Particles and Radiation

Question 1

Nucleons

Answer 1

Collective term for protons and neutrons

Question 2

Atoms are made up of three types of particles:

Answer 2

Protons
Neutrons
Electrons

Question 3

properties of each particle in SI units

Answer 3

Question 4

Specific Charge

Answer 4

specific charge is defined as:
The ratio of the total charge of a particle to its mass

Specific charge is measured in units of coulombs per kilogram (C kg–1)
The specific charge of the electron = (e / me) = 1.76 × 10^11 C kg–1
The specific charge of the proton = (e / mp) = 9.58 × 10^7 C kg–1

Question 5

An atom of mass: 24, atomic no: 12 Mg gains 2 electrons.

What is the specific charge of the ion?

Answer 5

Question 6

Isotopes

Answer 6

Nuclei that have the same number of protons but different numbers of neutrons

Question 7

Isotopic Data

Answer 7

The relative amounts of different isotopes of an element present within a substance

Question 8

the strong nuclear force

Answer 8

• an attractive force acting between all nucleons which is stronger than the electrostatic force
• acts between particles called quarks
• Protons and neutrons are made up of quarks, so the interaction between the quarks in the nucleons keeps them bound within a nucleus
• In comparison to other fundamental forces, the strong nuclear force has a very small range (from 0.5 to 3.0 fm)

Question 9

Properties of the Strong Nuclear Force

Answer 9

The strength of the strong nuclear force between two nucleons varies with the separation between them
This can be plotted on a graph which shows how the force changes with separation:

• The strong force is highly repulsive at separations below 0.5 fm
• The strong force is very attractive up to a nuclear separation of 3.0 fm
• The maximum attractive value occurs at around 1.0 fm, which is a typical value for nucleon separation
• The equilibrium position, where the resultant force is zero, occurs at a separation of about 0.5 fm

Question 10

Comparison of Electrostatic and Strong Forces

Answer 10

The graph below shows how the strength of the electrostatic and strong forces between two nucleons vary with the separation between them:

• The repulsive electrostatic force between protons has a much larger range than the strong nuclear force - However, it only becomes significant when the proton separation is more than around 2.5 fm
• The electrostatic force is influenced by charge, whereas the strong nuclear force is not. This means the strength of the strong nuclear force is roughly the same between all types of nucleon (i.e. proton-proton, neutron-neutron and proton-neutron). This only applies for separations between 0.5 and 3.0 fm (where the electrostatic force between protons is insignificant)
• The equilibrium position for protons, where the electrostatic repulsive and strong attractive forces are equal, occurs at a separation slightly below 0.5 fm

Question 11

radioactive decay

Answer 11

When nuclei are unstable, they can become more stable through the process of radioactive decay.
Three of the most common decay mechanisms are:
* Alpha decay
* Beta-minus decay
* Beta-plus decay

Question 12

Alpha Decay

Answer 12

The decay involves a nucleus emitting an alpha particle and decaying into a different nucleus
An alpha particle consists of 2 protons and 2 neutrons
This is equivalent to a helium nucleus

Question 13

Alpha decay equation

Answer 13

When an unstable nucleus (the parent nucleus) emits radiation, the constitution of its nucleus changes
As a result, the isotope will change into a different element (the daughter nucleus)

Question 14

Beta-Minus Decay

Answer 14

A beta-minus, β-, particle is a high energy electron emitted from the nucleus
β- decay is when a neutron turns into a proton emitting an electron and an anti-electron neutrino

Question 15

Beta-Minus Decay equation

Answer 15

When a β- particle is emitted from a nucleus:
The number of protons increases by 1: proton number increases by 1
The total number of nucleons stays the same: nucleon number remains the same
The new nucleus formed from the decay is called the “daughter” nucleus (nitrogen in the example above)

Question 16

Beta-Plus Decay

Answer 16

A beta-plus, β+, particle is a high energy positron emitted from the nucleus
β+ decay is when a proton turns into a neutron emitting a positron (anti-electron) and an electron neutrino

Question 17

Beta-Plus Decay equation

Answer 17

When a β+ particle is emitted from a nucleus:
The number of protons decreases by 1: proton number decreases by 1
The total number of nucleons stays the same: nucleon number remains the same

Question 18

Neutrino Emission

Answer 18

An electron neutrino is a type of subatomic particle with no charge and negligible mass which is also emitted from the nucleus
The anti-neutrino is the antiparticle of a neutrino

Question 19

alpha vs beta energy levels

Answer 19

Although the neutrino has no charge and negligible mass, its existence was hypothesised to account for the conservation of energy in beta decay
When the number of α particles is plotted against kinetic energy, there are clear spikes that appear on the graph
This demonstrates that α-particles have discrete energies (only certain values)
When the number of β particles is plotted against kinetic energy, the graph shows a curve
This demonstrates that beta particles (electrons or positrons) have a continuous range of energies
This is because the energy released in beta decay is shared between the beta particles (electrons or positrons) and neutrinos (or anti-neutrinos)
This was one of the first clues of the neutrino’s existence
The principle of conservation of momentum and energy applies in both alpha and beta emission

