Leaving Cert Physics Long Questions 2017 2002 15. Particle Physics

Maths questions involving protons colliding in a particle accelerator

2009 Question 10 (a)

In 1932 Cockcroft and Walton succeeded in splitting lithium nuclei by bombarding them with artificially accelerated protons using a linear accelerator.

Each time a lithium nucleus was split a pair of alpha particles was produced.

1. 
   How were the protons accelerated?
   
2. 
   How were the alpha particles detected?
   
3. 
   Write a nuclear equation to represent the splitting of a lithium nucleus by a proton.
   
4. 
   Calculate the energy released in this reaction.
   
5. 
   Most of the accelerated protons did not split a lithium nucleus. Explain why.
   

Cockcroft and Walton’s apparatus is now displayed at CERN in Switzerland, where very high energy protons are used in the Large Hadron Collider.

In the Large Hadron Collider, two beams of protons are accelerated to high energies in a circular accelerator. The two beams of protons then collide producing new particles. Each proton in the beams has a kinetic energy of 2.0 GeV.

6. 
   Explain why new particles are formed.
   
7. 
   What is the maximum net mass of the new particles created per collision?
   
8. 
   What is the advantage of using circular particle accelerators in particle physics?
   

(mass of alpha particle = 6.6447 × 10^–27 kg; mass of proton = 1.6726 × 10^–27 kg;

mass of lithium nucleus = 1.1646 × 10^–26 kg; speed of light = 2.9979 × 10⁸ m s^–1;

charge on electron = 1.6022 × 10^–19 C)
2011 Question 10 (a)

1. 
   List three quantities that are conserved in nuclear reactions.
   
2. 
   Write an equation for a nucleus undergoing beta-decay.
   
3. 
   In initial observations of beta-decay, not all three quantities appear to be conserved.
   

What was the solution to this contradiction?

4. 
   List the fundamental forces of nature in increasing order of their strength.
   
5. 
   Which fundamental force of nature is involved in beta-decay?
   
6. 
   In the Large Hadron Collider, two protons with the same energy and travelling in opposite directions collide. Two protons and two charged pi mesons are produced in the collision.
   

Why are new particles produced in the collision?

7. 
   Write an equation to represent the collision.
   
8. 
   Show that the kinetic energy of each incident proton must be at least 140 MeV for the collision to occur.
   

2008 Question 10 (a)

Baryons and mesons are made up of quarks and experience the four fundamental forces of nature.

1. 
   List the four fundamental forces and state the range of each one.
   
2. 
   Name the three positively charged quarks.
   
3. 
   What is the difference in the quark composition of a baryon and a meson?
   
4. 
   What is the quark composition of the proton?
   
5. 
   In a circular accelerator, two protons, each with a kinetic energy of 1 GeV, travelling in opposite directions, collide. After the collision two protons and three pions are emitted.
   

What is the net charge of the three pions? Justify your answer.

6. 
   Calculate the combined kinetic energy of the particles after the collision
   
7. 
   Calculate the maximum number of pions that could have been created during the collision.
   

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

mass of pion = 2.4842 × 10^–28 kg; speed of light = 2.9979 × 10⁸ m s^–1)

Pair annihilation

2016 Question 12 (d)

{this is the first time that Particle Physics did not come up as a full question. Pick your own adjective to describe the guy(s) who put that paper together. And yes it had to be a man.}

1. 
   The pair annihilation of an electron and a positron has been investigated for many years at CERN in Switzerland. Two gamma-ray photons are produced during this annihilation.
   What is a positron?
   
2. 
   Why are photons always produced in pairs during pair annihilation?
   
3. 
   Write an equation for this annihilation.
   
4. 
   Calculate the frequency of the gamma-radiation produced in this annihilation.
   
5. 
   The pair annihilation of a proton and an anti-proton is now being investigated at CERN.
   

Compare the energy produced in these two annihilations.

Explain your answer.

2014 Question 11 (a)

Read the following passage and answer the accompanying questions.

Cyclotrons and PET Scanners

Positron emission tomography (PET) scanners are designed to detect the pair of photons generated from the annihilation reaction between a positron and an electron.

A carbon–11 nucleus, which has a half-life of twenty minutes, decays with the emission of a positron. The positron travels only a short distance before colliding with an electron in the surrounding matter. Pair annihilation occurs. The emitted photons travel in opposite directions.
Cyclotrons are located in the same hospital as the PET scanners and are used to manufacture radioactive nuclei. Cyclotrons are circular devices in which charged particles are accelerated in a spiral path within a vacuum. The particles are accelerated by a rapidly alternating voltage and acquire high kinetic energies. They spiral outwards under the influence of the magnetic field until they have sufficent velocity and are deflected into a target producing radioactive nuclei, including carbon–11.

(Adapted from “Essentials of Nuclear Medicine Physics”;

Powsner & Powsner; 1998)

1. 
   Electrons are leptons.
   List the three fundamental forces that electrons experience in increasing order of strength.
   
2. 
   Write an equation to represent the pair annihilation described in the text.
   
3. 
   Calculate the frequency of each photon produced in this pair annihilation.
   
4. 
   Why do the photons produced in pair annihilation travel in opposite directions?
   
5. 
   Write a nuclear equation to represent the decay of carbon–11.
   
6. 
   What is the value of the decay constant of carbon–11?
   
7. 
   Explain why the carbon–11 nuclei used in the PET scanner must be produced in a cyclotron in, or close to, the same hospital as the scanner.
   
8. 
   Give an expression for the momentum of a particle in the cyclotron in terms of the magnetic flux density of the field, the charge on the particle and the radius of its circular path at any instant.
   

2012 Question 10 (a)

1. 
   What is a positron?
   
2. 
   When a positron and an electron meet two photons are produced.
   Write an equation to represent this interaction.
   
3. 
   Why are photons produced in this interaction?
   
4. 
   Explain why two photons are produced.
   
5. 
   Calculate the minimum frequency of the photons produced.
   
6. 
   Explain why the photons produced usually have a greater frequency than your calculated minimum frequency value.
   
7. 
   Why must two protons travel at high speeds so as to collide with each other?
   
8. 
   How are charged particles given high speeds?
   
9. 
   Explain why two positrons cannot annihilate each other in a collision.
   

2006 Question 10 (a)

During a nuclear interaction an antiproton collides with a proton. Pair annihilation takes place and two gamma ray photons of the same frequency are produced.

1. 
   What is a photon?
   
2. 
   Calculate the frequency of a photon produced during the interaction.
   
3. 
   Why are two photons produced?
   
4. 
   Describe the motion of the photons after the interaction.
   
5. 
   How is charge conserved during this interaction?
   
6. 
   After the annihilation, pairs of negative and positive pions are produced. Explain why.
   
7. 
   Pions are mesons that consist of up and down quarks and their antiquarks.
   

Give the quark composition of (i) a positive pion, (ii) a negative pion.

8. 
   List the fundamental forces of nature that pions experience.
   
9. 
   A neutral pion is unstable with a decay constant of 2.5 × 10¹² s^–1. What is the half-life of a neutral pion?
   

(mass of proton= 1.673 × 10^–27 kg; Planck constant = 6.626 × 10^–34 J s; speed of light = 2.998 × 10⁸ m s^–1 )