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Physics AS -‐ Unit 1 -‐ Particles, Quantum
Phenomena and Electricity -‐ Revision Notes
Particle Physics
Inside the Atom
∞ Electron (negatively charged) in shells and subshells around nucleus ∞ Nucleus composing of protons (positively charged) and neutrons ∞ Nucleons – protons and neutrons ∞ Coulomb (C) – Unit of charge equal to the electrical charge transferred by a steady current of 1 Ampere in 1 Second ∞ Elementary Charge ( e) -‐ Electric charge carried by a proton or equivalently the absolute value of the electric charge carried by a electron (as electron is negatively charged) e = 1.602176487×10 −
Particle Relative Mass Absolute Mass (Kg)
Relative Charge Absolute Charge (C) Proton 1 1.67x10 -‐27^ +1 +1.60x10 -‐ Neutron 1 1.67x10 -‐27^0 Electron Negligible 9.11x10 -‐31^ -‐1 -‐1.60x10 -‐
Z
A
X
A = Mass number/Nucleon Number Z = Atomic Number (Number of protons)
∞ Isotope -‐ an atom with the same number of protons (Atomic number) but a different number of neutrons (mass number). ∞ Each different type of nucleus is known as a Nuclide
Specific Charge
∞ Specific Charge – Charge of a specific particle divided by its mass
Nucleus of 11 H has a charge of +1.60x10 19 C and mass of 1.67x10 -‐27^ Kg hence its specific
charge = 9.58x10 7 CKg -‐
Fundamental Forces
∞ Current theories suggest that there are only four types of interaction in the universe between particles: o Gravity – This force acts between all particles in the universe and has an infinite range (however reduces in strength according the inverse square law). At an atomic scale it has negligible influence, as it is the weakest fundamental force in the universe. Gravitation is mediated by the graviton (undiscovered) o Electromagnetic Force – This force acts between any charged particles. It can either be repulsive (same charge) or attractive (different charges). The electromagnetic force is responsible for keeping molecules together. The electromagnetic force is mediated by virtual photons o Weak Interaction – This force acts on all known fermions or rather all particle with a ½ integer spin (quarks, leptons and baryons but not bosons-‐ elemental bosons and baryons). The weak interaction acts over a very short range (roughly an atto-‐meter 1x10 -‐18^ ). Over this range it is many times stronger than gravitation (roughly 10 33 ). The weak interaction is responsible for
electromagnetic decay. The weak interaction is mediated by W and Z Bosons (elemental particles) o Strong Interaction – This force is observable in two areas. On the smaller scale the strong interaction is responsible for holding quarks together in hadrons, on the larger scale it binds protons and neutrons together inside the atomic nucleolus (when talked about in terms of binding protons and neutrons together it is referred to as the strong nuclear force or the residual strong force). The strong force binding quarks together is mediated by gluons , while the mediator responsible for binding protons and neutrons together is the Pion or Pi Meson
Strong Nuclear Force (Residual Strong Force)
∞ Overcomes the electrostatic repulsion between ∞ Keeps the nucleus stable ∞ Attractive between 4-‐0.4fm (Femto-‐ Metre = 1x10 -‐15^ m) and repulsive below 0.5fm (otherwise the nucleus would collapse and be point like) ∞ Keep all nucleons together not just protons ∞ The mediators of the nuclear force are
Pions or Pi Mesons ( π 0 )
∞ Also called the residual strong force (as the strong nuclear is related to the strong force), the strong nuclear force is responsible for keeping nucleons together while the strong force is responsible for keeping quarks together (mediator – Gluons)
Radioactive decay
Alpha Decay ∞ Release alpha particles (positively charged helium ions)
α
∞ Reduces mass number of a nucleus by 4 and atomic number by 2 hence:
Z
A
X → (^2)
α
A − 4
X
Beta Decay
∞ 2 types of Beta Radiation: β+^ and β −
β +^ Decay (positron) ∞ Proton decays into a neutron emitting an electron neutrino and a positron:
p → n + ve + e
β -‐^ Decay ∞ Neutron decays into a proton emitting an electron and an electron anti-‐neutrino:
n → p + V (^) e + e
Note: bar above electron neutrino indicated that it is the anti-‐particle counterpart, the electron does not follow this rule and instead the positron is shown by a change of charge
Gamma Radiation ∞ When alpha or beta decay occurs the nucleus is usually left in an excited state it subsequently releases a high energy photon (gamma particle) to reduce this energy
∞ Photon^ γ^ -‐ no mass and no charge
E γ = 2 E 0
as (^) E = hf
hf = 2 E 0
Annihilation ∞ This occurs when a particle and its corresponding anti-‐particle meet and convert themselves to energy in the form of 2 photons as seen in diagram. ∞ As 2 photons are produced using the equations above it can be shown: 2 E γ = 2 E 0
Hence:
E = mc
hf = E 0
Particle Interaction
Electromagnetic Force ∞ Occurs only between charged particles: o Opposite charges attract o Same charges repel ∞ The Mediators of the force are virtual photons; they are called so as we cannot directly detect them as if we did we would stop the force from occurring.
