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What fraction of the $^{40} \mathrm{K}$ that was on Earth when it formed $4.5 \times 10^{9}$ years ago is left today?

0.0872

Physics 103

Chapter 31

Radioactivity and Nuclear Physics

Nuclear Physics

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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Well, our initial number off K 40 Adam is and not the initial. The initial number. The initial number off, uh, gave 40 is and not all right. And the current number is And, uh, and is the current number Karim's number. The right number off. Adams off Adams. Well, according to radioactive decay equation, we know date and equals and not and not is the original amount times e to the power minus. Lend a times t no, uh, we can write this secret gin and divided by and not is equal to speed to the power minus Lambda times. Um, t and we know it lender. It is decay. Constant is equal to zero point 693 Divided by half life, half life. Um, no, um, half life for K 40 uh, is one point to it. Multiply by 10 to the power mind years. Here, half life half life is equal to one point. Do eight. Multiply by 10 to the power mine years. All right. And the time he is given Time T is equal to 4.5 most of life. I tend to devour mine years, and hence the fraction is, um and not and not divided by n is the faction is equal to eat to the power Um minus zero point minus 0.6 mine three divided by half life, half life Multiply by t on DDE This equals you need to the power uh minus 0.6 mine three divided by well half life is one point. Do it multiply by 10 to the power mine years multiply by t He is 4.5 multiplied by 10 to the power mine ears and then for the fraction and not divided by n It's a cool too zero point on 0874 0874 So there's little point 0874 off the original key forties laughter today.

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