Problem 86 - College Physics

Question

\bullet Bubble chamber, I. Certain types of bubble chambers are filled with liquid hydrogen. When a particle (such as an electron or a proton) passes through the liquid, it leaves a track of bubbles, which can be photographed to show the path of the particle. The apparatus is immersed in a known magnetic field, which causes the particle to curve. Figure 20.77 is a trace of a bubble chamber image showing the path of an electron. (a) How could you determine the sign of the charge of a particle from a photograph of its path? (b) How can physicists determine the momentum and the speed of this electron by using measurements made on the photograph, given that the magnetic field is known and is perpendicular to the plane of the figure? (c) The electron is obviously spiraling into smaller and smaller circles. What properties of the electron must be changing to cause this behavior? Why does this happen? (d) What would be the path of a neutron in a bubble chamber? Why?

Step-by-Step Solution

Answer

To determine charge: use path curvature. Momentum: measure radius and use \( p=qBr \). Electron spirals shrink as it loses energy. Neutrons travel straight due to no charge.

Step 1: Determining the Charge Sign from the Path

To determine the charge sign of a particle from its path in a magnetic field, use the right-hand rule. For a positively charged particle, point the right thumb in the direction of the velocity vectors (tangent to the path) and your fingers point along the magnetic field direction. The palm point will show the centripetal force direction, which correlates with the curve. If the particle curves opposite to this force, it's negatively charged, like an electron.

Step 2: Determining Momentum and Speed

The radius of curvature of the particle's path in a known magnetic field can be used to find its momentum. For a particle of charge \( q \) moving at speed \( v \), and magnetic field \( B \), use \( r = \frac{mv}{qB} \), to find momentum \( p = mv = qBr \). Speed can be deduced by measuring \( r \) and knowing \( q \) and \( B \).

Step 3: Understanding Spiral Path Behavior

The spiraling of the electron into smaller radii indicates energy loss, likely due to radiation emitted when the electron accelerates in the magnetic field (synchrotron radiation). This reduces its momentum and speed, leading to smaller spirals.

Step 4: Path of a Neutron

A neutron, being neutral, carries no charge and hence won't be affected by a magnetic field, resulting in a straight line path in the bubble chamber. Neutrons are not detectable directly by this method.

Key Concepts

Charge Determination

In a bubble chamber, it’s possible to figure out if a particle is positively or negatively charged by observing the direction in which it curves when subjected to a magnetic field. This is done using the right-hand rule, a simple way to connect the direction of motion, magnetic field, and force. If you imagine a positively charged particle moving, point your right thumb in the direction of its velocity (tangent to the curve). Your fingers represent the direction of the magnetic field lines. The direction in which the palm faces mimics the force acting on the charge. In the photograph of the bubble chamber, if the curvature of the path contradicts this direction, the particle is negatively charged. This helps scientists confirm that particles like electrons, which curve opposite to the expected force, are indeed negatively charged.

Momentum Measurement

The path radius of a charged particle moving through a magnetic field in a bubble chamber provides critical insight into its momentum. As the particle moves, it creates a circular path due to the magnetic force acting as a centripetal force. This is governed by the formula \( r = \frac{mv}{qB} \), where \( r \) is the curvature radius, \( m \) is mass, \( v \) is velocity, \( q \) is charge, and \( B \) is the magnetic field strength.
By measuring the radius \( r \), and with known values of \( q \) and \( B \), we can solve for the momentum \( p \) using \( p = qBr \). This relationship shows that momentum is directly proportional to both the radius and magnetic field strength. Knowing the particle's charge type also assists in further calculations, enabling physicists to deduce its speed.

Spiral Path Behavior

As charged particles like electrons move in a bubble chamber, they can display spiral paths when they begin losing energy. This happens due to radiation emission, known as synchrotron radiation, which occurs when an electron accelerates in the magnetic field. Because energy is continuously drained due to this radiation, the particle's momentum and speed decrease with time.
This reduction in momentum causes the radii of the spirals to diminish gradually. As a result, the electron traces smaller and smaller circles until it may eventually come to rest. This spiral behavior is a critical observation, revealing the energy loss mechanisms and providing insights into the forces acting within the bubble chamber.

Neutron Path

Unlike charged particles, neutrons are not influenced by magnetic fields since they have no net charge. Consequently, in a bubble chamber, a neutron will proceed in a straight path, unaffected by the magnetism that curves charged particles’ paths.
Without direct interaction with the magnetic field, the neutron's path does not curve, and it leaves a straight line. This path reflects the inertial motion of the neutron. While neutrons themselves don't produce visible tracks, their interaction with other materials or particles in the chamber can produce secondary charged particles, which then create detectable tracks, indirectly indicating the neutron's presence in the bubble chamber.