Weak Nuclear Force ∞ Responsible for Beta decay (both types) ∞ Weak interaction only occurs with leptons and hadrons, this explains why neutrinos are so reluctant to react with anything ∞ The Mediators of this force are bosons of which there are 3 types: W +^ W -‐^ and Z, The W bosons are each others respective anti-‐particle (opposite charges) while the Z boson is its own and subsequently has no charge (Z bosons are not covered in the specification). ∞ W Bosons: o Non-‐zero rest mass o Short range; Bosons are relatively massive and consequently are high in energy which means they have a short lifetime which leads to them only being able to act over small distances (typically 10 -‐17^ m)
Annihilation Diagram (not Feynman diagram)
Feynman Diagrams
∞ Particle interactions and decays can be represented visually by the means of a Feynman diagram (names after Richard P. Feynman) ∞ The interaction is represented on the diagram as followed: o Following from the bottom to the top of the diagram shows the interaction’s/decay’s change with time o The other axis (left to right) shows the particles position in space at any given time Time
Space
Electron (K or L) Capture ∞ This occurs when a proton rich nucleus turns a proton into a neutron by capturing an electron from the K or L shell (1 st^ and 2 nd^ shell respectively) ∞ This process can also occur when a proton and an electron collide however if the electron has sufficient energy a different interaction will occur where a W -‐^ Boson is exchanged from the electron to the proton
e
Classification of Particles
∞ We can classify all types of particles according to their spin: (spin is a characteristic property of elemental particles; just as charge is): o Fermions § Have half-‐integer spin, i.e. a multiple of 1 2 § Can be a elementary or composite particle (composite particles are made up of a number of elementary particles) § All known fermions are Dirac fermions, that is for every particle there is a distinct anti-‐particle (a particle with certain opposite properties such as charge) § Fermions are the basic “building blocks” of matter – they make up protons and neutrons and include electrons which together is the composition of atoms § 12 types of fermions (ignoring anti-‐particles), 6 quarks and six leptons o Bosons § Have integer spin § The fundamental forces of nature (electromagnetism, strong and weak interaction and gravitation) are called gauge bosons § Can be a elementary or composite particle (composite particles are made up of a number of elementary particles)
Matter and Anti-‐Matter
Is made up of:
3 Quarks form the hadron group:
A Quark-‐Anti-‐ Quark Pair forms the hadron group:
There are 6 Leptons, 3 negatively charged leptons each with their own associated uncharged Neutrino
Quarks Classed as Fermions -‐ ½ Integer Spin When combined form Hadrons:
Leptons Classed as a Fermion -‐ ½ Integer Spin
Mesons Classed as bosons -‐ integer spin
Baryons Classed as fermions -‐ ½ integer spin
Include protons, neutrons and their antiparticles
Includes the Kaon and the Pion (Mediator of the strong nuclear force)
Quarks
∞ The building blocks of all hadrons (composite particles – ones made out of a combination of fundamental) ∞ Have half-‐integer spin ∞ Quarks can never be found by themselves due to colour confinement (based upon another characteristic property: colour) ∞ The quarks and some characteristic properties:
Name Symbol Anti-‐ Particle
Charge (In terms of elemental charge)
Mass (MeV/c 2 )
Baryon Number
Strangeness
Up u^ u + 2
Down d d − 1
Charm c^ c + 2
Strange s^ s − 1
-‐1 (+1 for s )
Top t^ t + 2
Bottom b b − 1
∞ All of the associated anti-‐quarks have opposite charge, baryon number and strangeness ∞ Up and down quarks have the lowest masses and the other quarks rapidly change into up and down quarks ∞ Note: only up down and strange quark characteristics needed for exam
Bosons
∞ Mediator particles (ones that are exchange particles for the fundamental forces of nature) are called gauge bosons ∞ The bosons and some characteristic properties:
