Leaving Cert Physics Long Questions 2017 2002 15. Particle Physics

Pair production

2010 Question 10 (a)

1. 
   What is anti-matter?
   
2. 
   An anti-matter particle was first discovered during the study of cosmic rays in 1932.
   

Name the anti-particle and give its symbol.

3. 
   What happens when a particle meets its anti-particle?
   
4. 
   What is meant by pair production?
   
5. 
   A photon of frequency 3.6 × 10²⁰ Hz causes pair production.
   

Calculate the kinetic energy of one of the particles produced, each of which has a rest mass of 9.1×10^–31 kg.

6. 
   A member of a meson family consists of two particles. Each particle is composed of up and down quarks and their anti-particles.
   

Construct the possible combinations. Deduce the charge of each combination and identify each combination.

7. 
   What famous Irish writer first thought up the name ‘quark’?
   

2003 Question 10 (a)

1. 
   Leptons, baryons and mesons belong to the “particle zoo”.
   

Give (i) an example, (ii) a property, of each of these particles.

2. 
   The following reaction represents pair production.
   

γ → e⁺ + e^–

Calculate the minimum frequency of the γ-ray photon required for this reaction to occur.

3. 
   What is the effect on the products of the reaction if the frequency of the γ-ray photon exceeds the minimum value?
   
4. 
   The reverse of the above reaction is known as pair annihilation.
   

Write a reaction that represents pair annihilation.

5. 
   Explain how the principle of conservation of charge and the principle of conservation of momentum apply in pair annihilation.
   

mass of electron = 9.1 × 10^–31 kg; speed of light, c = 3.0 × 10⁸ m s^–1 ; Planck constant, h = 6.6 × 10^–34 J s

Neutrinos

2015 Question 10 (a)

There are about a trillion neutrinos from the Sun passing through your hand every second.

Neutrinos are fundamental particles and are members of the lepton family.

Leptons are not subject to the strong nuclear force.

1. 
   What is the principal force that neutrinos experience?
   
2. 
   Electrons are also members of the lepton family. Name two other leptons.
   
3. 
   Name one fundamental particle that is subject to the strong nuclear force.
   
4. 
   Pauli proposed that a neutrino is emitted during beta-decay.
   

Why did he make this proposal?

5. 
   During beta-decay, a neutron decays with the emission of a proton, an electron and a neutrino.
   Write a nuclear equation to represent beta-decay.
   
6. 
   Calculate the energy released, in MeV, during beta-decay.
   
7. 
   An electron can be detected in a cloud chamber.
   However it is much more difficult to detect a neutrino. Explain why.
   
8. 
   In a cloud chamber an electron travels perpendicular to the direction of a magnetic field of flux density 90 mT and it follows a circular path.
   Calculate the radius of the circle when the electron has a speed of 1.45 × 10⁸ m s^–1.
   
9. 
   Describe the path of a neutrino in the same magnetic field.
   

2004 Question 10 (a)

1. 
   Beta decay is associated with the weak nuclear force.
   

List two other fundamental forces of nature and give one property of each force.

2. 
   In beta decay, a neutron decays into a proton with the emission of an electron.
   

Write a nuclear equation for this decay. Calculate the energy released during the decay of a neutron.

3. 
   Momentum and energy do not appear to be conserved in beta decay. Explain how the existence of the neutrino, which was first named by Enrico Fermi, resolved this.
   

During the late 1930s, Fermi continued to work on the nucleus.

His work led to the creation of the first nuclear fission reactor in Chicago during 1942.

The reactor consisted of a ‘pile’ of graphite moderator, uranium fuel with cadmium control rods.

