The early periodic table
During the 19th century, many scientists tried to find ways to classify elements based on their properties and atomic weights.
In 1863 Newlands proposed his law of octaves, which stated that similar properties were repeated every eighth element. He put the 56 known elements into seven groups according to their atomic weights. However, their properties didn't match very well within the groups so his ideas weren't accepted.
In 1869 Mendeleev produced a better table by leaving gaps for undiscovered elements. When some of the missing elements were discovered, they were found to have properties predicted by Mendeleev. Then other scientist more readily accepted his ideas. Mendeleev's table became the basis for the modern periodic table.
The modern periodic table
Scientists found out about protons and electrons at the start of the 20th century. Soon after, they made models of the arrangement of electrons in atoms. The elements were arranged in the periodic table in order of their atomic numbers. They were lined up in groups of similar chemical properties. They have similar properties because they all have the same number of electrons in their outer shell.
The modern periodic table
Within a group the reactivity of the elements depends on the total number of electrons. Going down a group, there are more occupied energy levels and the atoms get larger. As the atoms get larger, the electrons in the outer shell are less strongly attracted by the nucleus.
When metals react they lose electrons, so the reactivity of metals in a group increases going down the group
When non-metals react they gain electrons, so the reactivity of non-metals decreases going down a group.
Group 1 - the alkali metals
The Group 1 elements are reactive metals that are soft solids at room temperature (they have low melting and boiling points). The m.p's and b.p's decrease going down the group and the reactivity increases. They have low densities, so Li, Na and K float on water.
They all react readily with air and water. With water they produce H gas and a metal hydroxide (e.g. 2Li (s) + 2H2O (l) --> 2LiOH (aq) + H2 (g))
They react with the halogens to form salts that are white or colourless crystals (e.g. 2Na (s) + Cl2 (g) --> NaCl (s))
They all have one electron in their outer shell which they lost in reaction to form ionic compounds in which their ions have a single positive charge (e.g. K+)
Reactivity increases going down Group 1 because the outer electron is less strongly attracted to the nucleus so it is lost more easily.
Group 7 - the halogens
The halogens are non-metallic elements in group 7. They exist as small molecules made up of pairs of atoms (ie they are diatonic). They have low melting and boiling points that increase down the group. They all form ionic compounds with metals in which their ions have a charge of -1. They can also bond covalently with other non-metals, forming molecules. A more reactive halogen is able to displace a less reactive halogen in solution. Their reactivity decreases down the group because attraction of the outer electrons to the nucleus decreases as the number of occupied energy levels increases so they don't get attract that extra electron they need as strongly.
Should say I2 - halogens are diatonic
The transition elements
The transition elements are found in the periodic table between Groups 2 and 3. They are (obviously) all metals and (except mercury) have higher melting and boiling points than Group 1. Most are strong and dense and are useful as building materials, often as alloys. They are malleable, ductile and good conductors of heat and electricity so are very useful (also useful as catalysts). They only react slowly (or not at all) with oxygen and water at ordinary temperatures.
They can form positive ions with various charges (e.g. Cu+/Cu2+) because they have a small number of electrons in their outer shell and an incomplete lower energy level.
Compunds of transition metals are often coloured.