Particle Symbol Anti-‐ Particle
Charge (In terms of elemental charge)
Interaction Mediated
Existence
Photon^ γ^ Self 0 Electromagnetic
(Virtual Photon)
Confirmed
W Boson W −^ + 1
-‐1 ( (^) W +^ +1) Weak Interaction
Confirmed
Z Boson Z Self 0 Weak
Interactions
Confirmed
Higgs Boson
H^0 Self^0 None^ Unconfirmed
Gluon g^ Self 0 Strong
Interaction
Confirmed
Graviton G Self 0 Gravitation Unconfirmed
Note: Only boson to have an antiparticle is the W boson
Composite Particles
∞ Composite particles are particles that are made out of other elemental particles bound together, protons and neutrons are composite particles as are atoms and even molecules
Hadrons ∞ Hadrons are strong-‐interacting composite particles ∞ Hadrons are either: o Composite fermions (half integer spin), these are called baryons o Composite bosons (integer spin), these are called mesons ∞ All known hadrons are composed of quarks and antiquarks
Baryons (fermions)
∞ Baryons have half integer spin ∞ They are made up of three quarks (held together by the strong force) ∞ Anti-‐Baryons are made up of the anti-‐particle partners of the respective quarks in the normal baryon
∞ As every quark has a baryon number of +
, any baryon has a baryon number of +1 (as
a baryon is made up of 3 quarks). Likewise an anti-‐quark has a baryon number of −
therefor an anti-‐baryon has a baryon number of -‐1 (as made up of 3 anti-‐quarks)
∞ A Proton – has 2 up quarks and a down quark shown by uud
∞ A Neutron – has 2 down quarks and an up quark udd
∞ An Anti -‐ Proton – has 2 anti-‐up quarks and one anti-‐down quark udd
∞ The proton is the only stable baryon, even a free neutron (outside an nucleus) decays
into a proton releasing an electron and an electron anti-‐neutrino as in β −
Quarks and Beta Decay
∞ In the exam may be expected to represent β −^ or β+
with regard to quark change apposed to baryon change
∞ As stated before β −^ is a neutron decaying into a proton
with the emission of an electron and a anti-‐electron neutrino, in this decay a down quark is turning into an up quark which changes the quark composition from udd (a neutron) to uud (a proton). This change in quark composition can be represented in the Feynman diagram to the right
decay is a proton decaying into a neutron emitting a position and an electron neutrino. In this decay an up quark changes into a down quark. This changes the quark composition from uud (a proton) to udd (a neutron). This change in quark composition can be represented in the Feynman diagram to the left
Conservation Rules
∞ All particles obey certain conservation rules when they interact.
Conservation of Energy ∞ As in all changes in science, not juts particle interactions and decays, the amount of energy remains fixed in a system ∞ This also applies to the “rest energy” of a particle (energy may be seen to have been lost however this “lost” energy may have been converted into mass following the rule
E = mc^2
∞ No exceptions have been found for this law
Conservation of Charge ∞ In any interaction or decay the total of the charges of the particles before the interaction or decay is the same as the total of the charges of the particles afterwards ∞ No exceptions have been found to this law
Conservations of Lepton Number ∞ In any change, the total lepton number for each lepton branch before the change is equal to the total lepton number for that branch after the change ∞ All leptons have lepton number + ∞ All anti-‐leptons have lepton number -‐ ∞ Conservation of the branch of lepton also applies: o Lepton electron, muon and tau number is always conserved o This can be useful to find out which type of neutrinos are emitted during certain decays
Conservation of Strangeness ∞ In any strong interaction strangeness is always conserved ∞ The total of all the strangeness of the particles before the change is equal to the total strangeness of the particles after the change ∞ It is not conserved however when the weak interaction is involved