Question 20

How did the evidence in the graph below lead Pauli to predict the existence of the (electron anti)neutrino? (image)

Answer 20

Each beta decay releases the same amount of energy ✔ When the beta particle has less than the maximum energy the missing energy cannot be accounted for by the recoil of the daughter nucleus ✔, so there must be another particle to carry away the missing energy ✔

Question 21

Antimatter

Answer 21

• All particles of matter have an antimatter counterpart
  Corresponding matter and antimatter particles have:
• Opposite charges
• The same mass
• The same rest mass-energy

Question 22

rest mass-energy

Answer 22

The rest mass-energy of a particle is the energy equivalent to the mass of the particle when it is at rest

Question 23

The Photon Model

Answer 23

A massless “packet” or a “quantum” of electromagnetic energy
Each photon carries a specific amount of energy, or “quanta”, and transfers it all in one go, rather than supplying it consistently

Question 24

Calculating Photon Energy

Answer 24

Planck’s Constant = h = 6.63×10^-34 Js
speed of light = c = 3.0 x 10^8 ms^-1

This equation tells us:
The higher the frequency of EM radiation, the higher the energy of the photon
The energy of a photon is inversely proportional to the wavelength
A long-wavelength photon of light has a lower energy than a shorter-wavelength photon

Question 25

Annihilation

Answer 25

When a particle meets its corresponding antiparticle ✔, the mass of the two particles is converted to energy in gamma photons ✔, two photons are produced that travel in opposite directions so that momentum is conserved ✔

Question 26

The two most common particle-antiparticle pairs that are seen are:

Answer 26

Proton-antiproton annihilation Electron-positron annihilation

Question 27

The minimum energy of one photon after annihilation is...

Answer 27

Question 28

Pair Production

Answer 28

Photon (with sufficient energy) interacts with a nucleus ✔, energy of photon is used to create a particle-antiparticle pair ✔, excess photon energy is transferred to KE of particle-antiparticle pair ✔

Question 29

total energy formula

Answer 29

E(total) = Erest +Ekinetic

Question 30

The minimum energy required for a photon to undergo pair production is...

Answer 30

The minimum energy required for a photon to undergo pair production is equal to the total rest mass energy of the particles produced:

Question 31

Worked example Calculate the maximum wavelength of one of the photons produced when a proton and antiproton annihilate each other.

Answer 31

Question 32

The Four Fundamental forces / Interactions

Answer 32

The Four Fundamental forces / Interactions - strongest to weakest: * Strong Nuclear (or Strong Interaction) * Electromagnetism * Weak Nuclear * Gravity

Question 33

Range and particles affected by the 4 fundamental forces

Answer 33

**gravitational:** * infinite range * only affects particles with mass **electromagnetic:** * infinite range * only affects particles with charge **weak:** * range of up to 10–18 m * affects all particles **strong:** * range of ~ 10–15 m * only affects hadrons

Question 34

Exchange Particles

Answer 34

When two particles exert a force on each other, a virtual particle is created Virtual particles only exist for a short amount of time and carry the fundamental force between each particle

Question 35

repulsive exchange particles analogy

Answer 35

Two people are on skateboards and a ball is passed between them. Due to this, they start to move away from each other. The ball represents an exchange particle creating repulsion

Question 36

attractive exchange particles analogy

Answer 36

However, if one person throws a boomerang to the other, they will start to move closer together. The boomerang represents an exchange particle creating attraction

Question 37

Gauge Bosons

Answer 37

Exchange particles that mediate the four fundamental interactions.

Question 38

gravity exchange particle

Answer 38

Since gravity is so weak, it only has a noticeable effect on large masses, therefore, gravity does not play a part in particle interactions The theorised exchange particle for the gravitational force is the graviton, however, this has not yet been discovered

Question 39

The Electromagnetic Force exchange particle

Answer 39

The electromagnetic force is only between charged particles The exchange particle that carries this force is the virtual photon, γ The electromagnetic force is also responsible for binding electrons to atoms This is due to the attractive force between the negative electrons and positive nucleus

Question 40

Properties of the photon are:

Answer 40

It has no mass It has no charge It is its own antiparticle

Question 41

Hadrons

Answer 41

Hadrons are the group of subatomic particles that are made up of quarks Therefore, hadrons can feel the strong nuclear force

Question 42

two classes of hadrons:

Answer 42

* Baryons (3 quarks) - protons uud and neutrons udd * Mesons (quark and anti–quark pair) - pions and kaons

Question 43

two classes of Anti–hadrons:

Answer 43

Anti–baryons (3 anti-quarks) - anti-protons and anti-neutrons Anti–mesons (quark and anti–quark pair) - anti-pions and anti-kaons

Question 44

Quarks

Answer 44

* The three most common flavours of quarks are: up, down and strange * The majority of hadrons are made up of different combinations of these quarks * Each quark has a charge, baryon number and strangeness

Question 45

Anti-quarks

Answer 45

These are identical to quarks except with opposite relative charges, baryons numbers and strangeness

Question 46

Worked example A K- particle has a strangeness of –1. Determine the quark structure of this particle.

