Radioactive decay: 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 × Bq.

Question

Radioactive decay: 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 ×  Bq.

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

N(t) = N0 * (1/2)^(t/T)

where N(t) is the number of nuclei after time t, N0 is the initial number of nuclei, T is the half-life, and t is the elapsed time.

We know that the initial activity is 6.0 μCi, which is equal to 6.0 * 10^(-6) Ci or 6.0 * 10^(-6) * 3.7 * 10^(10) Bq = 2.22 * 10^5 Bq.

We can also find the decay constant, λ, using the half-life:

T = ln(2)/λ

λ = ln(2)/T = ln(2)/5.0 = 0.1386 h^(-1)

Now we can use the relationship between activity and number of nuclei:

A = λ * N

N = A/λ

At t=0, N=N0, so

N0 = 2.22 * 10^5 Bq / 0.1386 h^(-1) = 1.60 * 10^6 nuclei

Therefore, the answer is choice A, 5.8 × 10^5 nuclei.

Radioactive Decay: a Certain Substance Has a Half-Life of 5