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I. Introduction These decay processes are described by transition
probabilities per unit time characteristic of each
Muons are some of the most useful types of type of muon. In a sample of muons, the mean
particles in modern experimental physics. Evidence number of particles decaying in a time will be
of that can be found in the recent growth of fields given by
like muon radiography, or muon imaging, where
detectors are placed inside or nearby big = − , (3)
constructions like pyramids, to capture muons
passing through them in order to create an image
of their structure (O’Keefe, 2021). where we have assumed that is large enough so
that it can be considered continuous. Integrating
Since the number of applications of muon physics this expression leads to the usual exponential law
depends in great part of the development of new for the remaining amount ( ) of a sample of
techniques for their detection, measuring some of particles at a time t (Oda, 2005),
its properties like the mean lifetime and speed, can
have a great pedagogical value for graduate ( ) = − , (4)
0
students.
Where corresponds to the initial number of
0
Many previous projects (Liu, 2007) (Barnet et al, particles at = 0. It is more common to use the
2012) have determined both, the mean lifetime inverse of
and the speed of muons originated by cosmic rays.
The main goal of this work is to confirm previous 1
experimental results. This should be reproducible in = , (5)

any laboratory with scintillators with the
characteristics specified in this report, by anyone
with a basic graduate level knowledge of Physics. which is known as the mean lifetime, i.e., the time it
⁄
We also intend to determine how the results can be takes for the sample to decay to 1 of its initial
affected by the conditions of the experiment like concentration. In terms of the mean lifetime, the
the place where the detectors are located. power law can be expressed as

I. Theoretical Foundation ( ) = − / . (6)
0
A. The muon On the other hand, the half-life ⁄ is defined as
1 2
the time it takes for the sample to decay to one-
Cosmic rays are a form of high-energy radiation half of its initial concentration; that is, = ⁄
that originate from outside the solar system. When 1 1 2
they reach Earth, the rays collide with particles in when ( ) = ; from equation (4) we can write
0
2
the upper atmosphere to produce a "shower" of
particles, including muons. 1
= − 1 2 , (7)
⁄
2
Muons are the most numerous cosmic charged
particles at sea level. Most of them are produced calculating the logarithm of both sides, and
high in the atmosphere (typically 15km). Muons are dividing by − , we obtain
very similar to electrons, with an electric charge of
− and spin 1 2, but with a much higher mass and 1
⁄
they are unstable. The decay of muons and their ⁄ = 2 = 2. (8)
1 2

antiparticles, is mediated by the weak interaction,
and can be summarized as follows: B. Muon detection
−
−
→ + + (1) All detectors are based on the transference of part

or all of the kinetic energy to the detector mass,
+
+
→ + + . (2) where it is converted into some other form of

radiation to be analyzed. All modern detectors are
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Tlahuizcalli ISSN: 2448-7260 Año 10 Núm. 30 septiembre-diciembre 2024