Conservation of Baryon Number ∞ In any change the baryon number before the change is equal to the lepton number after the change ∞ All baryons have baryon number + ∞ All anti-‐baryons have baryon number -‐ ∞ All mesons or leptons have baryon number 0 ∞ This can be also thought of through quark change as each quark has baryon number +1/
Quantum Phenomena
Electromagnetic Waves
∞ The electric and magnetic fields are perpendicular both to each other and the direction of propagation of the particle ∞ There is no need for a medium for an electromagnetic wave to travel through ∞ Wavelength – Defined as the distance between two adjacent points in phase in a wave ∞ Period – The period of a wave is defined as the time taken for one whole wave to pass a point through space:
∞ P^ =^
1
f ∞ Wave Speed – Speed of the waves is equal to distance travelled by wave in one cycle divided by time taken for one cycle
C =
λ
f
Therefor c^ =^ f^ λ
The Photoelectric Effect
∞ The photoelectric effect is a type of quantum phenomena that shows that light can behave as a particle as well as a wave (the photoelectric effect can only be explained with regards to light acting as particles or “Quanta” of energy)
∞ Experiments showed that when light was shone on a metal electrons could be emitted from the surface of metal however the emission of these electrons were dependent on several factors: o Photoelectric emission of electrons from a metal surface does not take place if the frequency of the incident electromagnetic radiation is below a certain value known as the threshold frequency. The threshold frequency is dependent on the type of metal used Note: as c = f λ the wavelength of that incident light has to below a maximum value o The number of electrons emitted per second is proportional to the intensity of the electromagnetic radiation as long as the frequency of that electromagnetic radiation is above the threshold frequency as discussed before o Photoelectric emission occurs instantaneously provided the frequency of the incident electromagnetic radiation is above the threshold frequency
Explanation of the Photoelectric Effect – The Photon Model of Light ∞ Electromagnetic radiation consists of packets (quanta) of energy, known as photons. The energy of each photon can be found using the following formula:
E = hf
where h = Planck’s constant 6.63x10−^34 and f is the frequency of the electromagnetic radiation
∞ When light is incident on a metal surface, an electron at the surface absorbs a single photon from the incident light and therefore gains energy equal to hf, as calculated using the formula above
The Photoelectric Effect Represented on a Graph ∞ If the maximum kinetic energies of the emitted electrons at different frequencies are known the work function and threshold frequency of that metal can be calculated by means of a graphical method:
∞ The vertical axis represents the maximum kinetic energy of the electron that has been emitted o A positive energy represents the kinetic energy of the electron emitted o A negative energy represents how much energy the electron (that absorbs a photon) is lacking from being able to escape the metal
∞ The horizontal axis represents the frequency of the light striking the metal ∞ We can use the graph to find several things: o The x-intercept of the graph represents the threshold frequency of the metal. An emitted election will have zero kinetic energy if it has just absorbed a photon of the threshold frequency. o The y-intercept represents the negative value of the work function of that material. Photons with zero frequency have no energy. The receiving electrons would have gained no energy and therefore would need a certain amount of energy to be emitted – this is the work function
o Looking at the graph the gradient represents the change in energy divided by the change in frequency; that is how much the maximum kinetic energy would increase if the frequency increased by 1 Hz. Using the equation:
E = hf
Rearranging to find h:
h =
E
f
As
E
f
represents the gradient of the graph it can be seen that the gradient of the graph represents h
- Plank’s Constant!