4. 
   What is nuclear fission?
   
5. 
   What is the function of the moderator in the reactor?
   
6. 
   How did the cadmium rods control the rate of fission?
   

mass of neutron = 1.6749 × 10^–27 kg; mass of proton = 1.6726 × 10^–27 kg;

mass of electron = 9.1094 × 10^–31 kg; speed of light = 2.9979 × 10⁸ m s^–1

Solutions

2017 Question 12 (d)

1. 
   Explain how the protons were produced.
   ionisation / discharge tube
   
   
   
2. 
   Explain how the protons were accelerated.
   high voltage
   
   
   
3. 
   Explain how the alpha-particles were detected.
   

flashes / zinc sulphide / screen

4. 
   Write the nuclear equation for this reaction.
   +  + K.E.
   
   
   

For this reaction, calculate the loss in mass and hence the energy released (in MeV).
Mass beforehand (mass of reactants) = 1.1646 × 10^-26 + 1.6726 × 10^-27 = 1.33186 × 10^-26 kg

Mass afterwards (mass of products) = 2(6.6443 × 10^-27) = 1.32886 × 10^-26 kg

Loss in mass = 1.33186 × 10^-26 kg - 1.32886 × 10^-26 kg = 3.00 × 10^-29 kg

E = mc² or = (3.00 × 10^-29)(9 × 10¹⁶) = 2.7 × 10^-12 J

Converting to eV: 1.6 × 10^-19 J = 1 eV

2.7 × 10^-12 J = eV = 17.35 × 10⁶ eV = 17.35 MeV

5. 
   Explain the historical significance of this experiment.
   

Verified ��=����^��/ first transmutation by an artificially accelerated particle / important step in development of the particle accelerator / Nobel prize

2016 Question 12 (d)

1. 
   What is a positron?
   

Positively charged electron // anti-electron

2. 
   Why are photons always produced in pairs during pair annihilation?
   

To conserve momentum

3. 
   Write an equation for this annihilation.
   

4. 
   Calculate the frequency of the gamma-radiation produced in this annihilation.
   

Mass of electron = 9.1093826 × 10^-31 kg

Energy ‘released’ when one electron is annihilated = mc²

We only need to look at one electron because two electrons are annihilated to produce two photons, so it’s as if one electron is responsible for producing one photon.

E = (9.1093826 × 10^-31)(3 × 10⁸)²

E = 8.198444 × 10^-14 J
This energy now goes on to create a photon

Energy associated with a photon = hf

f = 1.237 × 10²⁰ Hz

5. 
   Compare the energy produced in these two annihilations.
   

Explain your answer.

Energy from proton annihilation is greater because a proton’s mass is greater

2015 Question 10 (a)

1. 
   What is the principal force that neutrinos experience? Weak (nuclear force)
   

2. 
   Name two other leptons. Muon, tau, positron
   

3. 
   Name one fundamental particle that is subject to the strong nuclear force. Quark
   

4. 
   Why did he make this proposal? Momentum/energy not conserved
   

5. 
   Write a nuclear equation to represent beta-decay.
   

6. 
   Calculate the energy released, in MeV, during beta-decay.
   
   
   

Page 46, 47 and 48 of log tables to get values for the mass of the particles.
Mass of neutron: 1.674 927 28 × 10^-27 kg Mass of proton: 1.672 621 71 × 10^-27 kg

Mass of electron: 9.109 3826 × 10^-31 kg

Mass of neutrino: see page 48 of log tables; the mass of the neutrino is given relative to the mass of an electron. Mass of neutrino = (4.305 × 10^-6)(9.109 3826 × 10^-31) = 3.921589209 × 10^-36 kg
Mass before = mass of neutron= 1.674 927 28 × 10^–27 kg
Mass after = mass of proton + mass of electron + mass of neutrino

= 1.672 621 71 × 10^-27 kg + 9.109 3826 × 10^-31 kg + 3.921589209 × 10^-36 kg

Total mass after = 1.673532652 × 10^-27 kg
Loss in mass = total mass beforehand – total mass afterwards

= (1.674 927 28 × 10^–27 kg) – (1.673532652 × 10^-27 kg)

Loss in mass = 1.395 × 10^–30 kg

To calculate the energy associated with this mass we need to use E = mc²

E = (1.395 × 10^–30)(2.997 924 58)² E = 1.25 × 10^-13 J
Now we need to convert from Joules to eV

1 eV = 1.602 176 53 × 10^-19 J {page 46 of log tables}

So we need to divide 1.25 × 10^-13 by 1.602 176 53 × 10^-19 E = 780188 eV

Now divide by 1×10⁶ to convert to MeV {M = mega = 10⁶} E = 0.78 MeV

7. 
   However it is much more difficult to detect a neutrino. Explain why.
   The neutrino has no charge and only a very small mass.
   

