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What is the half-life for the first-order decay of phosphorus- 32$?\left(_{15}^{32} {P} \longrightarrow_{16}^{32} {s}+{e}^{-}\right)$ The rate constant for the decay is $4.85 \times 10^{-2} {day}^{-1}$

14.29 days

Chemistry 102

Chapter 12

Kinetics

Rice University

University of Maryland - University College

Brown University

Lectures

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So this question says, what is the half life for the first order decay of phosphorus 32. But then gives us the chemical equation for ah, this reaction. And then it gives us the rate constant for the decaying, which it says is 4.85 times 10 to the negative, two per day. And so to start here, um, we just have to remember what the, um, half life equation for first order reaction is. And from there it becomes pretty simple to answer to the question. So, um, it is t 1/2 equals, um, the natural log of two over cake. And so you remember the question gives us the value for Kay, so I'm just gonna fill that in so t 1/2 equals and natural log of two over K, which they say is four point eight, five times 10 to the negative, too. And then day to the negative one. Nick. And so from here, we can just put this into her calculator. And when we do that, see, we get well, I'm 14 point three, and then our units just become days, and that is our answer.

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