Chapter 7 - Quantum, Atomic, and Nuclear Physics

Basics

• Einstein’s postulates of special relativity   * All laws of physics remain the same in a uniformly moving frame of reference   * The speed of light in a vacuum is always 3 x 10^8 no matter the motion of the source of light or the observer   * Summary: time and distance are relative according to your frame of reference
• ==E = mc^2==   * Mass is a solid form of energy and can be converted into energy and vice versa
• Big 4 subatomic particles   * Proton (p)     * Mass = 1.67 x 10^-27 kg = 1 amu     * Charge: positive   * Electron (e)     * Mass = 9.11 x 10^-31 kg     * Charge: negative   * Neutron (n)     * Mass = 1.67 x 10^-27 kg = 1 amu     * Charge: 0   * Photon (ɣ)     * Mass = 0     * Charge: 0
• Electron-Volts (eV)   * $Electron-Volt$: a unit of energy - the amount of energy needed to change the potential of an electron by 1 volt   * ==1 eV = 1.6 x 10^-17 J==
• Photons   * Light is made of photons   * ==E = hf = hc/λ==     * E: energy of a photon     * h: Planck’s constant = 6.63 x 10^-34 Js = 4.14 x 10^-15 eVs     * f: frequency (Hz)     * c: speed of light (3 x 10^8 m/s)     * λ: wavelength (m)

Photoelectric Effect

• Applications: solar panels, photosynthesis, tanning, photographic film
• __Photoelectric effect__: when incident light is shined on a metal, electrons detach
• ==K(max) = hf - ɸ==   * K(max): max kinetic energy of the emitted electron   * h: Planck’s constant   * f: frequency   * hf: energy of the incident photon   * ɸ: work function - the energy required to remove an electron from a specific element/material   * When the frequency of incident light increases, the maximum kinetic energy of the emitted electron increases linearly   * Threshold frequency: minimum frequency for electron emission
• Photon Momentum   * When a photon collides with an atom and the atom emits an electron, momentum and energy are conserved   * ==p = h/λ = E/c==

DeBroglie Wavelength

• If a particle has a shorter wavelength, it behaves more like a particle
• If a particle has a longer wavelength, it behaves more like a wave
• To find the wavelength for a particle (de Broglie’s wavelength), use ==λ = h/p = h/mv==   * λ: de Broglie’s wavelength   * p: momentum of particle
• Particles have a __wave function__ representing the probability of finding the particle at a specific location   * Ѱ: wave function   * Ѱ = 0: no probability of finding the graph

Energy Levels in an atom

• For an electron to move from one energy level to another, it will either have to absorb or emit energy in the form of a photon
• The nucleus of an atom is positive and electrons are negative so it takes energy to pull the electron away from the nucleus by overcoming their attractive force   * Electrons take less energy if they’re in a higher energy level
• Key points   * n1 is called the ground state - the lowest possible energy level for the electron   * Moving from lower to higher energy levels tells you the atom absorbed a photon   * Moving from higher to lower energy levels tells you the atom emitted a photon   * There are no intermediate levels between energy levels   * ==E (photon) = E (final) - E (initial)==
• If there is extra energy after jumping from one energy level to another, that energy is converted to kinetic energy of the emitted electron

Nuclear Decay

• Particles involved with nuclear decay:   * __Alpha particle (𝞪): two protons and two neutrons together (helium nucleus)   * $</strong><strong>Beta particle (β)</strong><strong>$: either an electron or positron   * Gamma particle (Ɣ__): a gamma ray photon - massless and chargeless
• Isotopes - same atomic number of an element but different mass numbers   * Notation for Isotopes: element symbol with two small numbers to the left (one on top of the other)     * Top number on the left side of the symbol: mass number = neutron # + proton #     * Bottom number on the left side of the symbol: # of protons in the nucleus = atomic number
• __Alpha (𝞪) decay__: a Helium nucleus is emitted from the original isotope
• __Beta (β) decay__: either a positron or electron is emitted   * β+ (also symbolized as e+): positron - +1 charge with negligible mass   * β- (also symbolized as e-): electron - -1 charge with negligible mass
• __Gamma (Ɣ) decay__: massless and chargeless photon   * The photon carries away some energy and momentum so the nucleus recoils
• __Neutron deca__y: a neutron is emitted
• __Mass defect__: the slight difference in mass between the total mass present before the decay and after the decay   * This difference in mass is destroyed and converted into kinetic energy     * ==E = Δmc^2==       * Δm: mass defect       * c: speed of light       * E: energy produced   * ==1 u = 931 MeV/c^2==   * The mass defect may become the nuclear binding energy and will be equal to the strong nuclear force that holds the nucleus together
• Half-life: the time it takes for a radioactive isotope to decay half its original amount

  \   * Longer half life → slow decay rate

• __Fission reactions__: when a heavy nucleus is split into two chunks   * Begun by shooting a neutron into the nucleus   * Nuclear power plants and weapons
• Fusion reactions: when two light nuclei combine to make a heavier and stable nucleus
• Induced Reaction: scientists bombard a nucleus with high-speed particles to induce the emittance of a proton
• Antimatter: every normal particle has an antimatter to match it (electron and positron)   * When matter and antimatter meet, they annihilate each other   * Ex: electron and positron can turn into photon energy   * ==E (electron) + E(positron) = (2m)c^2 = hf==     * m: mass of electron     * c: speed of light     * h: Planck’s constant     * f: frequency

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