Periodic Law - A periodic repetition of the element's chemical and physical properties is evident when they elements are sorted out by their increasing atomic number (Henry Moseley's periodic table).
Period - A row of elements in the periodic table. They all have the same number of atomic orbitals.
Group - A column of elements in the periodic table. They have the same number of valence electrons and are similar in chemical and physical properties.
Nuclear Charge (Zeff) (include in your definition of how this influences atomic radius, electronegativity, and ionization energy) - The total charge of all the protons present in the nucleus. Nuclear charge decreases as you go down a group, but increases as you go across a period. When nuclear charge increases, atomic radius decreases; when nuclear charge increases, electronegativity increases; when nuclear charge increases, ionization energy increases.
Nuclear Shielding (include in your definition of how this influences group trends only (for atomic radius, electronegativity, & ionization energy) - The attraction between the outermost electrons (valence electrons) and the nucleus. Nuclear shielding only plays an effect (increases) when you go down a group because of the increased energy levels. When nuclear shielding increases, the atomic radius increases; when nuclear shielding increases, electronegativity increases; when nuclear shielding increases, ionization energy increases.
Ionization Energy - The energy needed to get rid of an electron from a neutral atom.
Electronegativity - The attraction that an atom has to gain an added electron.
Atomic Radius - The distance between the radius of the center of the nucleus to the edge of the electron cloud.
Ionic Radius - Measure of the distance between the nucleus and the valence electrons in an ion