Strontium-90 is radioactive and has a half life of 28.8 years. Calculate the activity of a 4.9mg sample of strontium-90. Give your answer in becquerels and in curies. Be sure your answer has the correct number of significant digits.BqCi

To calculate the activity of a radioactive sample, we need to know the number of atoms in the sample and the decay constant of the isotope.

1. First, we need to calculate the number of atoms in the sample. The atomic mass of strontium-90 is approximately 90 g/mol. Therefore, a 4.9 mg sample is 4.9 x 10^-3 g.

   Number of moles = mass (g) / molar mass (g/mol) = 4.9 x 10^-3 g / 90 g/mol = 5.44 x 10^-5 mol

   Since 1 mol contains Avogadro's number (6.022 x 10^23) of atoms, the number of atoms in the sample is:

   Number of atoms = moles x Avogadro's number = 5.44 x 10^-5 mol x 6.022 x 10^23 atoms/mol = 3.27 x 10^19 atoms

2. Next, we need to calculate the decay constant. The decay constant (λ) is related to the half-life (t1/2) by the equation:

   λ = ln(2) / t1/2 = 0.693 / 28.8 years = 0.024 yr^-1

3. Finally, we can calculate the activity (A), which is the product of the decay constant and the number of atoms:

   A = λN = 0.024 yr^-1 x 3.27 x 10^19 atoms = 7.85 x 10^18 decays/yr

   Since 1 Bq is defined as one decay per second, and there are approximately 3.15 x 10^7 seconds in a year, the activity in becquerels is:

   A = 7.85 x 10^18 decays/yr x 1 yr / 3.15 x 10^7 s = 2.49 x 10^11 Bq

   And since 1 Ci is defined as 3.7 x 10^10 decays per second, the activity in curies is:

   A = 2.49 x 10^11 Bq x 1 Ci / 3.7 x 10^10 Bq = 6.73 Ci

So, the activity of a 4.9 mg sample of strontium-90 is approximately 2.49 x 10^11 Bq or 6.73 Ci.