Physics?? Atoms?? Half Life??

Question

Radon - 212 has a half-life of 24 minutes. Show that if you start with 96mg of radon-212 that you will have 91 mg of polonium-208 two hours later (and not 93 mg).

Answer 1

I'm assuming Radon-212 decays into Polonium-208 via alpha decay.

Remember that half-life is the term used to describe how much time it takes for half of a radioactive substance to decay.

Also, remember than 2 hours is 120 minutes. Since each half-life is 24 minutes long, 2 hours would be 5 half-lives.

So, what will follow is a "chart" showing how much Radon-212 is left and how much Polonium-208 is formed after each half-life.

0 half-lives 96mg Rn and 0 mg Po
1 half-life 48 mg Rn and 48 mg Po
2 half-lives 24 mg Rn and 72 mg Po
3 half-lives 12 mg Rn and 84 mg Po
4 half-lives 6 mg Rn and 90 mg Po
5 half-lives 3 mg Rn and 93 mg Po

I am not quite sure how your teacher has you show that there are 91 mg instead, but this is the basic reasoning behind how they got that there should be 93 mg of Po-208 made.

It will most likely take someone with more chemical knowledge than I to explain the loss of two milligrams of Polonium.