Materials

• Thermoelectric Cloud Chamber
• DC Power Supply
• Rechargeable 12V Batteries
• Laser
• Rubbing Alcohol
• Magnifying Glass (Optional)

Demo

A thermoelectric module makes use of the Peltier effect to cool an aluminum plate down to -30 degrees Celsius. The plastic chamber contains a sponge that is saturated with rubbing alcohol. When it is placed over the Peltier module, the alcohol vapor in the chamber condenses back into a liquid, and in the process, creates a cloud that can be used to detect muon decay events produced by cosmic rays.

Explanation

Muon Life Cycle

The life cycle of a muon begins when cosmic rays, composed of mostly high energy protons and alpha particles, interact with Earth’s atmosphere. The average kinetic energy of these particles is around K = 3 Gev.

For an alpha particle with mass m_α = 6.6e27 kg = 3.8 GeV/c², the average velocity is calculated to be

After colliding with air molecules, these high energy cosmic rays produce charged pi mesons that undergo leptonic decay,

resulting in muons and neutrinos.

Muons have the same spin and charge as electrons, however they are nearly 200 times more massive, m =1.8e-28 kg =90 MeV/c², and unstable. As a result, their lifespan is extremely short, measured at ~2e-6 s. Given that the atmosphere is roughly 10 km thick, with muons having an average speed of, 

where mc² = 90 MeV and K_avg = 3 GeV, how is it possible to detect a muon at the surface of the Earth? In a non-relativistic frame, muons will have little to no chance of reaching Earth’s surface, since for the duration of their lifespan, they only travel a distance of 0.6 km.

Time Dilation

However, taking into account relativistic effects, muons experience time dilation since they are moving at near the speed of light, as seen from a stationary observer on the surface of the Earth.

As a result, the time it takes for a muon to decay increases by a factor of 70. Moving at 0.999c in a lifespan of 1.4e-4 smeans that the muon travels a distance of 42 km, in the reference frame of the Earth, thus making it possible for the particle to reach the surface.

Length Contraction

Similarly, from the muon’s reference frame, the distance from the creation point to the ground is decreased by a factor of 70 due to the relativistic effect of length contraction. Rather than traveling through a 10 km thick atmosphere, the muon experiences the atmosphere to only be 0.14 km thick. As a result, the muon will be able to reach the ground and can be detected using a cloud chamber.

Detecting Muons

We can detect muons with a cloud chamber since they carry charge and ionize the air, resulting in visible tracks. Muons have a high kinetic energy, so the tracks produced by muons are thin and straight, similar to those produced by high energy electrons. These tracks are distinct from alpha particles which, being the heavier and slower particle, produce thicker tracks.

Detecting muon decay is another way of determining the presence of a muon within a cloud chamber. The Feynman diagram below illustrates muon decay, where a negatively charged muon transforms into a neutrino, and an electron-antineutrino pair, via a virtual W− boson.

A cloud chamber only displays ionizing radiation, so from this diagram we will be able to observe the straight track from the high-energy muon abruptly bending at decay, producing the second track from the high-energy electron. Below is possibly an example of muon decay, as seen by our cloud chamber:

Written by Lisette Birch