In 1911 Rutherford published his theory that the positive charges of an atom are found in a very small nucleus. This theory could explain the scattering of alpha particles when shot at a thin metal film. That data for different metals had been obtained by Geiger and Marsden a couple years earlier and is shown below.
| Metal | Atomic Weight | Scintillations per minute |
| Lead | 207 | 62 |
| Gold | 197 | 67 |
| Platinum | 195 | 63 |
| Tin | 119 | 34 |
| Silver | 108 | 27 |
| Copper | 64 | 14.5 |
| Iron | 56 | 10.2 |
| Aluminium | 27 | 3.4 |
vol. 82, p. 495-500
Scintillations refer to the alpha particles that were scattered back towards the source. We can take this to be a Poisson process. If the observations were 1 minute long, then we can calculate the probability of getting any whole number result. For each point calculate the odds of getting different numbers till the odds are less than 5% or greater than 95%. This is the 90% range of values one might expect to get. One can plot these using the plt.errbar() function.
Make a plot of the relationship between atomic weight and scintillations assuming all measurements were 1 minutes long. Now fit a power law to the data points including the errors. Rutherfords calculations showed that the rate of deflections should go as the atomic weight to the 5/2 power. Given the uncertainties what values to you find consistent with the data?
