Leaving Cert Physics Long Questions 2017 2002 15. Particle Physics

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Leaving Cert Physics Long Questions 2017 - 2002

15. Particle Physics
Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier

Contents

Key to answering particle physics maths questions 2

Energy conversions – all you need to know 3

Particle accelerators (including Cockcroft and Walton experiment) 4

Maths questions involving protons colliding in a particle accelerator 6

Pair annihilation 7

Pair production 9

Neutrinos 10

Solutions 12

Key to answering particle physics maths questions

Maths questions in this topic are all about energy conversions
The energy can take one of four forms.

1. It can be potential energy: W = QV

(Q is charge, V is potential difference)

Example: Linear accelerators

1. It can be kinetic energy: E = ½ mv2
(m is mass, v is velocity)

Example: Proton-proton collisions

1. It can be in the form of electromagnetic radiation where E = hf
(f is frequency, h is Planck’s constant)

Example: Pair production

1. It can be in the form of mass, in which case the energy equivalent is E = mc2

(m is mass, c is the speed of light)

Example: Large Hadron Collider, Pair annihilation

The context will determine which of the above equations you will need

Notes

1. Make sure you can convert from electron-Volts (eV) to Joules (J) and vice-versa

(1eV =1.6 x 10–19 Joules)

1. Be comfortable dealing with very large numbers and very small numbers on your calculator.

2. Be comfortable using the log-table to find all relevant information, particularly the mass of the particles.
In particular note that page 47 and page 83 are the most used pages.
Note also that on page 83, masses of nuclei are given in terms of the atomic mass unit (u).
You then need to go to page 47 to find the mass of one atomic mass unit.

Energy conversions – all you need to know

Linear Accelerator

potential energykinetic energy
QV
½ mv2

Cockroft and Walton experiment

Some of the mass beforehand disappears and is converted into kinetic energy of the new particles

mass → kinetic energy

+ + K.E.

mc2  K.E

Proton-Proton Collisions

The kinetic energy of the protons just before the collision is converted into the mass of the new particles which were created just after the collision

kinetic energy → mass

+ + kinetic energy = + + additional particles

{+ K.E. of the newly created particles}

K.E  mc2 {+ K.E.}

Pair Production

Energy in the form of electromagnetic radiation (associated with gamma radiation) is converted into mass.

e- + e+ {+ K.E. of the newly created particles}

hf 2c2

Pair Annihilation

Mass is converted into energy in the form of electromagnetic radiation.

2c2  2hf

Particle accelerators (including Cockcroft and Walton experiment)

2013 Question 10 (a)

In 1932 J.D. Cockroft and E.T.S. Walton accelerated protons to energies of up to 700 keV and used them to bombard a lithium target. They observed the production of alpha-particles from the collisions between the accelerated protons and the lithium nuclei.

1. How did Cockroft and Walton accelerate the protons?

2. How did they detect the alpha-particles?

3. Write the nuclear equation for the reaction that occurred and indicate the historical significance of their observation.

4. Calculate the speed of a proton that has a kinetic energy of 700 keV.

Many modern particle accelerators, such as the Large Hadron Collider (LHC) in CERN, have a circular design.

The diagram shows a simplified design of a circular accelerator.

1. Why is the tube evacuated?

2. What is the purpose of accelerating the particles to high velocities?

3. What is the purpose of the magnets?

4. Give an advantage of a circular accelerator over a linear accelerator.

5. Can an accelerator of this design be used to accelerate neutrons? Explain your answer.

2007 Question 10 (a)

Ernest Walton was one of the legendary pioneers who made 1932 the annus mirabilis of experimental nuclear physics. In that year James Chadwick discovered the neutron; Carl Anderson discovered the positron; Fermi articulated his theory of radioactive decay; and Ernest Walton and John Cockcroft split the nucleus by artificial means. In their pioneering experiment Cockcroft and Walton bombarded lithium nuclei with high-energy protons linearly accelerated across a high potential difference (c. 700 kV). The subsequent disintegration of each lithium nucleus yielded two helium nuclei and energy. Their work gained them the Nobel Prize in 1951.

(Adapted from “Ernest Thomas Sinton Walton 1903 –1995 The Irish Scientist” McBrierty; 2003)

1. Draw a labelled diagram to show how Cockcroft and Walton accelerated the protons.

2. What is the velocity of a proton when it is accelerated from rest through a potential difference of 700 kV?

3. Write a nuclear equation to represent the disintegration of a lithium nucleus when bombarded with a proton.

4. Calculate the energy released in this disintegration.

5. Compare the properties of an electron with that of a positron.

6. What happens when an electron meets a positron?

7. In beta decay it appeared that momentum was not conserved. How did Fermi’s theory of radioactive decay resolve this?

charge on electron = 1.6022 × 10–19 C; mass of proton = 1.6726 × 10–27 kg;

speed of light = 2.9979 × 108 m s–1

mass of lithium nucleus = 1.1646 × 10–26 kg; mass of helium nucleus = 6.6443 × 10–27 kg;
2017 Question 12 (d)

In the Cockcroft and Walton experiment, accelerated protons collided with lithium nuclei. In each collision a proton collided with a lithium nucleus to produce two alpha-particles, as shown in this commemorative coin.

1. Explain how the protons were produced.

2. Explain how the protons were accelerated.

3. Explain how the alpha-particles were detected.

4. Write the nuclear equation for this reaction.

5. For this reaction, calculate the loss in mass and hence the energy released (in MeV).

6. Explain the historical significance of this experiment.

2002 Question 10 (a)

1. Name the four fundamental forces of nature.

2. Which force is responsible for binding the nucleus of an atom?

3. Give two properties of this force.

4. In 1932, Cockcroft and Walton carried out an experiment in which they used high-energy protons to split a lithium nucleus. Outline this experiment.

5. When a lithium nucleus () is bombarded with a high-energy proton, two α-particles are produced.

Write a nuclear equation to represent this reaction.

1. Calculate the energy released in this reaction.

mass of proton = 1.6730 × 10-27 kg; mass of lithium nucleus = 1.1646 × 10-26 kg;

mass of α-particle = 6.6443 × 10-27 kg; speed of light, c = 3.00 × 108 m s-1.
2005 Question 11 (a)

Ernest Rutherford made the following point:

If the particles that come out naturally from radium are no longer adequate for my purposes in the laboratory, then maybe the time had come to look at ways of producing streams of fast particles artificially.

High voltages should be employed for the task.

A machine producing millions of alpha particles or protons would be required. These projectiles would be released close to a high voltage and would reel away at high speed. It would be an artificial particle accelerator. Potentially such apparatus might allow physicists to break up all atomic nuclei at will.

(Adapted from “The Fly in the Cathedral” Brian Cathcart; 2004)

1. What is the structure of an alpha particle?

2. Rutherford had bombarded gold foil with alpha particles. What conclusion did he form about the structure of the atom?

3. High voltages can be used to accelerate alpha particles and protons but not neutrons. Explain why.

4. Cockcroft and Walton, under the guidance of Rutherford, used a linear particle accelerator to artificially split a lithium nucleus by bombarding it with high-speed protons. Copy and complete the following nuclear equation for this reaction.

1. Circular particle accelerators were later developed. Give an advantage of circular accelerators over linear accelerators.

2. In an accelerator, two high-speed protons collide and a series of new particles are produced, in addition to the two original protons.

Explain why new particles are produced.

1. A huge collection of new particles was produced using circular accelerators. The quark model was proposed to put order on the new particles.

List the six flavours of quark.

1. Give the quark composition of the proton.

(Refer to Mathematics Tables, p. 44.)

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