Atoms have a small central nucleus made up of protons and neutrons around which there are electrons.

Atoms of the same element always have the same number of protons.

Isotopes are atoms of the same element but with different number of neutrons.

This gives rise to different mass numbers.

Relative abundance is the amount of each isotope as the percentage for that element occurring on the Earth

The simplest model of electrons has them orbiting in shells around the nucleus. Each successive shell is further from the nucleus and has a greater energy.

This model can be further refined by the concept of sub shells and orbitals.

Sub shells are known by letters s, p, d, and f. The s sub shell can contain 2 electrons, p 6, d 10 and f 14.

Electrons occupy negative charge clouds called orbitals, each orbital can hold only 2 electrons. Each type of shell has a different type of orbital.

Electrons fill the lowest energy level first this means it is generally easy to predict how the electrons will fill the orbitals (it gets more complicated with the transition metals).

First Ionisation Energy is defined as:

The energy required to remove one electron from each of one mole of gaseous atoms to an infinite separation.

M(g) → M⁺(g) + e^-

There are more filled energy levels between the nucleus and the outermost electrons.

These filled energy levels shield the outer electrons from the attractive force of the positive nucleus.

As the radius of the atom increases, the distance between the nucleus and the outer electron increases and therefore the force of attraction between the nucleus and outer most electrons is reduced.

These factors mean that less energy is needed to remove the first electron from an atom at the bottom of the group compared to one at the top of the group.

As we go across the period, there are more protons in each nucleus so the nuclear charge in each element increases. This increases the attractive force acting on the outermost electrons.

So, the nuclear charge increases as each proton is added and another electron is added to the outermost energy level. This electron is poorly shielded from the nuclear charge by the other electrons in its own energy level. Overall, the electrons are drawn closer to the nucleus and are harder to remove.

This would explain a steady increase from left to right. The dips between groups II and III and between V and VI require more explanation.