Answer 46

kaon = meson, so it is: quark and anti-quark. c = 0 s = -1

Question 47

Worked example In the nucleus of Iron 56, 26, Fe, how many 'up' quarks are there?

Answer 47

* The number of protons is from the proton number = 26 protons * Number of neutrons = 56 - 26 = 30 neutrons * Protons are made up of uud quarks = 2 up quarks * Neutrons are made up of udd quarks = 1 up quark * 6 protons × 2 up quarks = 52 up quarks * 30 neutrons × 1 up quark = 30 up quarks * Total number of up quarks = 52 + 30 = 82 up quarks

Question 48

Baryon Number

Answer 48

* The baryon number, B, is the number of baryons in an interaction * B depends on whether the particle is a baryon, anti-baryon or neither * Baryons have a baryon number B = +1 * Anti-baryons have a baryon number B = –1 * Particles that are not baryons have a baryon number B = 0

Question 49

The Proton as a Baryon

Answer 49

* The proton is the most stable baryon * This means it has the longest half-life of any baryon and is the particle which other baryons eventually decay to * It is the most stable baryon because it is also the lightest baryon * Radioactive decay occurs when heavier particles decay into lighter particles * A decay of the proton would therefore violate the conservation of baryon number * It is theorised that the proton has a half-life of around 1032 years and research experiments are still underway that are designed to detect proton decay

Question 50

Pions

Answer 50

* Pions (π–mesons) can be positive (π+), negative (π–) or neutral (π0) * The anti–particle of the positive pion is the negative pion (and vice versa) * The neutral pion is its own anti–particle * Pions are the lightest mesons, making them more stable than other types of meson * They were originally discovered in cosmic rays and can be observed in a cloud chamber

Question 51

Pions & The Strong Nuclear Force

Answer 51

* The strong nuclear force keeps the protons and neutrons bound together in a nucleus and is one of the four fundamental interaction. Each of these interactions is caused by a particle exchange * The pion is the exchange particle of the strong nuclear force * This means that the strong force is transmitted between a proton and neutron by the exchange of a pion * Pions are said to mediate (bring about) the strong nuclear force * The pion created is a temporary violation of energy and mass conservation but since it is a virtual particle, it is not directly observed

Question 52

gluon & The Strong Nuclear Force

Answer 52

The gluon is also an exchange particle of the strong force. The difference between pions and gluons as mediators of this force are: * Gluons are responsible for binding quarks together. This is referred to as the strong interaction * Pions are responsible for binding nucleons together. This is referred to as the strong nuclear force Collectively, these are referred to as the strong force

Question 53

Kaons

Answer 53

Kaons (K–mesons) can also be positive (K+), negative (K–) or neutral (K0) The anti–particle of the positive kaon is the negative kaon (and vice versa) Kaons can be produced by the strong interaction between pions and protons

Question 54

Kaon Decay

Answer 54

Kaons are heavy and unstable and normally decay into pions They are known to have unusually long lifetimes This is because kaons contain a strange quark and longer lifetimes are characteristic of particles containing strange quarks Kaons decay through the weak interaction An example of a kaon decay would be a neutral kaon decaying into a positive pion and negative pion: κ0 -> π+ + π-

Question 55

Leptons

Answer 55

Leptons are a group of fundamental (elementary) particles - This means they are not made up of any other particles (no quarks) Leptons interact with other particles via the weak, gravitational or electromagnetic interactions They do not interact via the strong nuclear force

Question 56

The most common leptons are:

Answer 56

* The electron, e– * The electron neutrino, ve * The muon, μ– * The muon neutrino, vμ

Question 57

# er comparison of masses and chharges of the most common Leptons

Answer 57

* The muon is similar to the electron but is slightly heavier * The mass of an electron is about 0.0005u, whereas the mass of a muon is about 0.1u * Electrons and muons both have a charge of -1e * Neutrinos are the most abundant leptons in the universe and have no charge and negligible mass (almost 0)

Question 58

Lepton Number

Answer 58

Similar to baryon number, the lepton number, L is the number of leptons in an interaction * Leptons have a lepton number L = +1 * Anti-leptons have a lepton number L = –1 * Particles that are not leptons have a lepton number L = 0

Question 59

Muon Decay

Answer 59

Muons (μ–) -> electron (e–) + anti-electron neutrino (ṽe) + muon neutrino (νμ): Charge: -1 -> -1 + 0 +0 Electron lepton number, Le 0 -> 1 - 1 + 0 muon lepton number, Le 1 -> 0 + 0 + 1 The numbers on each side of the equation are equal for charge, electron lepton number and muon lepton number, therefore, muon decay satisfies these conservation laws

Question 60

Quantum Number

Answer 60

A value which describes physical properties of subatomic particles e.g. baryon number, lepton number, strangeness. Quantum numbers can only take a certain set of integer values and must be conserved in particle interactions.

