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I came across this problem. Please help me solve it.

A radioactive sample S1 having an activity of $5\ \mathrm{\mu Ci}$ has twice the number of nuclei as another sample S2 which has an activity of $10\ \mathrm{\mu Ci}$. The half lives of S1 and S2 can be

(A) 20 years and 5 years, respectively

(B) 20 years and 10 years, respectively

(C) 10 years each

(D) 5 years each

All through out my high school i was never introduced to the idea that radioactivity could change depending on the number of nuclei. Can someone throw some light on this?

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closed as too localized by David Z Jun 16 '12 at 23:04

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can someone solve and tell me the answer? –  Ashu Jun 16 '12 at 17:41
    
This is a site for conceptual questions about physics, not general homework help. We're not going to give you the answer, but we will help you as much as you're willing to help yourself. The answers you've already gotten give you some excellent hints. If you edit your question to ask about the specific physics concept that is giving you trouble, I'll be happy to reopen this so you can get additional help answers. See our FAQ and homework policy for more information. –  David Z Jun 16 '12 at 23:07
    
@DavidZaslavsky well i got the answer. The reason i asked someone to solve the problem is that i couldnt get what to do with the value of the given activity i.e 5 & 10 $u$Ci –  Ashu Jun 17 '12 at 13:28
    
You could ask that directly, then. Explain why you don't understand how those numbers are relevant (e.g. do you not know the definition of a Curie?), and ask someone for an explanation of that, and it'd be a perfectly fine question. But don't ask someone to solve the problem for you. –  David Z Jun 17 '12 at 20:31
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3 Answers 3

up vote 2 down vote accepted

The decay rate is $$\left|\frac{\mathrm{d}N}{\mathrm{d}t}\right| = \lambda N.$$

Half-life is $$\tau_{1/2}=\frac{\ln 2}{\lambda}.$$

I think you can figure it now.

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Activity is the rate of nuclear events from a sample, measured in something like disintegrations per second. Think about how this would change with the amount of material, and also how it would be affected by a different half-life.

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All through out my high school i was never introduced to the idea that radioactivity could change depending on the number of nuclei.

Radioactivity doesn't change depending on the number of nuclei. I'd assume S1 and S2 are different elements.

Now you can build two rate equations and solve for the unknown. You know that N1 (number of nuclei for S1) is 2*N2 (the number of nuclei in sample 2.)

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well the answer is A. i dont know how –  Ashu Jun 16 '12 at 12:57
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