Collisions of Electrons with Atoms
The Electron Volt ∞ The electron volt is a unit of energy, and is used especially in atomic and nuclear physics where the energies that are used are very small ∞ The electron volt – is defined as the amount of energy gained by an electron as it is accelerated through a potential difference of 1 volt
1 eV = 1.6 × 10
J Note how the electron volt is closely related to the elementary charge
Excitation and Ionisation ∞ If a vaporised sample of an element has an electric current passed through it some of the electrons of the atoms of that element may absorb some energy as a result of a collision with the charge carriers passing through the vapour ∞ When electrons are in their lowest energy states, they are said to be in the ground state ∞ Excitation is when an atomic electron gains energy and as a results moves to a higher energy state (electronic orbit) ∞ Ionisation is when an atomic electron gains so much energy that it can break free of the atom and become totally dissociated from the atom ∞ Ions are charged atoms, they can be formed when electrons are removed or added ∞ A negative ion is formed where there are more electrons than protons ∞ A positive ion is formed when there are more protons than electrons
Line Spectra ∞ When electrons are excited by passing current though the vapour of an element, or by other means such as heating; the excited electrons do not stay in the excited state for long. They come down to lower energy states, giving off energy in the form of light. ∞ The light emitted can be separated into individual lines of differing wavelengths by using a diffraction grating (the angle a certain wavelength of light gets diffracted depends
upon on its wavelength and follows the formula d sin θ = n λ and is used in unit 2)
∞ This produces a line spectra ∞ The line spectra of hydrogen is shown below:
∞ The specific lines of the line spectra can be very useful in finding out how the electrons exist around the nucleus ∞ We can use these spectra lines to look at the “stationary states’ of the electrons around the nucleus ∞ The electron quantum states and their corresponding electron energies for the hydrogen atom can be seen below:
Fluorescent Tube ∞ A fluorescent tube emits visible light when excited by means of an electric current ∞ Inside the tube is mercury vapour at low pressure ∞ The inside of the tube is coated with a fluorescent compound, typically phosphor ∞ A very simplified explanation of how the tube works: o When the tubew is switched on, the electrode heats up and emits electrons o Ionisation and excitation of the mercury atoms occurs as the electrons emitted collide with the mercury’s atomic electrons o The mercury atoms emit Ultraviolet photon as well as visible photons and photons of much less energy when they de-‐excite o The ultraviolet photons are absorbed by the internal phosphor coating causing excitation of their atomic electrons o The atomic electrons then de-‐excite emitting visible photons
∞ Fluorescent lamps are much more efficient than filament lamps due to the fact they lose much less energy in the form of heat (a filament light bulb loses 90% of the energy supplied to heat while fluorescent only a few percent) ∞ Fluorescent tubes use mercury vapour at a low pressure in order to ensure the electrons gain enough energy between collisions for the collisions to result in the required excitation of the mercury atoms (in order to emit UV light), as the electrons move from one side to another they are being accelerated therefore gaining energy
Wave Particle Duality
∞ Light can behave as both particles and waves: o The wave light nature is observed thought diffraction o The particle like nature is observed through the photoelectric effect
Matter Waves ∞ If light can behave as a wave, so can other forms of matter ∞ Matter particles have a wave-‐particle nature ∞ The wave-‐like behaviour of mater is characterised by its wavelength also known as the De Broglie Wavelength, which is related to the momentum of the particle by the means of the equation:
λ =
h
p
where λ is the De Broglie wavelength of the particle, h is Plank’s constant (6.67x10i^34 ) and p is
the momentum of the particle (momentum is found by the equation: p = mv )
∞ Particles that have the same De Broglie wavelength have the same momentum!
∞ Particles display behaviour of both particles and waves, examples are: o Wave nature is shown in such experiments such as diffraction gratings o Particle nature is shown in photoelectric effect (atomic collisions)
Electricity
Current and Charge
∞ Electric current is defined as the rate at which electrically charged particles pass a point in a circuit 1 coulomb Per second = 1 Ampere
I =
Δ Q
Δ t Note: Where I is current, Q charge and T time
∞ The coulomb is a measure of charge ∞ In metallic conductors the charges particles and free electrons that travel from negative to positive (cathode to anode) ∞ Conventional current however and circuit diagrams regard current as traveling form positive to negative ∞ To make a current flow a potential difference must be present between 2 places in the circuit ∞ The magnitude of charge of 1 electron is 1.6x10 -‐19^ C
Energy and Potential Difference
∞ Potential Difference or voltage is defined as the energy or work done per unit charge ∞ It is measured in volts, 1 volt is defined as 1 joule of energy transferred to one coulomb of charged particles
V =
W
Q
or W^ =^ QV
Note: where v is voltage, w is the work done in moving the charged particles and q is the total charge of the charged particles ∞ The emf of a source of electricity is defined as the electrical energy produced per unit charge passing through the source. The unit of emf is the volt
Electrical Power and Current
∞ As Q = I Δ t (from definition of an amp) and W = QV we can see that:
W = I Δ tV ∞ Also because power is the rate of energy transfer (work done per unit time) or
p =
Δ E
Δ t
(where E is energy) we can see that:
p =
I Δ tV
Δ t
p = IV
∞ Also using V = IR we can sub V into p = IV to give:
p = I
R
∞ Using R =
V
I
we can again sub into to p^ =^ IV^ give:
p =
V
2
R
