Post date: Mar 03, 2015 4:6:32 PM
Recently, I needed to send some samples containing uranium from overseas to the UK. Although I'm not interested in the nuclear or radioactive properties (I say why here), these samples are slightly radioactive. There are lots of safety precautions in place when dealing with radioactive materials, and one thing I had to do was to figure out how radioactive my samples might be. At the time, we didn't have a way to easily and reliably measure the activity so I tried to calculate it instead.
These are quite simple calculations but there are quite a lot of steps. They only use the formulae for radioactive decay and some ideas about moles.
In the end the quantity we want to calculate is the activity or decay rate. This has units of s−1 and tells us how many decays there are per second. I was hoping that this number would be low - a low activity means that some of the safety constraints that make it more difficult to do experiments are relaxed.
The sample is made of UGa3 and we are told by the person providing it that it is 4.06x1.38x1.40 mm in size and has a mass of 61.2 mg. Ga is stable and so all the activity comes from U. This is all the information we need to calculate the activity.
I'll outline the important things we need to know beforehand
To calculate the activity, we will use the formula Activity=λN. This is a simple statement which says the activity depends on the decays constant (λ) and the number of atoms, N. If we have a high decay constant, the activity will be high. Also if we have a large number of atoms, then we will have a high activity.
We need to know how many uranium atoms we have N. We can calculate this based on the sample mass and knowing the composition (i.e. how many U compared to Ga).
The decay constant we look up and just depends on what element we have.
We will start by writing down what we know about the problem. I am doing this in ipython which allows me to see all the steps calculation. It also allows me to quickly repeat a calculation with a different input information (for example, the sample mass).