Question

Use the concepts of effective nuclear charge, shielding, and \(n\) value of the valence orbital to explain the trend in atomic radius as you move across a period in the periodic table.

Short answer

The atomic radius decreases across a period because the effective nuclear charge increases with an increase in protons, the shielding remains almost constant, and the n value of the valence orbitals does not change, resulting in a stronger pull on the valence electrons towards the nucleus.

Step-by-step solution

Understanding Effective Nuclear Charge

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom. The trend across a period in the periodic table is that Z_eff increases. This is because as you move from left to right across a period, the number of protons increases, which increases the nuclear charge without a corresponding increase in shielding effect since electrons are being added to the same energy level.

Explaining Shielding

Shielding effect occurs when inner electrons block the attraction between the nucleus and the valence electrons. In a given period, the inner electron configuration remains comparatively constant; as a result, the shielding effect does not significantly increase across a period. This means that the increasing nuclear charge has a greater effect on the valence electrons.

Assessing Valence Orbital's Principal Quantum Number (n)

The principal quantum number, n, represents the energy level of an electron’s orbital. Within the same period, the value of n for the valence orbitals remains the same. This consistency means that any changes in atomic size are primarily due to changes in Z_eff rather than changes in n.

Combining Concepts to Explain Atomic Radius Trend

Putting the concepts together, across a period in the periodic table, Z_eff increases due to an increased nuclear charge and constant shielding. The principal quantum number of the valence orbital remains constant. The increased Z_eff pulls the valence electrons closer to the nucleus, which reduces the atomic radius as you move from left to right across a period.

Key concepts

Effective Nuclear Charge

The effective nuclear charge (often abbreviated as Z_eff) is a fundamental concept that plays a crucial role in the atomic radius trend across the periodic table. Think of it as the genuine pull that a valence electron feels from the nucleus. It considers both the total positive charge of the protons in the nucleus and the negative charge of the electrons that lie between the nucleus and the valence electron—the latter influencing what is known as the shielding effect.

The importance of Z_eff lies in its increase as you move from left to right across a period. With each additional proton, the nuclear charge goes up, but because these protons are added within the same energy level, the shielding effect doesn't counterbalance this increase effectively. Therefore, the valence electrons experience a stronger attraction towards the nucleus, making the atomic radius smaller. Z_eff helps explain why elements on the right of the periodic table tend to be smaller than those on the left, as they feel a greater 'pull' from the center.

Shielding Effect

Diving into the shielding effect, imagine it as a game of 'cosmic keep-away' where inner electrons act as blockers between the football—the valence electron—and the quarterback—the nucleus. These inner electrons serve as a shield, reducing the full impact of the nuclear charge on the electrons in the outermost shell. However, across a period, the increase in nuclear charge is not significantly offset by an increase in shielding since the electrons are added to the same principal quantum level.

As a result, despite the core electron shield, the effective nuclear charge felt by the valence electrons steadily increases. In essence, as you move across a period, the shielding effect is relatively constant, but the constricting force of the nucleus is what intensifies, squeezing the outermost electrons closer in and thus shrinking the atom. It's this delicate balance between the increased pull from the nucleus and the consistent shielding that contributes to the atomic radius decreasing.

Principal Quantum Number

The principal quantum number (represented by the symbol n) signifies the size and energy level of an electron’s orbital. Essentially, it's akin to the floors of an electron's 'hotel,' where higher floors represent larger orbitals with greater energy. Within a period, or a 'row' on the periodic table, all the valence electrons are found on the same 'floor' as neighboring elements, meaning n remains consistent across that row.

This consistency is key to understanding the atomic radius trend. Since n isn't increasing across a period, the decrease in atomic radius isn't due to electrons being placed in higher energy levels, but rather the increased hold that the nucleus has on the same energy level—a hold that is determined by the effective nuclear charge.

Understanding the interplay between Z_eff, the shielding effect, and n allows us to appreciate why, even though electrons are added as we move across a period, the atomic size tends to decrease. It's a nuanced dance between the forces at play within an atom, illuminated by these concepts that are pivotal to grasp for anyone diving into the intricacies of chemistry.