a) Why do AVEEs increase as one goes from left to right across a period? b) What other periodic property has this same trend?

The atomic effective nuclear charge (often abbreviated as Z_eff) refers to the net positive charge experienced by an electron in a multi-electron atom. This is not the same as the actual nuclear charge (the total number of protons), because the full positive charge is mitigated by the presence of other electrons. These inner electrons act as a shield, reducing the effective nuclear charge felt by the outer electrons.

Imagine electrons living in a multi-story building (the atom), with the nucleus being the ground floor. Electrons on higher floors (outer energy levels) may not feel the full presence of those at the ground floor due to the floors (inner-shell electrons) in between. However, as you move from the left to right across a period on the periodic table, the number of 'ground floor' inhabitants (protons) increases, but the number of floors (energy levels) does not. This makes the pull from the ground floor (nuclear charge) feel stronger to those upstairs (valence electrons), hence an increase in the effective nuclear charge.

Electronegativity is essentially the atom's ability to attract and hold onto electrons. It is a crucial concept when discussing chemical bonds, as it determines how electron pairs are shared between atoms. The higher an atom's electronegativity, the more it tends to attract electrons towards itself.

On the periodic table, electronegativity increases as you move from left to right across a period. This trend coincides with that of the atomic effective nuclear charge. As the Z_eff increases due to an increasing number of protons while maintaining a consistent shielding effect, the pull on shared electrons strengthens. Consequently, the atoms toward the right side of the periodic table (excluding the noble gases) are much more electronegative, and pull electron pairs closer in a bond.

Electron shielding is the phenomenon where the repulsion between electrons in different energy levels causes the outermost electrons to be less attracted to the nucleus. It is often visualized as the inner electrons 'shielding' the outer electrons from the full force of the positive charge of the nucleus.

As you go across a period, there's a slight increase in shielding effect due to the increase in the number of electrons. However, this increase is minimal and does not effectively counterbalance the increase in effective nuclear charge. Consequently, the added electrons enter the same principal energy level and do not contribute substantially to the shielding effect, leading to a consistent increase in the pull from the nucleus across a period.

The periodic table is not just a list of elements, but a profound tool that reflects the underlying principles governing atomic structure and behavior. Its arrangement is in periods (horizontal rows) and groups (vertical columns), based on increasing atomic number. The structure reveals periodic trends, including those in atomic size, electronegativity, ionization energy, and metallic character, amongst others.

Understanding the layout of the periodic table allows us to predict the properties of elements based on their position. For example, elements in the same group typically have similar chemical properties, and as one moves across a period from left to right, properties such as electronegativity and the effective nuclear charge increase, while atomic radii decrease. These predictable patterns make the periodic table an indispensable tool for chemists.