Question 61

Strangeness

Answer 61

Strangeness is conserved in every interaction except the weak interaction This means that strange particles are always produced in pairs (e.g. K+ and K–)

Question 62

Answer 62

Question 63

exchange particle of the strong interaction

Answer 63

* The exchange particle of the strong interaction is either: * The pion (between nucleons) * The gluon (between quarks) * This means that leptons cannot interact with the strong force, since they are not made up of quarks

Question 64

The Weak Interaction

Answer 64

* The weak interaction is responsible for the radioactive decay of atoms * The exchange particle that carries this force is the W–, W+ or Z0 boson * The type of exchange particle depends on the type of interaction

Question 65

The Weak Interaction - β– decay

Answer 65

In β– decay, a neutron turns into a proton emitting an electron and an anti-electron neutrino.

Question 66

The Weak Interaction - β+ decay

Answer 66

In β+ decay, a proton turns into a neutron emitting a positron and an electron neutrino

Question 67

Electron Capture & Electron–Proton Collisions

Answer 67

Electrons and protons are attracted to each other via the electromagnetic interaction However, when they interact with each other, it is the weak interaction that facilitates the collision Both electron capture and electron-proton collisions have the same decay equation P + e- => n + Ve

Question 68

Electron Capture

Answer 68

Electron capture is when an atomic electron is absorbed by a proton in the nucleus resulting in the release of a neutron and an electron neutrino This decay is mediated by the W+ boson

Question 69

Electron–Proton Collisions

Answer 69

Electron-proton collisions are similar; when an electron collides with a proton, a neutron and an electron neutrino are emitted This decay is mediated by the W– boson

Question 70

Feynman Diagrams

Answer 70

Particle interactions and decays can be represented using Feynman diagrams They are a way of visualising particle equations and the exchange particles involved

Question 71

Rules for Feynman diagrams

Answer 71

The y-axis represents time and the x-axis represents space A vertex is where particles and exchange particles meet - these represent points of interaction (e.g. electromagnetic, weak or strong) Incoming particles come in at the bottom, and outgoing particles leave at the top Particles are represented by straight lines which have arrows Each straight line must have an arrow with its direction forward in time Exchange particles are represented by wavy lines which have no arrows The transfer of exchange particles is from left to right unless indicated by an arrow above the wavy line Hadrons/quarks are present on the left and leptons on the right, they must never meet at a vertex Charge, baryon number and lepton number must be conserved at each vertex Lines must not cross over

Question 72

Electromagnetic Interactions

Answer 72

When two electrons approach each other, they experience repulsion due to the electromagnetic force This can be represented on a Feynman diagram to show the exchange of a virtual photon

Question 73

Quark Composition: β– decay

Answer 73

β– decay is when a neutron turns into a proton emitting an electron and anti-electron neutrino More specifically, a neutron turns into a proton because a down quark turns into an up quark

Question 74

Quark Composition: β+ decay

Answer 74

β+ decay is when a proton turns into a neutron emitting an positron and an electron neutrino More specifically, a proton turns into a neutron because an up quark turns into a down quark

Question 75

Application of Conservation Laws - things that need to be conserved

Answer 75

All particle interactions must obey a set of conservation laws. These are conservation of: Charge, Q Baryon number, B Lepton Number, L Strangeness, S Energy (or mass-energy = rest energy) Momentum However, strangeness does not need to be conserved in weak interactions. It can change by either 0, +1 or –1 Quantum numbers such as Q, B, L and S can only take discrete values (ie. 0, +1, –1, 1/2) To know whether a particle interaction can occur, check whether each quantum number is equal on both sides of the equation If even one of them, apart from strangeness in weak interactions, is not conserved then the interaction cannot occur

Question 76

particles with a strangeness of 1

Answer 76

Question 77

particles with a strangeness of -1

Answer 77

Σ-, Σ0, Σ+

Question 78

Particles with strangeness of 0

Answer 78

Pion-, 0, + And others

Question 79

Answer 79

Question 80

k0 vs anti k0 and pi0 vs anti pi0

Answer 80

Question 81

Wavelength of visible light

Answer 81

380-700nm 3 - 1.5eV 400 - 750 thz