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AQA Physics AS A Level Year 1 summary notes

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AQA Physics AS A Level Year 1 summary notes written by A* student

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Module 1: Particles and radiation

Chapter 1: Matter and radiation
In the atom
Atomic structure
●​ Positively charged nucleus of protons and neutrons, electrons that surround nucleus
●​ Electrons negative while nucleus positive so held in atom by electrostatic force of attraction
●​ Most of mass in nucleus and 0.00001 times diameter of atom
●​ Isotopes: atom with same number of protons but different number of neutrons
Subparticle Relative mass Mass (kg) Relative charge Charge (C)

Proton 1 1.67 x 10-27 +1 +1.60 x 10-19

Neutron 1 1.67 x 10-27 0 0

Electron 0.0005 (0) 9.11 x 10-31 -1 -1.60 x 10-19
Specific charge
𝑒𝑥𝑎𝑐𝑡 𝑐ℎ𝑎𝑟𝑔𝑒
●​ 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑐ℎ𝑎𝑟𝑔𝑒 = 𝑒𝑥𝑎𝑐𝑡 𝑚𝑎𝑠𝑠
●​ Depending on question (nucleus/atom/ion), electrons’ charge may be included but not mass
Terms
●​ proton/atomic number: number of protons in atom
●​ nucleon/mass number: number of protons and neutrons in atom
●​ Nucleon: proton or neutron inside nucleus
●​ Nuclide: atoms with a distinct nucleus (number of neutrons and protons)

Stability of nuclei
Strong nuclear force
●​ Force overcoming electrostatic force of repulsion between protons in
nucleus and holds nucleus together
●​ Range: 3-4 femtometers (fm, 3-4 x 10-15m) - diameter of small nucleus
●​ Repulsive electrostatic force between two charged particles has infinite
range (decreases over range)
●​ Same effect between two protons as proton + neutron and two neutrons
●​ Is repulsive force below 0.5fm - prevents protons and neutrons being pushed into each other
Radioactive decay
●​ Alpha radiation:
234 230 4
○​ 2 protons and 2 neutrons - 92
𝑈 → 90
𝑇ℎ +2α (same as helium nuclei)
○​ Original nuclei becomes new element

●​ Beta- (β ) radiation:
○​ Neutron becomes proton, emits electron and antineutrino -
234 234 0
92
𝑈→ 93
𝑁𝑝 + −1
β + 𝑣
○​ Original nuclei (neutron-heavy) becomes new element
○​ Antiparticle with no charge (antineutrino 𝑣) emitted to conserve energy
+
●​ Beta+ (β ) radiation:
234 234 0
○​ Proton becomes neutron, emits positron and neutrino - 92
𝑈→ 91
𝑃𝑎 + +1
β + 𝑣
○​ Original nuclei (proton-heavy) becomes new element
○​ Particle with no charge (neutrino 𝑣) emitted to conserve energy

, ○​ Beta+-emitting isotopes don’t occur naturally - manufactured by placing stable isotope
in path of proton beam - some nuclei absorb protons to be unstable beta+-emitters
●​ Gamma radiation:
234 234
○​ EM radiation emitted by unstable nucleus - 92
𝑈 + 92
𝑈 + γ
○​ Emitted by nucleus with too much energy following alpha/beta radiation
NZ graph
●​ Shows how unstable nuclei will decay to become stable nuclei




