Atomic and Nuclear Structure

Atomic Structure and Spectra

Emission spectrum of hydrogen (Bohr model)

  • Bohr model:
    • An electron orbits the positively charged nucleus in the same way that the earth orbits the Sun.
    • Electrostatic attraction pulls the electron toward the nucleus.
    • The electron orbits at high speed to prevent it from crashing into the nucleus.
    • The electron can orbit at different energy levels: n=1, n=2, n=3 ...etc.
    • The higher the energy level, the larger the radius from the nucleus.
  • Emission spectrum of hydrogen:
    • When an electron transitions from a higher energy level to a lower energy level, it emits electromagnetic radiation.
    • The emission spectrum of hydrogen consists of sharp, distinct lines.

Atomic energy levels

  • quantized energy levels for electrons
    • The distinct lines of the emission spectrum prove that electron energy is quantized into energy levels.
    • If electron energy is not quantized, then a continuous spectrum would be observed.
    • The energy of the energy levels is governed by: hydrogen energy levels, where E is energy and n is the energy level.
      • The equation is negative, so all energies are negative.
      • Negative energies mean that it is energy that contributes to the "stability" of the system - the electron binding energy.
      • The more negative (lower) the energy, the more stable the orbit, the harder it is to knock out the electron.
      • The less negative (higher) the energy, the less stable the orbit, the easier it is to knock out the electron.
      • At the highest energy, 0 eV, there is no binding energy, so the electron dissociates.
      • For atoms other than hydrogen, the shape of the energy level curve stays the same. However, the numerator is a constant other than 13.6 eV.
      • The precise relationship for atoms other than hydrogen is: energy levels, where Z is the atomic number.
      • Higher Z values give more negative binding energy (more stable) because the more charge, the more electrostatic attraction.
  • calculation of energy emitted or absorbed when an electron changes energy levels
    • The wavelength of the emitted or absorbed radiation is governed by the Rydberg formula: Rydberg formula, where lambda is the wavelength, nf is the final energy level, ni is the initial energy level, and R is the rydberg constant.
    • The energy of the emitted or absorbed radiation is: energy of light, where E is energy, f and v both mean frequency and c is the speed of light.
    • Energy is emitted for transitions to lower energy levels (nf < ni).
    • Energy is absorbed for transitions to higher energy levels (nf > ni).

Atomic Nucleus

Atomic number, atomic weight

  • Atomic number = the number of protons.
    • The atomic number is what defines an element.
    • When two things have the same number of protons, they are the same element.
  • Atomic weight = the weighted average of atomic mass for all isotopes of a given atom.
    • Atomic mass = number of protons + neutrons.
    • The atomic mass is used for an isotope.
    • The atomic weight is used for an element.
  • In standard notation the atomic number is always at the bottom, and the weight is always on top: atomic notation
  • An easy way to remember this is that the atomic number is "fundamental" to the identity of the element, so it is located at the foundation.

Neutrons, protons, isotopes

  • Neutrons = neutral particles that reside in the nucleus.
  • Protons = positive particles that reside in the nucleus.
  • Isotopes = things with the same number of protons, but different number of neutrons.
Atomic particles
Name Mass (amu) Charge Location
Proton 1 +1 In the nucleus
Neutron 1 0 In the nucleus
Electron 0 -1 Surrounding the nucleus
  • Nucleons = protons or neutrons.


  • When two things have the same number of protons but different number of neutrons, they are isotopes of the same element.
  • Isotopes often have similar chemical properties, but different stabilities (some decay and give off radiation, some don't).

