Topic 7: Atomic, Nuclear, and Particle Physics
7.1 Discrete Energy and Radioactivity
Discrete energy levels (n)
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Definition: discrete (specific) energy values at which the electrons of an atom may be, which correspond to "allowed" orbitals.
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Energy levels: E ≤ 0, according to the energy supplied to take an electron out of the atom (ionization).
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Ground state (n = 1): ​Normal level.
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Levels above ground state (n > 1): Electron is excited.
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n = 2 (first excited state), n = 3 (second excited state), ...​
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Ionization state (n = ∞): Energy supplied = Ionization energy.
Transition between energy levels
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Definition: electrons jumping from one level to another, emitting photon(s).
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Jumping to a higher level: An electron must receive exactly the right amount (difference between 2 energy levels) from one photon to jump to a higher energy level.
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Relaxation: Rapidly, after jumping to a higher level, the electron goes to a lower energy level and emits a photon with energy equal to the energy difference between levels:
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Photon (γ): quantum or bundle of energy, having a specific wavelength and frequency.
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Photon energy: E = hf = hc/λ, where h = Planck's constant = 6.63 x 10^-34 Js.
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Spectra
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Continuum: all wavelengths within the visible range (e.g. light bulb or Sun).
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Emission: discrete wavelengths corresponding to energy levels in which the photons are emitted. (e.g. gas exposed to strong electric field).
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Absorption: black lines are the wavelengths absorbed by the gas
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For a specific gas: Emission spectra + Absorption spectra = Continuous spectra.
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Evidence for energy levels.​
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Nuclear structure​
Nucleons: protons and neutrons.
Atom: nucleus + electrons
proton
neutron
electron
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Representation of a nucleus: ​

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Example: Helium nucleus/alpha particle:

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Number of neutrons (N) = A - Z​.
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Nuclide: "nucleus with a specific number of protons and neutron."
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Isotopes:"nuclei (plural of nucleus) with the same number of protons, but different number of neutrons"​
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Conservation: charge, mass, and momentum are always conserved.
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Alpha decay (discrete energy): alpha particle (α) emission.​​

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Beta minus decay​ (continuous energy): neutron turns into a proton, emitting an electron (called beta minus particle, β-, before the conclusion it was an electron) and an electron anti-neutrino.

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Beta plus decay (continuous energy): proton turns into a neutron, emitting a positron (the anti-particle of the electron), also called the beta plus particle, β+, and a electron neutrino.

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Gamma decay (discrete energy): emission of a photon (γ) of high frequency, and thus high energy, often accompanied by an alpha or a beta decay.