●​

Photons
EM waves
●​ In vacuum, all EM travel at 3 x 108m s-1 (speed of light)
●​ 𝑤𝑎𝑣𝑒𝑠𝑝𝑒𝑒𝑑 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 × 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ (𝑣 = 𝑓λ)
●​ Light wavelength typically expressed in nanometres (1nm = 10-9m)
●​ EM waves have electric and magnetic wave - travel perpendicular to each other and direction
travelling in, in phase with each other (have peak and trough at same time)
Photons
●​ EM waves emitted by charged particle when it loses energy when:
○​ Fast-moving electron is stopped (eg. x-ray tube), slows down or changes direction
○​ Electron in a shell of an atom moves to lower energy shell (closer to nucleus)
●​ EM waves released as short bursts of waves that leave source in different directions
●​ Each burst is packet of EM waves (also called photon)
●​ Photon theory established by Einstein to explain photoelectric effect - emission of electrons
from metal surface when light is directed at surface
𝑃𝑙𝑎𝑛𝑐𝑘 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡×𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 ℎ𝑐
●​ 𝑝ℎ𝑜𝑡𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 × 𝑃𝑙𝑎𝑛𝑐𝑘 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
(𝐸 = 𝑓ℎ = λ
)
-34
●​ Planck constant: 6.63 x 10 Js
Laser power
●​ Laser beam consists of photons of same frequency
●​ Power of laser beam is energy transferred per second by photons
●​ 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑏𝑒𝑎𝑚 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑝𝑎𝑠𝑠𝑖𝑛𝑔/𝑠𝑒𝑐𝑜𝑛𝑑 × 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 × 𝑃𝑙𝑎𝑛𝑐𝑘 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (𝑃 = 𝑛ℎ𝑓)

Particles and antiparticles
Antimatter
●​ When antimatter and matter particles (make up everything in universe) meet, they destroy
each other and radiation is released
●​ Used in PET scanner - P is positron (antiparticle of electron)
○​ When used for brain scan, positron-emitting isotope administered to patient and some
reaches brain via blood system
○​ Positron travels < few mm before it meets electron and they annihilate each other
○​ Two gamma photons produced sensed by detectors to build up image of where
positron-emitting nuclei are in brain
●​ Einstein said mass of particle when it is stationary (rest mass 𝑚0) corresponds to rest energy
2
(𝑚𝑜𝑐 ) locked up as mass - rest energy must be included in conservation of energy
Annihilation
●​ Dirac predicted existence of antimatter particles (antiparticles) that would unlock rest energy
whenever particle and corresponding antiparticle meet and annihilate each other
●​ Dirac's theory predicted for a particle there is corresponding antiparticle that:

, ●​ Annihilates particle and itself if met, converting total mass into 2 photons
●​ Has exactly same rest mass and opposite charge to particle
●​ Minimum energy of each photon ℎ𝑓𝑚𝑖𝑛 given by equating energy of 2 photons 2ℎ𝑓𝑚𝑖𝑛 to rest
energy of particle + antiparticle (ℎ𝑓𝑚𝑖𝑛 = 𝐸0 where 𝐸0 is rest energy of particle)
●​ 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑝ℎ𝑜𝑡𝑜𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 = 𝑟𝑒𝑠𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 (ℎ𝑓𝑚𝑖𝑛 = 𝐸0)
Pair production
●​ Dirac also predicted opposite process of pair production:
●​ Photon with sufficient energy passing near nucleus or electron can suddenly
change into particle-antiparticle pair, which would then separate from each
other
●​ In pair production, photon creates particle and corresponding antiparticle and vanishes in
process
●​ For particle and antiparticle (each of rest energy 𝐸0) we can calculate minimum energy and
minimum frequency photon must have to produce particle-antiparticle pair
●​ 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛 𝑛𝑒𝑒𝑑𝑒𝑑 = 𝑟𝑒𝑠𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑎𝑛𝑡𝑖𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑝𝑎𝑖𝑟 (ℎ𝑓𝑚𝑖𝑛 = 2𝐸0)
●​ Example: electron has rest energy of 0.511MeV, therefore for pair production of electron and
positron from photon: 2 x 0.511 = 1.022MeV = 1.64 x 10-13J (minimum energy of photon)
Particles, antiparticles
●​ Energy of particle/antiparticle often expressed in millions of electron volts (MeV)
●​ 1 MeV = 1.60 x 10-13J
●​ 1 electron volt: energy transferred when electron is moved through voltage of 1V
●​ Given rest mass of a particle/antiparticle, its rest energy in MeV can be calculated by
2
𝐸 = 𝑚𝑐

