# The Effect of the Thickness of Aluminum on the Speed of Muons

**The Effect of the Thickness of Aluminum on the Speed of Muons**

Nathan Frazier (Cousino High School/ MMSTC), Seth Hall (International Academy of Macomb)

Mike Niedballa (Wayne State University)

Gil Paz (Wayne State University)

**Purpose**

The purpose of this experiment was to test the effect that different thicknesses of aluminum would play on the speed of muons. Prior experiments proved that with more aluminum shielding the flux of muons will decrease. Our experiment furthers this research. It is hypothesized that the thicker the aluminum is between the paddles, the slower the muons will travel.

**Method**

The method to this experiment is to run a time of flight study on the muons. The coincidence was set to two paddles one on top and one on the bottom (2.2 meters apart). First control data was collected without aluminum between the paddles. We then placed 77mm of aluminum between the paddles and collected data. Next 123mm, 225mm, and 300mm of aluminum were all placed between the paddles. Each collection of data was ran for at least 4 hours. The average time a muon was calculated given the certain amount of aluminum between the paddles. Our data from each thickness trial was graphed and a regression was fit to the data with the slope being the speed.

**Results**

Our data shows a direct relationship between the thickness of aluminum and the speed lost. There are some points that are far from the line but the r squared value is close to 1 so are data does fit the line of regression well.

**Meaning of Data**

Our data shows that there is a difference in speeds between the different thicknesses of aluminum because our p value of 0.0518 is so close to our alpha level of 0.05. Since we determined that there is a strong chance of the speeds being different, we ran some linear regression t-tests (one with the difference in speeds and one with the percent of the speed of light). The p-values for these two tests are both roughly 0.00674 which is less than the alpha level, so we can reject our null hypothesizes that there is no strong linear correlation. The slopes of these regression lines told us that, on average, for every millimeter of aluminum added the muons will slow 64525.5 m/s or 0.02% the speed of light. Since there was a difference in the speeds and it did follow a linear model, we accepted our hypothesis.

**Suggestions for further Research**

In future studies we can use bigger thicknesses to see if this linear trend continues and we can also try different materials to see if they slow down the muons at different rates.