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Penetrative power: ​α < β < γ.
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Ionization: ​γ < β < α.
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"Inverse process": Artificial transmutation: particle fired at a nucleus, leading to the formation of a new element.
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​Laws of radioactive decay
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Constant probability of decay.
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Rate of decay: proportional to the number of nuclei that have not yet decayed.
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Activity (A): number of decays per second, in becquerel (Bq).
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Half-life: "interval of time after which the activity/number of parent nuclei of a radioactive sample is reduced by a factor of two."
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Exponential decrease:
Radioactive decay simulation starting with 4 or 400 atoms.
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Background radiation: radioactivity activity of all other sources, e.g. cosmic rays from the Sun, which needs to be subtracted when measuring the activity of a certain radioactive sample.
Fundamental forces
Four types of interaction between particles
7.2 Nuclear Reactions
Patterns for stability in nuclides
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Nuclides with low proton number: stable when the neutron-proton ratio is close to one.
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Heavier elements: the neutron-proton ratio gradually increases, due to the attractive nature of the strong force between nucleons, but repulsive nature of the electromagnetic force between protons.
Binding energy
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Mass defect (δ): the difference between the total mass of the individual nucleons making up a nucleus and the actual mass of the nucleons.
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δ = total mass of nucleons - mass of nucleus.
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If it is an atom, remember to subtract the mass of electrons.
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Einstein's theory of relativity (relationship between mass and energy): E = mc^2.
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Binding energy definition: "the minimum energy required to completely separate the constituent nucleons of one nucleus".
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Binding energy = δc^2, i.e. the mass defect transformed into energy by E = mc^2.
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Graph: average binding energy per nucleon x nucleon number.
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Average binding energy for H is zero (only one nucleon).
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Peak: Maximum average binding energy per nucleon for Fe and Ni, especially 56 - Fe, the most stable nucleus.
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The curve drops gently after the peak.
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Explanation: A given nucleon can only interact with its near neighbors. Hence, for large nuclei, all nucleons interact with roughly the same number of nucleons.
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fission
fusion
Energy released in a decay
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Mass difference (∆m) must be calculated to determine whether a nuclear reaction happens.
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∆m = total mass of reactants - total mass of products. From this, energy can be calculated, using E = mc^2.
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If ∆m > 0, the reaction releases energy.
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If ∆m < 0, the reaction needs energy to be supplied.
Nuclear fission
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Definition: heavy nuclei (nucleon number > 56) splits up into lighter nuclei.
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Induced reaction: A slow moving neutron may collide with a fissile nucleus and trigger a fission reaction.
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Chain reaction: The production of neutrons is a feature of fission reactions, which may trigger a other reactions, and thus, a chain reaction.
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Critical mass: needed to trigger chain reaction, otherwise the neutrons will escape.
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Fission reaction types: Fission reactor: slowly; Atomic fission bomb: rapidly.
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Energy of the reaction given in the form of kinetic energy of the products and as gamma radiation.
Nuclear fusion
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Definition: joining two light nuclei (nucleon number < 56) into a heavier one.
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Sun conditions: high temperatures and pressure, to overcome coulombic repulsion.
and energy..!
Deuterium
Tritium
Ethics and morals
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Nuclear energy: dangerous knowledge, since it may be used to craft atomic bombs.
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Examples: radioactivity at Hiroshima and Nagasaki.
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​​
neutron + energy + He
7.3 The Structure of Matter
Thomson's "plum pudding" model of the atom
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A number of electrons buried in a cloud of positive charge.
spherical cloud of positive charge
negatively charged electron
Rutherford, Geiger and Marsden experiment
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Alpha particles directed at a thin gold foil in a vacuum chamber.
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Vacuum chamber: avoid​ collisions with air particles
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Thin foil: avoid multiple deflections.
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Results: great majority of particles passed through the gold foil with little or no deviation, but, occasionally, some alpha particles were detected at large scattering angles.
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Thomson's model: only the small deflections could be understood.
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Consequences: there must be an enormous force to reflect alpha particles, which means that the positive charge is not distributed, but concentrated in a small positive nucleus.
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New model!​
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Anti-particles
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Definition: have the same mass as their corresponding particles, but all other properties are opposite, such as electric charge. They are denoted by a bar on the top.
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Particle annihilation: when a particle and its corresponding anti-particle collide, they annihilate, producing energy.
Elementary particles (according to the Standard model)
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Definition: particles that are, theoretically, not made out of any smaller components.
Quarks: have six different types of flavors, split into three generations of increasing mass.
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Hadron: particles built from quarks​.
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Baryon: made out of 3 quarks, e.g. proton (uud) or neutron (udd).
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Meson: made out of a quark and an anti-quark, e.g. pions.
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Quark confinement: It is not possible to observe isolated quarks. Interacting by the strong nuclear force, moving them away stores more energy in the interaction, and thus, more energy is needed to free them.
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Baryon number (B): For quarks: +1/3; For anti-quarks: -1/3.
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Hence, for baryons: +1; for mesons: 0.​
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Strangeness: indicates a surprisingly long lifetime (10^-10 s instead of 10^-15 s).​
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Conservation only in strong interactions.​
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Leptons: six different types, split into three generations of increasing mass.
increasing mass
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No confinement: found out by themselves, since they interact by the weak interaction.
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Lepton number (L): For leptons and neutrinos: +1; For their antiparticles: -1.
Exchange particles: "virtual" particles, not detected during the exchange. Their mediator effect, however, is felt by the interacting particles, e.g. force between particles, transfer energy etc.
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Analogy: Invisible ball.
Feynman diagrams
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Use: represent particles interactions.
this wavy line represents the exchange of a virtual particle
The Higgs particle
It is a particle responsible, through its interactions, for the mass of the particles of the Standard Model.