CHE 1302 Lecture Notes - Lecture 25: Exponential Decay, Alpha Decay, Half-Life
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226ra decays by alpha emission with a half life of 1. 60 103 years. If a sample initially contains 1. 00 mg of. Firstly we"ll use the half life to calculate the decay constant: Next we can use the integrated form of the radioactive decay law: Instead of numbers of atoms (n) we can use mass of 226ra this will be proportional to number of atoms anyway. Now we substitute for n0, k and t: so k = 0. 693/t = 0. 693/(1. 60 103 y) = 4. 33 10 4 y 1 and so nt = n0e kt. = 1. 00 mg e (4. 33 10 4 y 1 3. 00 103 y) Remember to do a reality check on your answer: t = 3000 y is a little less than 2 half-lives so the answer should be a little more than. 0. 25 the starting mass as observed. k = 0. 693/t = 0. 693/5730 y = 1. 209 10 4 y 1.
