Atomic Structure and Isotopes

Particles

• An atom has three constituents: protons, neutrons, and electrons.
• Protons and neutrons form the nucleus and are known as nucleons.
• Electrons orbit the nucleus in shells.

Properties of Particles

• Particles exhibit properties described in SI and relative units.
• Specific charge is the ratio of charge to mass, calculated by dividing a particle's charge by its mass.
• A proton has a charge of +1.6 × 10⁻¹⁹ C and a mass of 1.67 × 10⁻²⁷ kg, resulting in a specific charge of 9.58 × 10⁷ Ckg⁻¹.
• Z denotes the proton number, or number of protons in an atom.
• A denotes the nucleon number, or number of protons and neutrons.
• 'X' represents the element's symbol in the notation ᴬZ X.

Isotopes

• Isotopes are atoms with the same number of protons but different numbers of neutrons.
• Carbon-14 dating determines the age of organic material by measuring carbon-14 percentage and using its half-life.

Stable and Unstable Nuclei

• Keeps nuclei stable by counteracting electrostatic repulsion between protons
• Only acts on nucleons and has a short range attraction up to 3 fm and is repulsive below 0.5 fm. repulsive below separations of 0.5 fm.
• Unstable nuclei decay due to an imbalance in the number of protons and/or neutrons.

Alpha Decay

• Occurs in large nuclei with too many protons and neutrons.
• Results in a decrease of 2 in the proton number and 4 in the nucleon number.

Beta-Minus Decay

• Occurs in neutron-rich nuclei.
• Boosts the proton number by 1 while the nucleon number stays the same.
• Neutrinos were hypothesised to account for the energy not conserved during beta-minus decay and later observed.

Particles, Antiparticles, and Photons

• Each particle has an antiparticle with the same rest energy and mass, but opposite properties.
• Example: a positron is the antiparticle of the electron.
• Electromagnetic radiation such as photons transfer energy and have no mass.
• Photon energy is proportional to electromagnetic radiation frequency: E = hf = hc/λ, where h is Planck's constant (6.63 × 10⁻³⁴ Js).

Annihilation

• Particle and antiparticle collide, converting mass into energy released as two photons in opposite directions.
• Application in PET scanners involves positron-emitting radioisotopes annihilating with electrons, emitting detectable gamma photons.

Pair Production

• A photon converts into matter and antimatter.
• Involves the photon exceeding total rest energy of both particles, with excess energy converted to kinetic energy.

Particle Interactions

• Fundamental forces include gravity, electromagnetism, weak nuclear force, and strong nuclear force.
• Forces are caused by exchange particles which transfer energy and momentum.

Interactions and Exchange Particles

• Strong: Gluon, range of 3 × 10⁻¹⁵ m, acts on Hadrons
• Weak: W boson (W⁺ or W⁻), range of 10⁻¹⁸ m, acts on all particles
• Electromagnetic: Virtual photon (γ), infinite range, acts on charged particles
• Gravity: Graviton (not on specification), infinite range, acts on particles with mass
• The weak nuclear force is responsible for beta decay, electron capture, and electron-proton collisions.

Electron Capture Equation

• p + e⁻ → n + vₑ

Electron-Proton Collision

• p + e⁻ → n + vₑ
• Equations for electron capture and electron-proton collisions are the same, but a different exchange particle is used.

Beta-Plus Decay

• p → n + e⁺ + vₑ

Beta-Minus Decay

• n → p + e⁻ + v̄ₑ

Classification of Particles

• Particles are classified as either hadrons or leptons
• Leptons are fundamental particles and do not experience the strong nuclear force.
• Hadrons are formed of quarks and experience the strong nuclear force.
• Hadrons are further separated into baryons, antibaryons, and mesons.
• Baryons are formed of 3 quarks, antibaryons are formed of 3 antiquarks, and mesons are formed from a quark and antiquark.

Baryon Number

• Indicates if a particle is a baryon (1), antibaryon (-1), or neither (0).
• Baryon number is always conserved in particle interactions.
• The proton is the only stable baryon, and all baryons will decay into a proton.

Lepton Number

• Indicates if a particle is a lepton (1), antilepton (-1), or neither (0).
• Electron lepton number and muon lepton number represent the named particle.
• Lepton number is always conserved in particle interactions.
• Muons are sometimes called "heavy electrons" and decay into electrons.

Strange Particles

• Produced by the strong nuclear interaction but decay by the weak interaction.
• The only strange particles you are expected to know about are kaons, which decay into pions, through the weak interaction.

Strangeness

• A property of particles indicating that strange particles must be created in pairs, as strangeness must be conserved in strong interactions.
• In weak interactions, strangeness can change by 0, +1, or -1.
• Scientific investigations in particle physics rely on international collaboration due to high costs and large data volumes.

