Identify the element with the higher first ionization energy in each of the following pairs: (a) iron and nickel; (b) nickel and copper; (c) osmium and platinum; (d) nickel and palladium; (e) hafnium and tantalum.

The periodic table is an arrangement of elements that provides valuable insights into the properties and behaviors of these fundamental components of matter. One critical trend observed in the periodic table is the variation in first ionization energy as you move across a period or down a group. Ionization energy refers to the energy needed to remove an electron from an atom in its gaseous state.

As we move from left to right across a period, ionization energy typically increases. This is due to the fact that atoms have more protons, leading to a stronger attraction between the nucleus and the electrons, and consequently, it takes more energy to remove one. The presence of additional electrons also does not shield the increased nuclear charge effectively, thus not reducing the ionization energy in this direction.

Conversely, as one descends down a group, there is a decrease in ionization energy. This trend is attributed to the increase in atomic size and the additional electron shells that effectively shield the outermost electrons from the nucleus, making them easier to remove despite the increase in the total positive charge.

Nuclear charge is the total charge of the nucleus, which is the product of the number of protons (positive charge) it contains. This charge plays a pivotal role in an atom's first ionization energy. A higher nuclear charge equates to a stronger attractive force exerted on the valence electrons, requiring more energy to remove one of them.

In essence, as the nuclear charge increases with the addition of protons in each element across a period, the effective nuclear charge also increases. This is because the inner electrons do not completely shield the additional positive charge, resulting in a higher net pull on the outermost electrons. For example, nickel has a greater nuclear charge than iron, thus it exhibits a higher first ionization energy. It is this increased pull that becomes a key factor in understanding the differences in ionization energies among elements in the same period of the periodic table.

Valence electrons are the outermost electrons of an atom and are vital in determining an element's chemical properties, including its ionization energy. These electrons are the ones involved in chemical bonding and reactions. When discussing first ionization energy, we refer to the energy required to remove one of these valence electrons.

The more valence electrons that are present, and the tighter they are held by the nucleus, the more energy it will take to remove one. This is due to the effective nuclear charge that these electrons feel. However, valence electrons in the same period experience similar shielding effects but differ in their distance from the nucleus and the overall nuclear charge they experience. Hence, elements situated to the right of a period would generally have valence electrons more tightly bound to the nucleus, leading to a higher ionization energy when comparing elements in the same period, such as nickel and copper.