I want to make sure I am approaching this problem correctly:

Element X has a half-life of 100 years. If I have a 128 Curie sample of element X, how long will I have to wait until its radioactivity has decreased to 0.5 Curies?

I believe I can use the radioactive decay law? Where N(T) = .5 Curies, inital is 128 Curies... etc. I am not sure and the unit of Curies is confusing to me. $$N(T) = N_{0} \cdot e^{-\frac{ln2}{half-life}t}$$

• If you have a $128\,\mathrm{Ci}$ sample of anything you'd better know a lot about radiation protection ... – dmckee Nov 30 '17 at 20:29

The Curie is a less used measure of activity of a radioactive substance $($Personally I'm a lot more familiar with the Bequerel$)$. So, in short, yes you can use that equation to calculate the final activity.

Looking at the units you can see that in the power of $e$ part you essentially have $\frac{t}{t}$ which cancels out, leaving you with just $Ci=Ci$, so it checks out :p.

• What do you mean it cancels out? – user7252850 Nov 30 '17 at 20:14
• In the same way that in 9/9 the top it 'cancels out' to 1, the units of time in t/t 'cancel out' to 1, as in they disappear. – CooperCape Nov 30 '17 at 20:15
• "I'm sure we're all more familiar with the Bequerel" Really depends on your age. That thing wasn't established as an SI unit until after I was born and hadn't come to dominate in the textbooks until I was already in grad school. – dmckee Nov 30 '17 at 20:27
• @dmckee Apologies - Being younger I didn't think about that - lemme edit it :) – CooperCape Nov 30 '17 at 20:30
• No need to apologize. Most of SI has been around for a long time, so the few cases where something is "recent" cause unexpected generation gaps. I almost always write in Bequerels, but I sometimes still think in Curies (or mostly in microCuiries). – dmckee Nov 30 '17 at 20:35