Quarks and Antiquarks

• Quarks are fundamental particles that make up hadrons, with three types of quarks to know.
• Antiquarks have opposite signs for their properties compared to quarks.

Quark Combinations

• uud forms a proton (charge +e, baryon number +1).
• udd forms a neutron

Finding Quark Combination of Antibaryon

• Change the quarks into their respective antiquarks.
• The same is true for mesons.

Quark Combinations for Mesons

• π⁰: uū or d̄d, Charge: 0, Strangeness: 0
• π⁺: ud, Charge: +1, Strangeness: 0
• π⁻: ūd, Charge: -1, Strangeness: 0
• K⁰: d̄s or d̄s, Charge: 0, Strangeness: ±1
• K⁺: us, Charge: +1, Strangeness: +1
• K⁻: ūs , Charge: -1, Strangeness: -1

Applications of Conservation Laws

• Must be conserved in particle interactions: energy, momentum, charge, baryon number, electron lepton number, muon lepton number.
• Strangeness is conserved during strong interactions.
• To evaluate conservation laws, compare property values before and after the interaction.

Beta-Minus Decay of a Neutron

• n → p + e⁻ + v̄ₑ (Strangeness does not need to be conserved)
• Before Interaction: Charge 0, Baryon number 1, Electron lepton number 0, Muon lepton number 0, Strangeness 0
• After Interaction: Charge 1+(-1)+0=0, Baryon number 1+0+0, Electron lepton number 0+1-1, Muon lepton number 0+0+0, Strangeness 0+0+0
• Change: 0 for all properties; therefore, the interaction is possible.

Quark Type Changes

• Beta-minus and beta-plus decay are caused by the weak interaction because there is a change of quark type.
• In beta-minus decay, a down quark changes into an up quark (neutron to proton).
• The opposite happens in beta-plus decay.

The Photoelectric Effect

• Photoelectrons are emitted from the surface of a metal after light of a certain frequency shines on it. This frequency is called the threshold frequency and varies for different metals.
• EM waves travel in discrete packets called photons, which have an energy directly proportional to frequency.
• The electron can absorb a single photon, so a photoelectron is only emitted if the frequency is above the threshold frequency.
• If the light’s intensity is increased above the threshold, more photoelectrons are emitted per second.

Work Function

• The work function (φ) is the minimum energy required for electrons to be emitted from the surface of a metal.

Stopping Potential

• V(s) is the potential difference needed to stop photoelectrons, allowing the determination of maximum kinetic energy: E(k max) = eV(s).

Photoelectric Equation Formula

• The photoelectric equation, E = hf = φ + E(k max), relates work function, maximum kinetic energy, and light frequency.

Collisions of Electrons with Atoms

• Electrons in atoms exist in discrete energy levels.
• Excitation is when electrons gain energy from collisions and move up energy levels.
• Ionisation occurs when electrons gain enough energy to be removed from the atom entirely.
• Ionisation occurs if the energy of the free electron is greater than the ionisation energy.
• Excited electrons return to their ground state, releasing energy as photons.
• Fluorescent tubes use mercury vapour and a high voltage to produce light via excitation and photon emission.

Conversion of electron volts

• An electron volt is the energy gained by one electron passing through a potential difference of 1 volt.
• 1 eV = e × 1 = 1.6 × 10⁻¹⁹ J

Converting from eV to joules

• Multiply your value by 1.6 × 10⁻¹⁹

Converting from Joules to eV

• Divide your value by 1.6 × 10⁻¹⁹

Energy Levels and Photon Emission

• Passing light from a fluorescent tube through a diffraction grating or prism produces a line spectrum.
• Each line represents a different wavelength of emitted light corresponding to the energies emitted.
• Discrete wavelengths in the spectrum indicate that electrons in atoms can only transition between discrete energy levels.
• Passing white light through a cooled gas results in a line absorption spectrum.
• Black lines in the spectrum represent photons of energy absorbed by atoms in the gas.

Energy Difference Formula

• An equal specific photon energy is emitted by a fluorescent tube.
• ΔΕ = Ε₁ - Ε₂, where E₁ and E₂ represent energy levels.
• As E = hf, therefore hf = E₁ - E₂.

Wave-Particle Duality

• Light exhibits both wave (diffraction and interference) and particle properties (photoelectric effect).
• Electrons also exhibit both wave and particle properties as they can participate in electron diffraction, as only waves can experience diffraction.

De Broglie

• The equation relating the wavelength (λ) of an object to its momentum (mv): λ = h/mv, where h is Planck’s constant.
• As momentum increases, wavelength decreases, and diffraction decreases.
• As momentum decreases, wavelength increases, and diffraction increases.

Acceptance of Duality

• Experimental evidence (electron diffraction, photoelectric effect) led to the recognition of wave-particle duality.
• Scientific concepts evolve with experimental evidence, peer review, validation, and community acceptance.