146.Particle Paths

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Number 146

Particle Paths Alpha particles and beta particles

The paths followed by subatomic particles in different situations can provide information about the particles. These include: • charge • momentum • energy • ionising properties

These two radioactive decay particles give very different results when their paths are observed in a cloud chamber: (a)Alpha decay

These paths can also provide evidence of particle annihilation and creation, and of particle decay. Alpha Source

How we observe these paths We cannot observe the particles themselves, but we can make them leave evidence of their passing. The two standard devices used have been the bubble chamber and the cloud chamber. This factsheet is not intended as a study of these devices, but the way in which they work is worth a mention.

We observe that: • the paths are straight • the paths are distinct • the paths are of equal length We can conclude from this that alpha particles suffer very little deflection during the ionisation process, that they are strongly ionising, and that they all have the same initial kinetic energy.

(a) Bubble Chamber Charged particles ionise the molecules in a super-heated liquid as they pass through. Bubbles form around the ions created. These trails of bubbles then indicate the path of the charged particle.

This fits in with our knowledge of alpha particles ( 24 He ) as relatively massive charged particles.

(b) Cloud Chamber

Example 2: Why should the alpha particles emitted from a source all have the same energy?

The cloud chamber contains a supersaturated vapour. Charged particles ionise molecules in the vapour as they pass through. The ions act as centres for droplet formation (condensation). The paths of the particles can be seen as mist trails through the vapour.

Answer: The decay equation is identical for each unstable nucleus in the sample. Mass defect is converted into kinetic energy in the process.

This diagram shows some typical particle paths seen in a cloud or bubble chamber.

238 92

4 U → 234 90 Th + 2 α

(b) Beta decay Beta Source

This time we observe that: • the paths are erratic • the paths are faint • the paths are of unequal length

Both detectors only show the paths of charged particles. Uncharged (neutral) particles cannot be seen. However sometimes their paths can be inferred from other evidence.

The conclusion for beta particles is that they are easily deflected during collisions, and that they are only weakly ionising. They also seem to have different kinetic energies.

Example 1: Why can the paths of neutral particles not be detected?

The first two conclusions fit in with our ideas that beta decay is

Answer: Ionisation is caused by a Coulomb force between the approaching particle and atomic electrons. An uncharged particle cannot exert a Coulomb force.

composed of tiny charged particles −10 e . However the final conclusion concerning kinetic energies is an important one.

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Physics Factsheet

146. Particle Paths When beta decay occurs, lepton number conservation dictates that an antilepton must be emitted along with the beta particle (electron). This extra particle is the electron antineutrino. It carries away the rest of the kinetic energy.

Example 5: An alpha source has an average activity of 9000Bq. Each alpha particle creates 1.5×104 ion-pairs. What current will be measured in the external circuit?

Total decay energy = KE of electron + KE of antineutrino 14 14 0 6 C → 7 N + -1 β + v

Answer: I = Ane = 9000×1.5×104×1.6×10-19 = 2.2×10-11 Amperes With beta particles, a spectrum of kinetic energies exists. The rest of the energy is taken by the antineutrino. This is a typical energy spectrum graph for beta particles:

It should be remembered that a similar process for a positron also occurs, with an electron neutrino carrying away the “missing” energy.

Calculations for alpha and beta particles Alpha particles lose about 30eV in creating one ion-pair when travelling through air.

Number of electrons emited

Example 3: An alpha particle has a kinetic energy of 8.2×10-13J. Find its kinetic energy in electron-volts. Then find the number of ionpairs it would create in air.

0.531 MeV

Answer: KE = 8.2×10-13 / 1.6×10-19 = 5.1×106eV = 5.1MeV Number of ionisations = 5.1×106 / 30 = 1.7×105 ion-pairs

0

0.2

0.4

Beta particle K.E/MeV

Example 6: One partcular beta particle is emitted with a kinetic energy of 0.517MeV. Find the energy of the accompanying antineutrino.