Particle interactions
Electromagnetic force
●​ When unequal force acts on object, momentum is changed
●​ 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝑚𝑎𝑠𝑠 × 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑝 = 𝑚𝑣)
●​ When two objects interact, they exert equal opposite forces on each other -
momentum transferred between objects by forces if no other forces act on them
eg. if 2 protons approach each other they repel and move away from each other
●​ Feynman said EM force between 2 charged objects is due to exchange of virtual
photons - virtual as can’t be detected otherwise force is stopped from occurring
Interaction model of above
●​ Analogy 1 (same charged particles): ball thrown from one person (who
recoils), momentum transferred to receiver who recoils, therefore both repel
each other - possible
●​ Analogy 2 (oppositely charged particles): boomerang thrown from one person
(who attracts) away from other person and swings round to other person
(who attracts) - not possible
Weak nuclear force

●​ Strong nuclear force holds neutrons and protons in nucleus together but doesn’t cause β or
+
β decay - can’t be EM force as neutron is uncharged
●​ Different force in nucleus causing decay - must be weaker than strong nuclear force to not to
affect stable nuclei - called “weak nuclear force”
●​ In both decay, new particle and antiparticle created but not particle-antiparticle pair
●​ Neutrinos, antineutrinos hardly interact with other particles but sometimes happen:

○​ Neutrino interacts with neutron & changes it to proton - β (electron)
emitted

, +
○​ Antineutrino interacts with proton & changes it to neutron - β (positron) emitted
○​ Both are opposite of
●​ Interactions are due to exchange of particles (called W bosons) - unlike photons, these
exchange particles:
○​ Have a non-zero rest mass
○​ Have < 0.001fm range
○​ Positively charged (w+ boson) or negatively charged (w- boson) to conserve charge
− +
●​ Weak interaction only occurs for β , β , electron-capture and electron-proton collisions
W boson in beta decay

●​ W-boson meets neutrino from neutron: changes into electron (β ) and antineutrino
+
●​ W-boson meets antineutrino from proton: changes into positron (β ) and neutrino
●​ If no neutrino/antineutrino present:

○​ W- boson decays into β particle and antineutrino
+
○​ W+ boson decays into β particle and neutrino
●​ Charge is conserved
Electron capture/proton-electron collision
●​ Proton in proton-rich nucleus can turn into neutron due to interaction with inner
shell electron outside nucleus (electron capture) using W+ boson
●​ Same change can happen when proton and electron collide at very high speed -
for electron with sufficient energy, overall change could happen as W- exchange
●​ W+ exchange: proton to electron, electron changes to neutrino
●​ W- exchange: electron to proton, electron changes to neutrino
Force carriers
●​ Virtual (photon): EM force
●​ W/Z boson: weak nuclear force
●​ Gluon or pion: strong nuclear force
●​ Graviton: gravitational force, not yet observed
●​ Higgs: mass
Determining force in reaction
●​ Strong: typically between hadrons
●​ Weak: typically between leptons and decay (strangeness not always conserved), mention
leptons and hadrons in question if both are present
●​ Gravity: typically everything
●​ EM: only typically between charged particles



Chapter 2: Quarks and leptons
Particle zoo
Cosmic rays
●​ High-energy particles that travel through space from stars
●​ When they enter Earth’s atmosphere, they create photons, short-lived particles & antiparticles
●​ Most cosmic rays are fast-moving protons or small nuclei - collide with gas atoms in
atmosphere, creating showers of particles and antiparticles detected at ground
●​ By cloud chambers & other detectors, new types of short-lived particles & antiparticles found:
○​ Muon (μ): heavy electron (negative charge), 200x rest mass as rest mass of electron
○​ Pion/ℼ meson: can be negative/neutral/positive
○​ Kaon/K meson: can be negative/neutral/positive
○​ Proton > kaon > pion > muon > electron

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