Which element in each of the following sets has the smallest first ionization energy, and which has the largest? (a) Li, Ba, K (b) B, Be, Cl (c) Ca, C, Cl

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. It is a key factor in determining an element's reactivity and is influenced by the atomic size and the effective nuclear charge. Generally, ionization energy increases across a period due to increasing nuclear charge and decreases down a group as the outer electrons are further from the nucleus.

Periodic trends refer to the predictable patterns observed in the properties of elements as you move across periods (rows) and down groups (columns) in the periodic table. For ionization energy, it typically increases from left to right across a period and decreases from top to bottom within a group. Understanding these trends helps in predicting the ionization energies of different elements.

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner electrons that reduces the full nuclear charge. A higher effective nuclear charge leads to a stronger attraction between the nucleus and the outer electrons, resulting in higher ionization energies, especially for elements with fewer electron shells.