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Problem 21 Hard Difficulty

After 2.00 days, the activity of a sample of an unknown type radioactive material has decreased to 84.2% of the initial activity. What is the half - life of this material?

Answer

8.06 d

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Elyse G.

Cornell University

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Hope College

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McMaster University

Video Transcript

from number 21 after two days. Uh, samples activity has reduced, so it's only 84.2% of the original When we want to know what was 1/2 life. I like to use this equation. The one weird's the number of nuclei. Oh, you think the original number of nuclei 1/2 of the number of ways like the number of half lifes. I think that's just a easy equation to deal with. So I know I'm not dealing with number nuclear, the rest male activity. But if I just multiply both sides of this equation by the Dick Avery now, this is activity. So now this is the original activity. 1/2 raised to the number of half lifes will give me the new activity. Oh, and this problem, I know that it's 84.2% of what it waas. So if it was originally are one No, it was originally are not. Now it's 0.84 two times, Cornel. So if I can just find with number of half lifes, that is, I can figure out what the half life ISS because you know my gun. Divide both sides. We are one, and I just of math. Um all right, take the log of both sides. So the log of 0.842 over here, the log of 1/2 raised the end. And if you remember your long rules this raising two exponents that just brings it in the front. So this is n log of 1/2 over here. Still log 0.842 Bye. Divide both sides by the water of 1/2. I got in by itself. So now I just need to the calculator log of 0.84 to divide by log of 1/2 and I get 0.248 Remember what that is, though That's the number of half Life's That's not the half life. So if I, you know, so it's is less than half life, so its point, you know, it's point 248 oh, 1/2 life you're here. And that was remember, this was two days to do that. So my half life is eight point of six, and that, too, was in days of this isn't days

University of Virginia
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Meghan M.

McMaster University