Question

Krypton- 87 has a rate constant of \(1.5 \times 10^{-4} \mathrm{~s}^{-1}\). What is the activity of a 2.00 -mg sample?

Short answer

Answer: The activity of the 2.00 mg sample of Krypton-87 is 2.06 x 10^4 Bq.

Step-by-step solution

Find the amount of Krypton-87 in moles

We are given the mass of Krypton-87 sample as 2.00 mg. We can convert this to moles by using the molar mass of Krypton-87, which is 87 g/mol. Amount (in moles) = (Mass of the sample) / (Molar mass of Krypton-87) Amount (in moles) = (2.00 x 10^{-3} g) / (87 g/mol)

Calculate the number of Krypton-87 nuclei

Now we can calculate the number of Krypton-87 nuclei using Avogadro's number (6.022 x 10^{23} atoms/mol). Number of Krypton-87 nuclei = (Amount in moles) x (Avogadro's number) Number of Krypton-87 nuclei = (2.00 x 10^{-3} g / 87 g/mol) x (6.022 x 10^{23} atoms/mol)

Calculate the activity of the Krypton-87 sample

Finally, we can find the activity by multiplying the number of Krypton-87 nuclei by the given rate constant. Activity (A) = (Number of Krypton-87 nuclei) x (Rate constant) Activity (A) = (2.00 x 10^{-3} g / 87 g/mol) x (6.022 x 10^{23} atoms/mol) x (1.5 x 10^{-4} s^{-1}) After calculating the above expression, we get: Activity (A) = 2.06 x 10^4 Bq The activity of the 2.00 mg sample of Krypton-87 is 2.06 x 10^4 Bq.