Bubble Chamber Tracks Energetic gamma rays like those coming...

Bubble Chamber Tracks Energetic gamma rays like those coming from outer space can disappear near a heavy nucleus producing a rapidly moving pair of particles consisting of an electron and a positron. (A positron is a small positively charged particle that has the same mass and amount of charge as an electron). This process is called pair production. A device called a bubble chamber allows one to observe the path taken by electron-positron pairs produced by gamma rays. The study of bubble chamber tracks in the presence of magnetic fields has revealed a great deal about high-energy gamma rays, the processes of pair production, and the loss of energy by electrons and positrons. A sample bubble chamber track is shown in Fig. $29-41$. (a) If the magnetic field is uniform pointing into the paper, which trajectory (the upper one or the lower one) shows the motion of the positron? Explain your reasoning. (b) In which part of the spiral does the positron have the greatest energy $-$ the large radius part or the small radius part? Explain the reasons for your answer. (c) Is the electron moving faster, slower, or at the same speed as the positron at the point in time when the two particles are created? Cite the evidence for your answer. (d) Suppose the bubble chamber photograph in Fig. $29-41$ is an enlargement of the actual event so that the length $L$ is actually only $2.4 \times 10^{-3} \mathrm{~m} .$ Show that the radius of curvature of the electron path just after the electron is created is approximately $0.8 \times 10^{-3} \mathrm{~m} .$ Hint: Measure $L$ in picture units to find a scale factor and then measure the appropriate feature of the electron path in picture units and use the scale factor to find $R$ in meters. (e) Use the Lorentz force law and the expression for centripetal force to find the equation relating the speed of the electron to $B, R, e$, and $m .$ (f) Suppose the magnitude of the magnetic field in the bubble chamber is $B=0.54 \mathrm{~T}$. Calculate the approximate speed of the electron when it is first created in the bubble chamber.

Bubble Chamber Tracks Energetic gamma rays like those coming from outer space can disappear near a heavy nucleus producing a rapidly moving pair of particles consisting of an electron and a positron. (A positron is a small positively charged particle that has the same mass and amount of charge as an electron). This process is called pair production. A device called a bubble chamber allows one to observe the path taken by electron-positron pairs produced by gamma rays. The study of bubble chamber tracks in the presence of magnetic fields has revealed a great deal about high-energy gamma rays, the processes of pair production, and the loss of
energy by electrons and positrons. A sample bubble chamber track is shown in Fig. $29-41$.
(a) If the magnetic field is uniform pointing into the paper, which trajectory (the upper one or the lower one) shows the motion of the positron? Explain your reasoning. (b) In which part of the spiral does the positron have the greatest energy $-$ the large radius part or the small radius part? Explain the reasons for your answer. (c) Is the electron moving faster, slower, or at the same speed as the positron at the point in time when the two particles are created? Cite the evidence for your answer. (d) Suppose the bubble
chamber photograph in Fig. $29-41$ is an enlargement of the actual event so that the length $L$ is actually only $2.4 \times 10^{-3} \mathrm{~m} .$ Show that the radius of curvature of the electron path just after the electron is created is approximately $0.8 \times 10^{-3} \mathrm{~m} .$ Hint: Measure $L$ in picture units to find a scale factor and then measure the appropriate feature of the electron path in picture units and use the scale factor to find $R$ in meters. (e) Use the Lorentz force law and the expression for centripetal force to find the equation relating the speed of the electron to $B, R, e$, and $m .$ (f) Suppose the magnitude of the magnetic field in the bubble chamber is $B=0.54 \mathrm{~T}$. Calculate the approximate speed of the electron when it is first created in the bubble chamber.

Key Concepts

Energy and Momentum Relationship from Track Curvature

The radius of curvature of a charged particle’s path in a magnetic field is directly related to its momentum; a larger radius indicates higher momentum and kinetic energy, assuming a constant magnetic field. Analyzing the curvature of tracks in devices such as bubble chambers enables researchers to infer the energy levels and dynamic behavior of particles produced in high-energy interactions.

Circular Motion and Centripetal Force

In a uniform magnetic field, a charged particle undergoes circular motion because the Lorentz force acts as a centripetal force. By equating the magnetic force to the centripetal force (m*v^2/R), one can relate a particle’s velocity, mass, charge, magnetic field strength, and the radius of its circular path. This relationship is central to determining the energy and momentum characteristics of charged particles in experimental setups.

Lorentz Force Law

The Lorentz force law formalizes the force acting on a charged particle moving in a magnetic field, given by F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. This fundamental principle is used to derive the equations of motion for charged particles and is key to understanding how track curvature in a magnetic field reflects a particle’s momentum and energy.

Bubble Chamber

A bubble chamber is a detection device used in experimental particle physics that visualizes the paths of charged particles. As energetic particles move through a superheated liquid, they leave behind trails of bubbles, which record their trajectories. This tool is essential for examining particle interactions, such as pair production events, and helps in deducing the kinematics of the resulting particles.

Pair Production

Pair production is a quantum process in which a high-energy photon, typically a gamma ray, transforms into an electron-positron pair in the vicinity of a heavy nucleus. This process conserves both energy and momentum and is a crucial phenomenon in high-energy physics, providing insights into the interactions between electromagnetic radiation and matter.

Magnetic Field Effects on Charged Particles

When charged particles enter a magnetic field, they experience a force perpendicular to both their velocity and the magnetic field direction. This Lorentz force deflects the particles, causing them to follow curved paths. The curvature of these paths depends on the particle’s charge, velocity, and the magnitude of the magnetic field, making it a vital concept for analyzing particle motion in detectors like bubble chambers.

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