Elements are arranged in the periodic table in order of increasing atomic number.
The periodic table allows chemists to make accurate predictions of physical properties and chemical behaviour for any element, based on its position.
Properties which follow a regular pattern across or down a periodic table are said to be periodic properties.
Features of the table are:
→ groups; groups are vertical columns within the table which contain elements with similar chemical properties resulting from a common number of electrons in the outer shell.
→ periods; periods are rows of elements in the table arranged with increasing atomic number, demonstrating an increasing number of outer electrons and a move from metallic to non-metallic characteristics.
The first 20 elements in the periodic table are categorised according to bonding and structure.
The elements $Li$, $Be$, $Na$, $Mg$, $Al$, $K$, $Ca$ are metallic elements

The elements $H_2$, $N_2$, $O_2$, $F_2$, $Cl_2$, $P_4$, $S_8$ and fullerenes — e.g. $C_{60}$ — are covalent molecular elements.
In general with the molecular elements, there are strong covalent bonds within discrete molecules — intramolecular forces — and weak London dispersion forces between molecules — intermolecular forces. The larger the molecule — i.e. the more atoms present in a molecule — the more electrons are present, the stronger the London dispersion forces $\therefore$ the higher the melting and boiling points of the element, as more energy is needed to break intermolecular bonds.
$H_2$, $N_2$, $O_2$ and the halogens exist as individual diatomic molecules and have weak London dispersion forces between the molecules — intermolecular forces — and strong covalent bonds between the atoms in the molecules — intramolecular forces. Due to only weak London dispersion forces between the molecules in these elements, they exist as gases at room temperature.



The London dispersion forces in the larger sulfur and phosphorus molecules are stronger than in diatomic molecules as there are more electrons present in the former than the latter — as a greater number of atoms means more electrons in total in the molecule — so a greater temporary dipole can be created leading to a stronger electrostatic force of attraction between the positive and negative regions of molecules.
Sulfur and phosphorus are discrete molecules with stronger weak London dispersion forces between the molecules — intermolecular forces — and strong covalent bonds between the atoms in the molecules — intramolecular forces. As the London dispersion forces between sulfur and phosphorus molecules are stronger, they have higher melting and boiling points than the halogens and other elements that exist as diatomic molecules, and they exist as solids at room temperature.
Sulfur exists in molecules with 8 atoms — $S_8$. This is often referred to as a puckered ring or sulfur crown due to its shape.

Phosphorus exists in molecules with 4 atoms — $P_4$ — that have a pyramidal shape.

Carbon can exist as large discrete molecules known as fullerenes, with strong covalent bonds between the atoms within the molecule and weak London dispersion forces between the molecules. Fullerene molecules can be spherical (as $C_{60}$) or tube/plane shaped as graphene; they have relatively high boiling and melting points due to the stronger weak London dispersion forces between molecules as the molecules are so large.
$C_{60}$ is an example of a spherical fullerene, it made up of carbon atoms arranged in hexagons and pentagons.
Graphene is an example of a sheet shaped fullerene that can be rolled to make a tube, it is made up of carbon atoms arranged in hexagons.

Two on the left and bottom right are relevant to above information about carbon in the form of covalent molecules, top right is graphite which is in the next category of covalent network.
The elements $B$, $Si$ and $C$ in the form of diamond and graphite are covalent networks.
Carbon can exist as two large covalent networks, graphite and diamond.
Carbon exists as a covalent network in the form of diamond.

Carbon in the form of diamond
Carbon also exists as a covalent network in the form of graphite.

Carbon in the form of graphite
Boron and silicon exist as covalent networks which means all atoms are held together by strong covalent bonds, resulting in high boiling and melting points.

covalent network of boron atoms
Silicon is a tetrahedral covalent network.

Silicon has a slightly lower melting and boiling point than the other two elemental covalent networks as it has a greater number of occupied electron shells, meaning the valence electrons present in the covalent bonds of silicon are one shell farther away from the positive nucleus and the screening effect due to inner shell electrons is slightly greater. This means the electrostatic force of attraction between the negative bonding electrons and the positive nuclei in the covalent bonds is lower, making the covalent bonds slightly weaker.
The noble gases — group 8 — are monoatomic elements.
The covalent radius is a measure of the size of an atom.

The covalent radius of elements increases down a periodic group as the number of occupied electron shells increases, which increases the overall size of the atom as the outer electrons are farther away from the nucleus and screened from its positive charge by an increased number of inner electron energy levels.
Although the number of protons also increases down a group, which generally decreases the covalent radius as there is an increased nuclear charge which pulls the electron shells closer which decreases the atom’s size, the increase in occupied electron shells, due to the screening effect of the increased number of inner electron shells, overpowers this.
The covalent radius decreases across a period as the increased number of protons in the nucleus of atoms leads to a greater nuclear charge meaning the occupied electron shells have a greater attraction to the nucleus and therefore held closer which decreases the atomic size.
There is no impact of number of occupied electron shells as this remains constant across a period, as the only increase in electrons across a period is within the same shell, which also means the screening effect of increasing the number of inner electron shells plays no part in diminishing the increased nuclear charge.

The first ionisation energy is the energy required to remove one mole of electrons from one mole of gaseous atoms. The second and subsequent ionisation energies refer to the energies required to remove further moles of electrons.
→ i.e. the second ionisation energy is the energy required to remove two moles of electrons from one mole of gaseous atoms, the third ionisation energy is the energy required to remove three moles of electrons from one mole of gaseous atoms, etc.
→ NB: an element can only have as many ionisation energies as it does electrons
Ionisation energy equations can be written to show the the first ionisation energy and second ionisation energy of any element, etc., as follows.
→ NB: These must show one mole of the element in the gaseous form, as per the definition of the ionisation energy.
→ These equations can also be found printed on the top of page 12 of the data booklet.
$$ E_{(g)} \rarr E^+_{(g)}+e^- $$
$$ E^+{(g)} \rarr E^{2+}{(g)}+e^- $$
The first ionisation energy increases across a period, due to the increased positive nuclear charge which leads to a greater electrostatic attraction between the negative outer electron and the positive nucleus so more energy must be supplied to remove it.
The first ionisation energy decreases down a group, due to the increase in atomic size — as the number of occupied electron shells increases — meaning the outer electron is further away from the positive nucleus so the attraction between them is decreased and less energy is required to remove it. The increase in inner electron shells also leads to a screening effect which shields the negative outer electron from the positive nucleus and decreases the electrostatic attraction between them so less energy is needed to remove the electron.

Subsequent ionisation energies are generally higher than the first ionisation energy as the positive nuclear charge is shared between fewer electrons, so the remaining electrons experience a greater electrostatic attraction to the nucleus and more energy is required to remove them.