Periodicity
In Chemistry, periodic trends are the tendencies of certain elemental characteristics to increase or decrease as one progresses from one corner of the Periodic table of elements.

# Acidity
The Lewis acidity of each element tends to increase when moving from left to right in the periodic table. However, it decreases going down the table. This is due to the electronegativity of the elements. Elements to the right tend to have a greater way of attracting electrons then those on the left, making the left ones more basic whilst the right ones are acidic. The Lewis acidity decreases going down however in a group as is evident to increasing metallic nature of the elements in group four.

# Atomic radius
The atomic radius is the distance from the atomic nucleus to the outermost stable electron orbital in an atom that is at equilibrium.  The atomic radius tends to decrease as one progresses across a period because the effective nuclear charge increases, thereby attracting the orbiting electrons and lessening the radius.  The atomic radius also will usually increase as one descends a group of the period table because the energy level (shell) increases down the group causing the outer shell electrons to be further away from the nucleus, thereby heavily increasing the atomic size. However, diagonally, the number of protons has a larger effect than the sizeable radius. For example, lithium (145 pm) has a smaller atomic radius than magnesium (150 pm). Atomic radii decrease left to right across a period. (it's just that simple...)

# Ionization potential
The ionization potential (or the ionization energy) is the miniumum energy required to remove one electron from each atom in a mole of atoms in the gaseous state.  The first ionization energy is the energy required to remove one, the nth ionization energy is the energy required to remove the atom's nth electron, not including the n-1 electrons before it.  Trend-wise, the ionization potentials tend to increase while one progresses across a period because the greater number of protons (higher nuclear charge) attract the orbiting electrons more strongly, thereby increasing the energy required to remove one of the electrons.  As one progresses down a group on the periodic table, the ionization energy will likely decrease, due to the greater number of shells, thereby positioning the valence electrons further from the protons, which attract them less, thereby requiring less energy to remove them.  There will be an increase of ionization energy from left to right of a given period and a decrease from top to bottom.  As a rule, it requires far less energy to remove an outer-shell electron than an inner-shell electron.  As a result the ionization energies for a given element will increase steadily within a given shell, and when starting on the next shell down will show a drastic jump in ionization energy.  Simply put, the lower the principal quantum number, the higher the ionization energy for the electrons within that shell.

# Electron affinity
The electron affinity is (officially) the energy required to detach an electron from a singly-charged anion.  More commonly, the electron affinity measures the energy released when an electron is added to a stable atom, thereby creating an anion.  As one progresses across a period, the electron affinity will increase, due to the larger attraction from the nucleus, and the atom "wanting" the electron more as it reaches maximum stability.  Down a group, the electron affinity decreases because of a large increase in the atomic radius and the number of electrons that decrease the stability of the atom, repulsing each other.

# Electronegativity
Electronegativity is a measure of the ability of an atom or molecule to attract electrons in the context of a chemical bond.  The type of bond formed is largely determined by the difference in electronegativity between the atoms involved, using the Pauling scale.  Trend-wise, as one moves horizontally across a period in the periodic table, the electronegativity increases due to the stronger attraction that the atoms obtain as the nuclear charge increases.  Moving down a group, the electronegativity decreases due to the larger distance between the nucleus and the valence electron shell, thereby decreasing the attraction, making the atom have less of an attraction for electrons or protons

# Metallic character
Metallic character refers to the chemical properties associated with elements classified as metals.  These properties, which arise from the element's ability to lose electrons, are: the displacement of hydrogen from dilute acids; the formation of basic oxides; the formation of ionic chlorides; and their reduction reaction, as in the thermite process.  As one moves across a period from left to right in the periodic table, the metallic character decreases, as the atoms are more likely to gain electrons to fill their valence shell rather than to lose them to remove the shell.  Down a group, the metallic character increases, due to the lesser attraction from the nucleus to the valence electrons (in turn due to the atomic radius), thereby allowing easier loss of the outer electrons or protons

# Nuclear charge
Increases going from top to bottom, and left to right across the periodic table.
The increase in nuclear charge is greater going from top to bottom of the periodic table, than going from left to right in the periodic table.  This is due to as you go from left to right in the periodic table an extra proton is added to the nucleus, the proton carries a positive charge, so the charge of the nucleus increases for each proton added. Whereas when you go down a group there is a greater increase, this is due to there being a larger number of protons added each time.  The increase in nuclear charge is equal to the number of elements between the element in the period after the first element in the group and the number before the element in the next period. For example, the nuclear charge from Carbon to Silicon will increase by 8, this is because an extra proton is added for each element, nitrogen, oxygen, fluorine, neon, sodium, magnesium, aluminium and one more added to the nucleus of silicon.

# Shielding
The shielding of outer level electrons increases as you go down the groups in the periodic table.  This is because there are extra levels of electrons between the nucleus and outer electrons.
However as you go across a period the shielding does not increase.  This is because there are no extra levels of electrons between the nucleus and outer level of electrons, only extra electrons  are added to the outer level of electrons as you go across the period.