The half-life of ³⁰P is 2.50 minutes. If a sample of ³⁰P has 1.60 × 10¹⁰ nuclei present, what is its activity?

Question

Quizplus · Accepted Answer

The formula for activity is:
Activity = λN
where λ is the decay constant and N is the number of radioactive nuclei. 
First, we need to find the decay constant (λ):
t1/2 = 2.50 minutes
We know that the half-life (t1/2) is related to the decay constant (λ) as follows:
t1/2 = ln(2)/λ
Solving for λ, we get: 
λ = ln(2)/t1/2 = ln(2)/2.50 min = 0.2773 min^-1
Now we can calculate the activity:
Activity = λN = (0.2773 min^-1)(1.60 × 10^110) = 7.43 × 10^17 Bq = 7.4 × 10^17 Bq (to 2 significant figures)

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