The atomic radius of an atom is useful to understand as it helps to understand many properties of atoms and how they react. Atomic radius is the distance from the atoms nucleus to the outermost electron orbital and a lot of trends in the periodic table rely on this property due to its relation to nuclear charge and shielding.
In general as we progress down the group the number of electrons and shells increases and so does the size of the nucleus meaning atomic radius will increase as we progress down a group. For example the atomic radius of Lithium is 152x10-12 m but if we progress down to caesium the atomic radius of caesium is 262x10-12m as caesium has 6 electron shells and also a greater number of protons but due to the large number of shells the outer valence electron is much further away.
Across a period the atomic radius decreases as the number of protons in the nucleus increases, this means the nucleus has a higher nuclear charge and can attract electrons more closely due to the attraction of the positive protons to the negative electrons. At the same time when elements are in the same period they have the same number of shells, this means the shielding of this layer of electrons is the same for all elements in a period but the number of protons and nuclear charge increases. This means the electrons are pulled in closer to the nucleus reducing the size of the atomic radius. For example Sodium in period 3 has an atomic radius of 186 x10-12 m and chlorine in the same period has an atomic radius of 99x10-12 m as Chlorine has a larger number of protons and a higher nuclear charge to attract the electrons to the nucleus and make the radius smaller.
Nuclear charge is the attraction exerted by the nucleus on electrons due to the positive charge of the protons and negative charge of the electron
Shielding is the effect of inner shell electrons close to the nucleus reducing the nuclear charge on the valence electron.
The valence electron is the outermost electron of an atom
The shell is the path that electrons follow outside the nucleus. Shells can be considered as energy levels and the further away from the nucleus the higher in energy.
The nucleus is the term given to the centre of the atom comprising of the proton and neutron
A proton is a positive particle that makes up the atom in the nucleus with a positive charge
A neutron is a neutral sub atomic particle that makes up the nucleus with the proton
The electron is the smallest sub atomic particle that make up the atom. Has a negative charge and is located in shells that orbit the nucleus