8. 
   Calculate the radius of the circle when the electron has a speed of 1.45 × 10⁸ m s^–1.
   

The force experience by a charged particle in a magnetic field is given by the equation F = Bqv.

The force experience by a particle moving in a circle is given by the equation F = mv²/r

Equating both expressions:

r = 9.16 × 10^–3 m

9. 
   Describe the path of a neutrino in the same magnetic field.
   No deviation
   

2014 Question 11 (a)

1. 
   List the three fundamental forces that electrons experience in increasing order of strength.
   gravitational, weak (nuclear) and electromagnetic
   

2. 
   Write an equation to represent the pair annihilation described in the text.
   

e− + e+ → 2hf

OR

3. 
   Calculate the frequency of each photon produced in this pair annihilation.
   

Mass of electron = 9.1093826 × 10^-31 kg

Energy ‘released’ when one electron is annihilated = mc²

We only need to look at one electron because two electrons are annihilated to produce two photons, so it’s as if one electron is responsible for producing one photon.

E = (9.1093826 × 10^-31)(3 × 10⁸)²

E = 8.198444 × 10^-14 J
This energy now goes on to create a photon

Energy associated with a photon = hf

f = 1.237 × 10²⁰ Hz

4. 
   Why do the photons produced in pair annihilation travel in opposite directions?
   momentum is conserved
   

5. 
   A carbon–11 nucleus, which has a half-life of twenty minutes, decays with the emission of a positron. Write a nuclear equation to represent the decay of carbon–11.
   {This is the first time we have come across what is known as beta-positive decay, where instead of a neutron decaying into a proton plus electron (beta-minus decay), we have a proton decaying into a neutron plus a positron. Physicists must have done some serious head-scratching the day that baby was born. Technically, there was nothing to say that this was on the syllabus. Then again, technically, there was nothing to say it wasn’t.}
   

6. 
   What is the value of the decay constant of carbon–11?
   
   
   

T_1/2 = λ = Half-life is 20 minutes = (20)(60) = 1200 seconds
λ = λ = 0.000578 s⁻¹

7. 
   Explain why . . .
   Because of their short half-life - too many would have decayed before they could be used.
   

8. 
   Give an expression . . .
   The word ‘radius’ is the clue that tells us we’re talking about a centripetal force, the term ‘magnetic flux density’ is the clue that tells us that we’re talking about a magnetic force.
   

Equate the expression for both and rearrange so that we get mv (momentum) on one side:

Centripetal force = magnetic force

Cancel one v on both sides and multiply both sides by r to get rid of the r on the left hand side.
 mv = Bqr

2013 Question 10 (a)

1. 
   How did Cockroft and Walton accelerate the protons?
   High voltage / large electric field
   
   
   
2. 
   How did they detect the alpha-particles?
   When the alpha particles hit a zinc sulfide screen it resulted in flashes of light
   
   
   
3. 
   Write the nuclear equation for the reaction that occurred.
   

+  + K.E.

4. 
   Indicate the historical significance of their observation.
   

It was the 1^st experimental verification of E = mc² / first artificial splitting of the nucleus (atom) /
first transmutation using artificially accelerated particles

5. 
   Calculate the speed of a proton that has a kinetic energy of 700 keV.
   The kinetic energy is 700 keV, so we need to convert this to Joules.
   

