / 9.46 x 10^8 s = 7.33 x 10^-10 s^-1.

Step 4: Calculate the activity in Bq. The activity (A) in Bq is λ x number of atoms = 7.33 x 10^-10 s^-1 x 4.17 x 10^19 atoms = 3.06 x 10^10 Bq.

Step 5: Convert the activity to Ci. 1 Ci = 3.7 x 10^10 Bq, so 3.06 x 10^10 Bq = 3.06 x 10^10 Bq / 3.7 x 10^10 Bq/Ci = 0.827 Ci.

So, the activity of a 9.5 mg sample of Cesium-137 is approximately 3.06 x 10^10 Bq or 0.827 Ci.