The half-life of radon-222 is 3.8 days. If a sample currently has 3.1 grams of radon-222, how much radon-222 did this sample have 15.2 days ago?

A) 12.4 grams (WRONG)
B) 47.1 grams
C) 49.6 grams (apparent right answer but how?)
D) 57.8 grams
E) 92.7 grams

Obviously the right answer is 49.6 grams

Explanation: When you know what the half life is, how much time has passed and how many grams of a sample there is left, the only thing you really need to do is figure out how many half lifes have passed during the 15.2 days. Here's how you do that:

15.2 / 3.8 = 4

So 4 half lifes have passed since then. That means the weight of the Radon-222 has decreased by 1/2 four times. In order to figure out how much we started with, we need to do this:

3.1 (our starting number!) x 2 = 6.2 grams

6.2 x 2 = 12.4 grams

12.4 x 2 = 24.8 grams

24.8 x 2 = 49.6 grams

Hope this helped!

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