Example 4: Would an alpha particle with twice the kinetic energy have twice the range through air?

Answer: Energy = 0.531 – 0.517 = 0.014MeV

Answer: No. Alpha particles do not cause ionisations at a steady rate. As they slow down, the chance of a collision causing a successful ionisation increases markedly (they become more strongly ionising as they slow down). This leads to a graph of this form:

Applied Magnetic Fields Often a magnetic field is applied perpendicular to the base of the cloud chamber. Any charged particle travelling across the chamber will be deflected in a curved path. From circular motion theory: Bqv = mv2 / r and so

p = mv = Bqr

where p is momentum

As most particles have charge +e or –e, the momentum of the particle can be found.

Range in air

And the charge can be determined as positive or negative by the direction of the deflection. Example 7: A particle of charge +e follows a track of radius 0.4m in a perpendicular field of 4 Tesla. Find the momentum of the particle.

Initial K.E

Answer: p = Bqr = 4×1.6×10-19×0.4 = 3×10-19 kgms-1

In a device called an ionisation chamber, the ion-pairs created in air each contribute one electron to the current around an external circuit. The current flow is expressed as:

However charged particles never travel in a circle in a cloud or bubble chamber. They slow down (lose energy) as they travel through the medium: (a) they lose energy through ionisation (b) charged particles emit e.m. radiation as they accelerate — in this case they are accelerating because they are changing direction in the magnetic field.

I = Ane where A is the activity of the alpha source in Bq n is the number of ion-pairs created by each alpha particle e is the electron charge in coulombs

This loss of speed causes the particle to spiral inwards. This effect is shown for an electron in the diagrams below. As a charged particle in a magnetic field slows down, the radius of its path decreases.

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Physics Factsheet

146. Particle Paths Standard particle paths observed: (a)

(b)

(a) Electrons and positrons curve in opposite directions in the magnetic field. (b) An electron loses energy quickly through e.m. radiation, and it spirals inwards in the applied field. (c) A particle coming to rest leaves a dense track near the end, as its ionising power increases.

(c)

(d)

(d) A neutral particle (which cannot be seen) decays into two charged particles which travel in straight lines in the absence of a magnetic field. (e) A charged particle has emitted a neutral particle (unseen) and changed direction (conservation of momentum).

(e)

Practice Questions 1. An alpha source produces the following pattern in a cloud chamber. Explain what is happening.

Alpha Source

2. Find the radius of curvature of the track of a positron as it travels through an applied field of flux density 4.5 Tesla. The instantaneous momentum of the positron is 6.5×10-19kgms-1. 3. An alpha source in an ionisation chamber has an activity of 16 000 Bq. The ionisation current in the external circuit is measured as 1.9×10-12A. (a) Find the number of ion-pairs created by each alpha particle. (b) If it takes 35eV to create an ion-pair, find the energy (in eV) of each alpha particle. (c) Convert this energy to Joules.

Answers 1. The sample emits alpha rays of a single energy. The nuclei decay into daughter nuclei which are also unstable, and emit alpha rays of a different energy. p 6.5 × 10-19 = = 0.90m Bq 4.5 × 1.6 × 10-19 1 1.9 × 10-12 3. (a) n = = = 740 ion-pairs Ae 16000 × 1.6 × 10-19

2. r =

(b) E = 740×35 = 26 000eV (c) E = 26 000×1.6×10-19 = 4.2×10-15J

Acknowledgements: This Physics Factsheet was researched and written by Paul Freeman The Curriculum Press,Bank House, 105 King Street,Wellington, Shropshire, TF1 1NU Physics Factsheets may be copied free of charge by teaching staff or students, provided that their school is a registered subscriber. No part of these Factsheets may be reproduced, stored in a retrieval system, or transmitted, in any other form or by any other means, without the prior permission of the publisher. ISSN 1351-5136

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