First, we have atomic and ionic radii which, as the name suggests, refer to the size of the atom, or the ion in the latter case. Radii increase as you go down a group (i.e. Halogens), since the number of orbitals used increases. On the contrary, radii decrease as you go from left to right, in the same period, because the number of electrons in the outer orbital increases, hence the number of protons in the nucleus increases, resulting in a higher attraction between the two causing the atom being more closely "packed" in space.Secondly, electronegativity is another property with which we measure the ability of an atom to attract a bonding electron pair. Unlike the radii, electronegativity tends to increase across a period and decrease down a group. The reason behind that as we go down a group, the number of orbitals increase and hence the outer orbital will be further away and less attracted by the nucleus. As a consequence, the same goes for the outer bonding pair of electrons. On the other hand, as previously stated, as you go across a period from left to right, the atoms become more and more closely packed, with their outer electrons being closer to and more attracted by the nucleus.Finally, we have electron affinity which appears to have the same trending as electronegativity (decrease down a grup and increase across a period). Electron affinity represents the ability of an atom to become negatively charged, that is "take up" an extra electron. Again, due to the same principles of nucleus attraction, that is more likely to happen as you go across a period or up a group, where the attraction of the nucleus for the outer shell increases.