Question

The half life of radium 222 is 38 seconds if you had a 12 gram sample how much would be left after 72 seconds

Answer 1

3.2 grams The first thing to do is calculate how many half lives have expired. So take the time of 72 seconds and divide by the length of a half life which is 38 seconds. So 72 / 38 = 1.894736842 So we're over 1 half life, but not quite 2 half lives. So you'll have something less than 12/2 = 6 grams, but more than 12/4 = 3 grams. The exact answer is done by dividing 12 by 2 raised to the power of 1.8947. So let's calculate 2^1.8947 power = 12 g / (e ^ ln(2)*1.8947) = 12 g / (e ^ 0.693147181 * 1.8947) = 12 g / (e ^ 1.313305964) = 12 g / 3.718446464 = 3.227154167 g So rounded to 2 significant figures gives 3.2 grams.