In 1900 Rutherford published this manuscript showing that intensity of radiation from a radioactive sample of thorium oxide was decreasing at an exponential rate. He also showed that when a new source was introduced the build up of radioactivity would proceed exponentially.
Table III and IV from that publication are the following
| Time | Current |
|---|---|
| 0 | 1 |
| 28 | 0.69 |
| 62 | 0.51 |
| 118 | 0.23 |
| 155 | 0.14 |
| 210 | 0.067 |
| 272 | 0.041 |
| 360 | 0.018 |
| Time | Current |
|---|---|
| 0 | 2.4 |
| 7.5 | 3.3 |
| 23 | 6.5 |
| 40 | 10.0 |
| 53 | 12.5 |
| 67 | 13.8 |
| 96 | 17.1 |
| 125 | 19.4 |
| 184 | 22.7 |
| 244 | 25.3 |
| 304 | 25.6 |
| 484 | 25.6 |
Plot the values from the two tables on an axis. You will notice that the y range of one Table is much larger than the other. One can divide by the maximum y value to make the two tables have a similar range. Then the y label would be fraction of maximum current.
One might notice that the curves look like one goes up when one goes down. You could check this by plotting 1 – y/ymax for the 2nd Table as a 3rd line.
Then make a second plot taking the log of the y-values (current). Fit a line to the x, log(y) values and determine the equation for these curves from the line. Plot those lines on the first axis. Calculate the residuals between your fit and the points and make a histogram for them for each line. Determine the mean and standard deviation of your residuals. Does the exponential seem to be a good fit to this data? What would the errors on the measurements have to be for you to feel confident with your fit?
