Khan Chapter 1 Summary

1.1 – 1.2: The Atom & Nucleus

  • The atom is made up of a nucleus and a surrounding electron cloud that orbits the nucleus.
    • The atom is defined by the mass number (A superscript; number of nucleons) and the atomic number (Z subscript, number of protons).
      • A = number of nucleons in the nucleus.
      • Z = number of protons in the nucleus.
  • The atom can be classified as isotopes, isotones, isobars, or isomers.
    • Isotopes have the same number of protons, but different number of neutrons, i.e., the same atomic number, but different mass number.
    • Isotones have have the same number of neutrons, but different number of protons, i.e., different atomic and mass number.
    • Isobars have the same number of nucleons, but different number of protons, i.e., the same mass number, but different atomic number.
    • Isomers have the same number of protons and neutrons, but have different energy states (metastable), i.e., the same atomic and mass number.
  • The neutron to proton ratio can yield important information about an atom:
    • For about Z < 20, stable elements have a 1:1 neutron to proton ratio.
    • For about Z > 20, stable elements have greater than a 1:1 neutron to proton ratio.
    • A nuclei that has neutrons and protons that are mutually paired, i.e. even-even nuclei, is said to be more stable which is suggested by even-even nuclei accounting for more than half of the stable isotopes.
    • Odd-odd nuclei is said to be the least stable as only 4 stable odd-odd nuclei exist.

1.3: Atomic Mass and Energy Units

  • The atomic weight is the average atomic mass units (amu) of an element based on how frequent each isotope is found in nature.
    • 1 amu is equal to 1/12 the mass of a Carbon-12 atom. Thus, a Carbon-12 atom is equal to 12 amu.
    • 1 amu in mass is equal to 1.66 * 10^-24 g.
  • Given that a helium atom has an atomic weight of 4.0026, what is the grams/atom, atoms/grams, and electrons/gram?
    • 1 He atom = 4.0026 amu.
    • If 1 amu = 1.66 * 10^-24 g, then 4.0026 amu = 6.64 * 10^-24 g.
    • Thus, 1 He atom = 6.64 * 10^-24 g, or 6.64 * 10^-24 g/atom.
    • 1 He atom / 6.64 * 10^-24 = 1 g, or 1.51 * 10^23 atoms/g.
    • 1.51 * 10^23 atoms/g * 2 (Z of He = 2) = 3.01 * 10^23 electrons/g.
  • The masses of an electron, proton, and neutron in amu is, respectively, 0.000548 amu, 1.00727 amu, and 1.00866 amu.
    • Taking the sum of all of the particles in an atom will not exactly equal its atomic weight. This difference is attributed to the mass defect which is analogous to glue that keeps the nucleons together. This energy is also referred to as the binding energy of the nucleus which is the required energy to separate the nucleus into individual nucleons.
  • Energy of an electron that moves across a potential difference is given by the equation: Coulombs (Q) * Volts (V) = Energy in Joules (J).The units of energy can instead be expressed as an electron volt (eV) which is the energy acquired by an electron that moves across a potential difference of 1 volt. The eV is a more convenient unit that is scaled by the charge of an electron (1.602 * 10^-19 C).
    • 1.602 * 10^-19 C * 1 V = 1.602 * 10^-19 J.
    • 1 e− * 1 V = 1 eV.
  • The energy of an electron at rest can be determined by Einstein’s equation: E = m * c^2.
    • Given that the speed of light (c) = 3 * 10^8 m/s and the mass of an electron at rest = 9.1 * 10^-31 kg, what is the energy equivalent?
      • 9.1 * 10^-31 kg * (3 * 10^8 m/s)^2 = 8.19 * 10^-14.
      • 8.19 * 10^-14 J / 1.602 * 10^-19 J = 511,236 eV.
      • 511,236 eV = 0.511 MeV.

1.4 – 1.5: The Distribution of Orbital Electrons & Atomic Energy Levels

  • The electrons which orbit around the nucleus exist within shells.
    • The innermost shell is the K shell with the subsequent shells being the L, M, N, and O shell.
    • The maximum number of electrons that can occupy a shell can be calculated by the equation 2 * n^2 (n = shell number).
    • The electrons in the shells have binding energies that vary based on the magnitude of the Coulombic attraction between the electron and the nucleus.
      • Atoms with a high Z will have a greater binding energy.
      • Electrons that reside in a shell closer to the nucleus will have a greater binding energy.
    • If a sufficient amount of energy is imparted onto an electron, it can become ejected from the atom and leave a vacancy in the shell. An outer shell electron can fill the vacancy and radiation will be emitted as the electrons transition to its new shell.
      • The energy of the emitted radiation will equal to the difference between the binding energies of the respective shells.
      • As the emitted radiation leaves the shell, it may eject a different electron which will result in a repeat of the process mentioned above. The ejected electron is referred to as the Auger electron.

1.6 – 1.7: Nuclear Forces & Nuclear Energy Levels

  • The strong force is a short-range force that is responsible for overcoming the electrostatic repulsion of the protons to keep the nucleus intact.
    • When the distance between two nucleons become less than the nuclear diameter, the strong force will take into effect.
    • A positively charged particle that approaches the nucleus is normally repelled, but if the particle is able to get within the range of the strong force, it will enter the nucleus and become “trapped”.
  • A nucleus can be made radioactive when the nucleus is bombarded with nucleons.
    • The radioactive nucleus will fall to a lower and stable energy state by giving off energy in steps, and the energy emitted will equal the energy difference between the two states.
    • The nucleus can “decay” in multiple pathways based on probability, and so these pathways are often plotted on a decay scheme.

1.8 – 1.10: Particle Radiation, Elementary Particles, & Electromagnetic Radiation

  • Louis de Broglie had hypothesized that all matter has a wave-particle duality. Electrons exhibit wave-like properties such as interference, and photons exhibit particle-like properties such as momentum.
    • The electromagnetic wave model is represents electromagnetic radiation by an oscillating electric (E; X-axis) and magnetic (H; Y-axis) fields that are perpendicular to one another and propagated in the direction of the Z-axis at the speed of light. Electromagnetic waves are observed on a spectrum of increasing/decreasing wavelength and frequency that can be determined by the equation: c = v (frequency; cycles/s) * λ (wavelength; m).
    • The quantum model represents electromagnetic radiation as a particle, and its energy can be determined by the equation: E = h (Planck’s constant; 6.626 * 10^-34 J-sec) * v.  Combining this equation with the one mentioned just above will give: E = h * c / λ.
  • Protons, neutrons, and electrons were previously named elementary/fundamental particles, but this label is now given to these particles’ substructure, i.e., subatomic particles.
    • Hadrons such as protons and neutrons are made up of elementary particles known as quarks. Quarks are fermions (particles of matter) which are particles that have a spin of an odd half-integer (1/2, 3/2, 5/2, etc.). The six “flavors” of quarks are the following: up (u), down (d), charm (c), strange (s), top (t), and bottom (b). These quarks are held together by gluons which are messenger particles of the strong force.
    • Leptons are also fermions, and its six flavors are the following: electron (e), electron neutrino (v_e), muon (μ), muon neutrino (ν_μ), tau (τ), and tau neutrino (v_τ).
    • For a fermion to approach the speed of light, the fermion will accelerate by increasing its mass to increase its energy, as opposed to increasing its speed. Thus, particle accelerators that can accelerate particles near the speed of light are limited by the greater mass of these particles.

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