Electron affinity and electronegativity are related but distinct concepts. Electron affinity refers to the energy change when an electron is added to a neutral atom to form a negative ion. It's a measurable quantity, representing the energy released or absorbed during this process. Electronegativity, on the other hand, is a qualitative measure of an atom's ability to attract and bind with electrons in a chemical bond. It doesn't directly measure an energy change but rather provides a scale (like the Pauling scale) to compare atoms' relative abilities to attract electrons within a bond.

When an atom loses electrons to form a cation, the electron cloud shrinks. The loss of electrons results in a greater positive charge in the nucleus relative to the number of electrons, leading to a stronger pull on the remaining electrons and hence a smaller radius. Conversely, when an atom gains electrons to form an anion, the added electrons increase the electron-electron repulsion, causing the electron cloud to expand. Thus, the ionic radius increases. The magnitude of these changes also depends on the effective nuclear charge and the amount of shielding from inner electron shells.

Periodicity in the properties of elements is intrinsically linked to their electronic structure. As you move across a period, electrons are added to the same energy level, but the nuclear charge increases. This leads to trends like increasing ionisation energy and electronegativity. Similarly, as you move down a group, new electron shells are added, increasing atomic and ionic sizes. The repeating patterns or trends in properties observed when elements are arranged in order of increasing atomic number (which means the same order as their electronic configurations) is the essence of periodicity. This predictability in properties is primarily because of the systematic filling of electron orbitals.

The anomalous values in ionisation energy observed between certain pairs of elements can be attributed to electron configurations. For example, boron has an electron configuration ending in 2p¹, whereas beryllium's ends in 2s². It's easier to remove the p electron from boron than the s electron from beryllium because p orbitals are at a higher energy level. Similarly, the decrease in ionisation energy from oxygen to nitrogen is due to the repulsion between electrons paired in oxygen's 2p⁴ configuration. It's easier to remove an electron from the more repelled paired electrons in oxygen than from the singly occupied p orbitals in nitrogen.

As one moves from left to right across a period, the atomic radius decreases due to an increase in the nuclear charge without a substantial increase in shielding. With every added proton in the nucleus, the nuclear charge increases, pulling the electron cloud closer to the nucleus. Simultaneously, these additional electrons are added to the same main energy level, meaning that there isn't a substantial increase in shielding to counterbalance the increasing nuclear charge. Thus, even though more electrons are being added, they are pulled inwards more strongly, resulting in a smaller atomic radius.