1eV =1.6 x 10^–19 Joules

700 keV = (700 x 10³)(1.6 x 10^–19) Joules

Kinetic energy = 1.12 × 10^–13 J
Now we use E_kinetic = ½mv²

1.12 × 10^–13 = ½ mv²

Mass of proton = 1.6730 × 10^-27 kg



v = 1.16 × 10⁷ m s⁻¹

6. 
   Why is the tube evacuated?
   So that particles do not collide with gas particles
   

7. 
   What is the purpose of accelerating the particles to high velocities?
   To overcome repulsive forces // to create new matter
   

8. 
   What is the purpose of the magnets?
   To contain the particles (in a circular path)
   

9. 
   Give an advantage of a circular accelerator over a linear accelerator.
   Takes up less space // particles can achieve greater energy / speed
   

10. 
    Can an accelerator of this design be used to accelerate neutrons? Explain your answer.
    No
    Neutrons have no charge and are therefore not affected by electric / magnetic fields
    

2012 Question 10 (a)

1. 
   What is a positron?
   

A positron is an electron with a positive charge.

2. 
   When a positron and an electron meet two photons are produced.
   

Write an equation to represent this interaction.


OR

3. 
   Why are photons produced in this interaction?
   

The mass of the electron and positron gets converted into energy

4. 
   Explain why two photons are produced.
   

To conserve momentum.

5. 
   Calculate the minimum frequency of the photons produced.
   

Two electrons ‘disappear’ and two photons are created, so we can assume that the each electron ‘is converted to’ a photon.

Mass of electron = 9.1093826 × 10^-31 kg

The energy associated with an electron is given by E = mc²

E = (9.1093826 × 10^-31)(3 × 10⁸)²

E = 8.198444 × 10^-14 J
This now becomes the energy of the photon: E = hf



f = 1.237 × 10²⁰ Hz

6. 
   Explain why the photons produced usually have a greater frequency than your calculated minimum frequency value.
   

In addition to rest mass the colliding particles have kinetic energy.

7. 
   Why must two positrons travel at high speeds so as to collide with each other?
   

To overcome the force of repulsion

8. 
   How are charged particles given high speeds?
   

Particle accelerators / linear accelerator / cyclotron /synchrotron/magnetic fields/electric fields

9. 
   Explain why two positrons cannot annihilate each other in a collision.
   

This would involve a conflict with conservation of charge.

2011 Question 10 (a)

1. 
   List three quantities that are conserved in nuclear reactions.
   

Momentum, charge, mass-energy

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?

The discovery of the neutrino which accounted for the missing momentum.

4. 
   List the fundamental forces of nature in increasing order of their strength.
   

gravitational < weak (nuclear) < electromagnetic < (strong) nuclear

5. 
   Which fundamental force of nature is involved in beta-decay?
   

The weak force.

6. 
   Why are new particles produced in the collision?
   

The kinetic energy of the protons is converted into mass.

7. 
   Write an equation to represent the collision.
   

p + p + KE p + p + ⁺ + π^- + KE

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

We need to find out how much energy is required to produce {just} two pions {with no kinetic energy}.

So we will be using E = 2m_πc² where m_π represents the mass of one pion.

But we don’t have a value for the mass of a pion, just it’s mass relative to the mass of an electron.
Mass of π⁺ = (273)(m_e) = 273(9.109×10^-31 kg) = 2.4869×10^-28 kg
E = 2m_πc²

E = 2(2.4869×10^-28)(3×10⁸)² = 44.76 ×10^-12 J

We now need to convert this to eV. 1 eV = 1.602 ×10^-19 Joules, so we need to divide the our number in Joules by 1.602 ×10^-19 to get the equivalent value in eV.


This is the total kinetic energy associated with two protons, so the kinetic energy of each proton must be 140 MeV.


2010 Question 10 (a)

1. 
   What is anti-matter?
   

Antimatter is material/matter/particles that has the same mass as another particle but opposite charge.

2. 
   Name the anti-particle and give its symbol.
   

positron / anti-electron

3. 
   What happens when a particle meets its anti-particle?
   

Pair annihilation occurs and the mass gets converted to energy.

4. 
   What is meant by pair production?
   

Pair production involves the production of a particle and its antiparticle from a gamma ray photon.

5.