
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: , 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: , 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: , 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: , 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:
 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.
Isotopes
 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, halflife, exponential decay, semilog plots
 Alpha decay: . Ejection of a helium nucleus at relatively low speed.
 Beta decay: . Ejection of a high speed electron.
 Gamma decay: . Release of high energy electromagnetic wave.
Name 
Notation 
Information 
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 

More energy than an alpha particle. Can be stopped by aluminum foil. It is a high speed electron. 
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.
 halflife is the time it takes for the amount of something to half due to decay.
 After 1 halflife, the amount of the original stuff decreases by half.
 After 2 halflives, the amount of the original stuff decreases by a factor of 4.
 After 3 halflives, the amount of the original stuff decreases by a factor of 8.
 The mathematical expression for this is: , 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 halflife equation, people like to multiply rather than to divide. Therefore, a more user friendly equation is:
 Stability
 When something is stable, it doesn't decay.
 When something is unstable, it decays.
 The more unstable something is, the shorter the halflife.
 Exponential decay:
 Semilog plots: for the purposes of the MCAT, semilog 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 semilog plot graphs the log of amount vs. time.
 For exponential decay, a semilog plot is a straight line with a negative slope.
 The semilog plot intercepts the x axis where the original y value is 1.

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
 M_{nucleons} = M_{atom} + binding energy/c^{2}
 M_{nucleons} > M_{atom} because some of the M_{nucleons} is converted to binding energy that holds the nucleons together.
 M_{nucleons} = mass of all the nucleons that make up the atom in their free, unbound state.
 M_{atom} = mass of the atom.
 M_{nucleons}  M_{atom} = mass deficit (also called mass defect) = ΔM.
 Binding energy = converting ΔM into its equivalent in energy = ΔM c^{2}.
 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:
 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 2nucleon 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.

