How can radioactivity change depending on the number of nuclei? [closed]

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.)