A 4.50-mg sample of a newly discovered radioactive nuclide was analyzed and found to contain only 3.25 mg after a period of 25.9 h.What is the half-life of the nuclide?

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

N = N₀e^(-λt)

Where:
N₀ = initial quantity
N = quantity after time t
λ = decay constant
t = time elapsed

We know that N₀ = 4.50 mg and N = 3.25 mg after 25.9 h. We can solve for λ:

N/N₀ = e^(-λt)
3.25/4.50 = e^(-λ*25.9)
0.722 = e^(-λ*25.9)
ln(0.722) = -λ*25.9
λ = -ln(0.722)/25.9
λ = 0.0274 h^-1

Now we can use the formula for half-life:

t(1/2) = ln(2)/λ
t(1/2) = ln(2)/0.0274
t(1/2) = 25.3 h

Therefore, the half-life of the nuclide is 25.3 h, which is closest to choice B (55.2 h).

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