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

  

  • 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