# Physics and Astronomy Labs/Radioactive decay with dice
## Lede

This will be the Lede. It should mention the application to radioactive dating in OpenStax Astronomy. Remove the header Lede when this has been written.

## Excel Spreadsheet

Column roll denotes the number of rolls. We rolled 201 dice 18 times, removing the "one" each time. Column exp denotes the number of dice removed on each roll in our experiment. Columns sim1 through sim5 represent five simulations. Column theor represents the theoretical value one is most likely to obtain: the first value is 201 divided by 6, and each consecutive value is 5/6 times smaller, representing exponential decay.
Column SEexp is the square of the error associated with the experiment. For the first role, this is obtained as follows:
    $SEexp(1)=(33-33.5)^{2}=0.25$
Columns SE1 through SE5 represent the squared errors associated with the 5 simulations.
These squared errors are summed at the last row. The values of SoS (Sum of Squares) represent a measure of how well the simulation or the experiment matched the theoretical ideal. If the experimental SoS sufficiently exceeded any of the simulated SoS values, we might wish to question the experimental method.
| roll | exp | sim1 | sim2 | sim3 | sim4 | sim5 | theo | SEexp | SE1 | SE2 | SE3 | SE4 | SE5 |
| 1 | 33 | 33 | 27 | 29 | 35 | 37 | 33.50 | 0.25 | 0.25 | 42.25 | 20.25 | 2.25 | 12.25 |
| 2 | 25 | 34 | 25 | 28 | 30 | 23 | 27.92 | 8.51 | 37.01 | 8.51 | 0.01 | 4.34 | 24.17 |
| 3 | 21 | 18 | 22 | 27 | 23 | 23 | 23.26 | 5.13 | 27.71 | 1.60 | 13.96 | 0.07 | 0.07 |
| 4 | 18 | 20 | 26 | 24 | 17 | 15 | 19.39 | 1.92 | 0.38 | 43.74 | 21.28 | 5.70 | 19.24 |
| 5 | 17 | 18 | 14 | 21 | 13 | 14 | 16.16 | 0.71 | 3.40 | 4.65 | 23.47 | 9.96 | 4.65 |
| 6 | 14 | 13 | 20 | 13 | 15 | 12 | 13.46 | 0.29 | 0.21 | 42.73 | 0.21 | 2.36 | 2.14 |
| 7 | 11 | 13 | 9 | 15 | 14 | 8 | 11.22 | 0.05 | 3.17 | 4.92 | 14.30 | 7.73 | 10.36 |
| 8 | 13 | 6 | 9 | 12 | 9 | 10 | 9.35 | 13.33 | 11.22 | 0.12 | 7.03 | 0.12 | 0.42 |
| 9 | 12 | 9 | 9 | 6 | 6 | 16 | 7.79 | 17.72 | 1.46 | 1.46 | 3.21 | 3.21 | 67.39 |
| 10 | 9 | 5 | 3 | 3 | 5 | 4 | 6.49 | 6.29 | 2.23 | 12.20 | 12.20 | 2.23 | 6.21 |
| 11 | 5 | 6 | 4 | 4 | 11 | 7 | 5.41 | 0.17 | 0.35 | 1.99 | 1.99 | 31.24 | 2.53 |
| 12 | 4 | 4 | 6 | 6 | 1 | 6 | 4.51 | 0.26 | 0.26 | 2.22 | 2.22 | 12.31 | 2.22 |
| 13 | 2 | 4 | 3 | 5 | 2 | 3 | 3.76 | 3.09 | 0.06 | 0.57 | 1.54 | 3.09 | 0.57 |
| 14 | 1 | 4 | 3 | 1 | 4 | 4 | 3.13 | 4.54 | 0.76 | 0.02 | 4.54 | 0.76 | 0.76 |
| 15 | 2 | 5 | 6 | 3 | 2 | 3 | 2.61 | 0.37 | 5.72 | 11.50 | 0.15 | 0.37 | 0.15 |
| 16 | 1 | 3 | 1 | 1 | 3 | 3 | 2.17 | 1.38 | 0.68 | 1.38 | 1.38 | 0.68 | 0.68 |
| 17 | 1 | 2 | 2 | 0 | 0 | 2 | 1.81 | 0.66 | 0.04 | 0.04 | 3.28 | 3.28 | 0.04 |
| 18 | 0 | 0 | 3 | 1 | 0 | 1 | 1.51 | 2.28 | 2.28 | 2.22 | 0.26 | 2.28 | 0.26 |
| sums | 201 | | | | | | | 67 | 97 | 182 | 131 | 92 | 154 |

## Matlab codes

To know if the random error is consistent with the laws of probability for such a decay process, we use matlab codes. These codes simulate any number of labs for an arbitrary number of dice.

### Collects data from a data file

This code allows the user to enter classroom data into an Excel file that can be opened by matlab.

### Future project(s)

Matlab codes have been used to make spagetti plots. In the future, it would be nice to also use matlab to perform the sum of squares analysis.This can be of ultimate usefulness because of radioactivity of some elements under the hood.

### HTW fall 19

22 21 21 16 10 11 6
* ↑ https://cnx.org/contents/LnN76Opl@13.120:niEjH03V@3/Dating-Planetary-Surfaces