Aim: To obtain the half-life of two radioisotopes by graphical means, using data from a simulated experiment.
Theory: Half-life( t_{½}) is the time it takes any particular mass of a radioisotope to be reduced to one half. Half-life is also the time for the Activity (counts per unit time) to be reduced by half.
The decay curve is defined by the relation
A = A_{0 }e^{-kt}
Where A is the number of counts per unit time, t is the time and I_{0} and k are constants.
A_{0} is the activity when t=0 and k is the "decay constant", which is a measure of how quickly the decay occurs.
If we take the natural log of this relation, we obtain:
log_{e}A=log_{e}A_{0} - kt
so that plotting a graph of log_{e}Avs t should produce a linear graph and enable us to find the value of the constants A_{0} and k.
Note that when A = ½ A_{0} we get t_{½} = - ln½/k
Note: ln = log_{e}
Method:
For each isotope:
1. Follow instructions to obtain a set of data and using Excel, plot a graph of True Activity against Time. From the graph, estimate the half-life, showing clearly how you obtained your result.
2. Plot a graph of lnAvst for your data and from it find the values of A_{0} and k.
3. From your value of k, determine the half-life of your isotope. Compare this with the known value of the half-life (found from the internet or other source). What is the % difference?
4. For each of the following isotopes, identify the type of decay and write down the equation by which it decays. Calculate the mass difference (in u) and hence the energy released (in MeV).