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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)
    • Beta particle (β): 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 decay: 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

    Example of a half-life graph

    • 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