Nuclear forces

  • Two forces are at work in the nucleus: the strong force and the electromagnetic force.
  • The strong force binds the nucleons together, and therefore contributes to the binding energy.
  • The electromagnetic force is due to electrostatic repulsion between the positively charged protons in the nucleus.
  • The nucleus stays together because the strong force is much stronger than the electromagnetic repulsion.
  • The strong force is also called the "nuclear force".
... see forces section

Radioactive decay: alpha, beta, gamma, half-life, exponential decay, semi-log plots

  • Alpha decay: alpha decay. Ejection of a helium nucleus at relatively low speed.
  • Beta decay: beta decay. Ejection of a high speed electron.
  • Gamma decay: beta decay. Release of high energy electromagnetic wave.
  • Name Notation Information
    Alpha particle alpha particle Weakest form of radiation. Can be stopped by a sheet of paper. It is essentially a relatively low speed helium nucleus.
    Beta particle beta particle More energy than an alpha particle. Can be stopped by aluminum foil. It is a high speed electron.
    Gamma ray gamma ray Strongest form of radiation. It is a high energy electromagnetic wave. Can be stopped by a thick layer of lead or concrete.
  • Some notes on α, β, and γ decay
    • Conservation of mass dictates that total atomic weight before the decay equal the total atomic weight after.
    • Conservation of charge dictates that the total atomic number before the decay equal the total atomic number after.
    • Don't get thrown off by particles you do not recognize. As long as they have a weight and a charge, just incorporate these numbers in your calculations.
    • MCAT problems on identifying decay products are just math work.
    • Remember: the atomic number (the bottom number) determines what element it is.
  • half-life is the time it takes for the amount of something to half due to decay.
    • After 1 half-life, the amount of the original stuff decreases by half.
    • After 2 half-lives, the amount of the original stuff decreases by a factor of 4.
    • After 3 half-lives, the amount of the original stuff decreases by a factor of 8.
    • The mathematical expression for this is: half life equation, where N sub t=0 is the amount the original starting material. N sub t is the amount of the original material that is still left. Lastly, t is time.
    • Although the above is the official half-life equation, people like to multiply rather than to divide. Therefore, a more user friendly equation is: alternative half-life equation
  • Stability
    • When something is stable, it doesn't decay.
    • When something is unstable, it decays.
    • The more unstable something is, the shorter the half-life.
  • Exponential decay:
    exponential decay
  • Semi-log plots: for the purposes of the MCAT, semi-log plots convert exponential curves into straight lines.
    • Something that curves up becomes a straight line with a positive slope.
    • Something that curves down becomes a straight line with a negative slope.
    • For exponential decay, a semi-log plot graphs the log of amount vs. time.
    • For exponential decay, a semi-log plot is a straight line with a negative slope.
    • The semi-log plot intercepts the x axis where the original y value is 1.
    • semi-log plot of exponential decay

General nature of fission

  • Fission = one nuclei splitting apart.
  • Uranium undergoes fission when struck by a free neutron.
  • The fission of uranium generates more neutrons, which goes on to split other Uranium nuclei. This is called a chain reaction.

General nature of fusion

  • Fusion = two nuclei coming together.
  • The Sun works by fusion.
  • Hydrogen in the Sun fuses to form helium.

Mass deficit, energy liberated, binding energy

  • Mnucleons = Matom + binding energy/c2
  • Mnucleons > Matom because some of the Mnucleons is converted to binding energy that holds the nucleons together.
    • Mnucleons = mass of all the nucleons that make up the atom in their free, unbound state.
    • Matom = mass of the atom.
    • Mnucleons - Matom = mass deficit (also called mass defect) = ΔM.
    • Binding energy = converting ΔM into its equivalent in energy = ΔM c2.
    • Energy liberated = binding energy.
  • The conservation of mass and energy: the total mass and energy before a reaction is always the same as the total mass and energy after the reaction.
  • If the total mass before the reaction is different from the total mass after the reaction, then the difference in mass is made up for by energy.
  • The difference in mass before and after a reaction is called the mass deficit or mass defect.
  • The energy that makes up for the mass deficit is calculated by: mass deficit
  • Energy is liberated when mass is lost during a reaction.
  • Energy is absorbed with mass is gained during a reaction.
  • More notes on binding energy:
    • Binding energy most commonly refers to nuclear binding energy (the energy that binds the nucleons together).
    • Binding energy is due to the strong force. ...more on forces
    • Binding energy per nucleon is strongest for Iron (Fe 56).
    • Binding energy per nucleon is the weakest for Deuterium (the 2-nucleon isotope of hydrogen).
    • Less commonly used is the electron binding energy. This is because electron binding energy is more commonly referred to as the ionization energy.