The nuclide ¹⁸⁸W decays by a first-order process with a rate constant of 1.0 × 10^-2 d^-1.How long will it take for 88% of the initial amount of ¹⁸⁸W to be consumed?

Question

Quizplus · Accepted Answer

The half-life (t1/2) can be determined using the following equation:
t1/2 = ln(2)/k

t1/2 = ln(2)/1.0 × 10-12 d-1
t1/2 = 6.93 × 1011 d

We can use the half-life to determine the time it takes for 88% of the initial amount to be consumed:
ln(Nt/N0) = -kt
ln(0.12) = -(1.0 × 10-12 d-1)t
t = ln(0.12)/(-1.0 × 10-12 d-1)
t = 210 d

Therefore, the answer is D) 210 d.

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The Nuclide ¹⁸⁸W Decays by a First-Order Process with a Rate