Bubble Chamber Lesson 6 Spirals

Introduction to the teacherThis lesson plan discusses the properties of the spiral bubble chamber tracks characteristic of electrons and positrons. No new principles are used in this analysis. It is, however, an opportunity to introduce students to the idea of antimatter.

The interactions:

An electron spiral A positron decay and subsequent pair productionObjectives:Students understand how the Lorentz force explains that behavior of particles in the bubble chamber.

Students explain the characteristic spiral tracks left by electrons and positrons using the Lorentz force and the conservation laws.

Students explain the spiralling pattern of electrons and positrons in the bubble chamber.

Students identify the existence of anti-electrons (positrons) in bubble chamber reactions

Introduction:

Students see a bubble chamber photo that shows characteristic spiralling of an electron being ejected from a hydrogen atom with negligible affect on the path of the incoming beam particle. Students also see a photo showing the creation of an electron-anti-electron pair.

Ask students to explain the first interaction – at this point they should be able to recognize that it is an ejected electron.

Questions that may be posed (but not yet anwered):

Why do electrons spiral? What does the spiral tell us about the electron after the interaction?What can we say about the two tracks in the second photo? Students may notice that their paths are similar – but in opposite directions..

Class objective is to explain and understand what particles cause these spiral interactions and what the spiral tells us about the particles.

Teaching Strategy

1. Looking at the electron interaction.What do we know about the electron?Ans: We know charge, mass, and that momentum and energy are significantly lower than the kaon beam.

2. What causes the electron to move in a circular path?We established in Lesson 1 that there must be a force acting on the particle. A magnetic field exerts a force on a moving, charged particle. This is called the Lorentz force (which actually includes electric and magnetic field forces)

Examining Lorentz force: (This discussion uses magnitudes only, since the magnetic field and velocity vectors are always perpendicular in the bubble chamber – teachers of more advanced classes may prefer to include the vector form of the Lorentz equation).

In SI units:Force = charge x velocity x magnetic field strengthF = qvB

Important: the direction of the force, velocity and magnetic fields must all be perpendicular to each other.

The example to the right illustrates the relative orientation of the velocity,

magnetic field, and force acting on a positive charge moving through a bubble chamber.

The direction of the magnetic field is into the page.- indicated by the “x”.

The orientation of F, v and B can be foundusing the appropriate left hand rule (LHR) or right hand rule (RHR) in accordance with local custom.

x x x x

x v x

F +q

x x x x

Note that the direction of F depends on charge, q. For a negatively charged particle, like our electron, the force would be oriented in the opposite direction from that found in the example. Be careful when applying LHR and RHR’s.

3. The Lorentz force is equal to the centripetal force.

Looking at the diagram above it is apparent that the force acting on the charge will continually change the direction of the velocity – causing the charge to move in a circle. (Perhaps remind students that since the force acts perpendicular to the velocity that no work is done on the particle, so it does not increase the kinetic energy.)

Centripital Force: Fc = mv2/r

Equating the two forces yields: qvB = mv2/rWhich simplifies to: qB = mv/rand finally: mv = qBr or p = qBr

We used this in Lesson 1 to establish that r is proportional to momentum.

In the units used in particle physics, p is expressed in GeV/c, and q is always ±1 eV. The equation then reduces (using c = 3 x 108 m/s) to:

p = .3Br

4. What does the spiral tell us?

Student will note that since is B is fixed – so in order for r to decrease p must decrease. And in order for the momentum, p, of a particle to decrease, its kinetic energy must decrease.

Have students examine the spiral more closely.How many turns in the spiral do they see?What happens to the radius with each turn? (Possibly measure the distance from the center of the spiral to points on different turns.)Students should see that r is decreasing quickly, therefore p is decreasing quickly, therefore the particle must be losing kinetic energy at lease as quickly.

By what mechanism is the particle losing energy?The acceleration of the electron (as it moves in a circle) causes it to radiate energy – called bremsstrahlung (braking radiation). This is a characteristic of all accelerating particles. Recalling first, that acceleration if inversely proportional to mass (a = F/m), and second, that an electron’s mass is 1/1000 that of the incident kaon beam, the affect of this radiation is orders of magnitude greater for the electron than for other particles in the bubble chamber – therefore the pronounced spiral as the electron radiate energy at a rapid rate. As a result, the electron is the

only particle that produces observable bremsstrahlung spiraling in the bubble chamber.

5. Explaining the second photograph – pair creation.

Explain the second photo – what can you say? Students should note that two particles appear – they must be the product of a neutral decay.

Two particles are observed – both with spirals characteristic of an electron. The photo provides two pieces of evidence that one must be positive. What are they?

(The direction of the curvature and the fact that the two particles come from the decay of a neutral particle – so charge conservation dictates that if one is positive, the other must be negative.)

Do the tracks provide evidence regarding the relative mass of the two particles?

Students should note that both particles spiral. Since we have concluded that this spiraling is a product of bremstrsahlung, which is only evident for particles with a mass on the order of an electron, we can conclude that both particles have comparable, small mass.

In summary – a neutral particle decays into two particles. These particles have similar mass, but opposite charge. One particle is an electron (we can see that), the other is an electron with a positive charge – called an anti-electron or a positron.We are seeing the decay of a photon into an electron – positron pair.

6. Anti-matter? We thought that was science fiction.

The existence of anti-matter was predicted by theorists. Anti-matter counterparts have been found to exist for all known particles. These particles have properties that are identical to their normal counterparts – except that for charged particles, the anti-particle has an opposite charge. So an anti-electron (positron) is positive, an anti-proton is negative.

When an anti-matter particle such as a positron or anti-proton interacts with normal matter, both particles annihilate into a photon. The lifetime of these particles, except in a vacuum, is very short. In fact – careful examination of the photograph shows the annihilation of a positron producing the photon which subsequently decays into the pair.

Wrap-up

The spirals tell us the story of the charge, momentum and mass of a particle. By comparing that radius of curve of two tracks, we can compare the momentum of the particles that created them. The rate at which the radius decreases shows the rate of bremsstrahlung, which is an indication of the mass of the particle. So these spirals are signature characteristics of the motion of the lowest mass particles – electrons and positrons. We also observed direct evidence of the decay of a neutral particle, a photon, into a matter – anti-matter pair.

Suggested Exercises

1. In the bubble chamber interaction shown:a. Identify the electron spiralsb. Identify the electron positron pairsc. Use the radius template [link to template] to compare the radius of the

incoming beam to the initial radius of an electron knocked from the path of the beam. Compare the momentum of the two particles.

2. A the radius of a track in a bubble chamber is estimated to be approximately .3 m., in a magnetic field of 1.78 T. Calculate the approximate momentum of the particle.