A certain substance has a half-life of 5.0 hours. How many nuclei of the substance are required to give an initial activity of 6.0 μCi? 1 Ci = 3.7 × 10¹⁰ Bq.

Question

Quizplus · Accepted Answer

First, we need to convert the initial activity from μCi to Bq:
6.0 μCi x (3.7 x 10^10 Bq/1 Ci) = 2.22 x 10^9 Bq

Next, we can use the formula for radioactive decay: 
N = N0 (1/2)^(t/T)

where N0 is the initial number of nuclei, N is the final number of nuclei after time t, T is the half-life, and the exponent is the number of half-lives that have elapsed (t/T).

Since we want to find N0, we can rearrange the formula:
N0 = N / (1/2)^(t/T)

Plugging in the values we have:
N0 = (2.22 x 10^9 Bq) / (1/2)^(0/5) 
(Note that t=0, since we are starting at the initial activity)

Simplifying:
N0 = 2.22 x 10^9 Bq

Finally, we convert back to the original units of nuclei:
N0 = 2.22 x 10^9 Bq x (1 Ci/3.7 x 10^10 Bq) = 5.8 x 10^19 nuclei

Therefore, the answer is choice A: 5.8 x 10^19.

A Certain Substance Has a Half-Life of 5