Energy Distribution in Atmospheric Muons

This study models the parameters of atmospheric muons that decay at altitudes ranging from 200 to 4200 meters. Using experimental data, this research determined the correlation between the most likely number of decayed muons, the altitude of decay and the distance traversed before decaying. Next, using the data obtained, this study determined the fraction of total decayed muons that exhibited a certain velocity and determined their altitude of decay. The velocities of the fractions of decayed muons were further used to determine their corresponding kinetic energies. The study also presented equations that give the relation between the kinetic energy of a muon and its altitude of decay. Furthermore, an equation relating the energy of a muon to the fraction of muons corresponding to that energy was also created in the present study. To diminish the standard deviation in the data obtained thus far, this paper also determines and plots the relation between the specific energy of atmospheric muons and the fraction of muons with a kinetic energy greater than or equal to the specified energy. Overall, this study describes, plots, and generates equations for the kinetic energies of muons and calculates the muon fraction for different energies to determine the energy distribution for atmospheric muons that decay between 200 meters and 4200 meters.