Final answer:
First ionization energies decrease down a group as atomic size increases, and increase across a period due to higher effective nuclear charge and smaller atomic radius.
Step-by-step explanation:
The statement regarding first ionization energies is that they generally decrease down a group and increase across a period. This is because the ionization energy is linked to the atomic radius and the effective nuclear charge experienced by the valence electrons in an atom. As the size of the atom increases down a group, it is easier for the electron to be removed due to its greater distance from the nucleus. Conversely, as we move across a period, the atomic radius decreases, the effective nuclear charge increases, and the energy required to remove an electron becomes higher.
These periodic trends are important in understanding the chemical reactivity and properties of the elements. For instance, elements with low ionization energies are more likely to form cations and participate in chemical reactions, demonstrating metallic characteristics.