Question

The following species are isoelectronic with the noble gas krypton. Arrange them in order of increasing radius and comment on the principles involved in doing so: \(\mathrm{Rb}^{+}, \mathrm{Y}^{3+}, \mathrm{Br}^{-}, \mathrm{Sr}^{2+}, \mathrm{Se}^{2-}.\)

Short answer

The order of increasing radius of the given isoelectronic species is \( \mathrm{Y}^{3+}< \mathrm{Sr}^{2+}< \mathrm{Rb}^{+}< \mathrm{Br}^{-}< \mathrm{Se}^{2-}\).

Step-by-step solution

Identify Isoelectronic Species

List the isoelectronic species. They have the same electron configuration as Krypton (\(Kr\)), which is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\). The species are \(\mathrm{Rb}^{+}, \mathrm{Y}^{3+}, \mathrm{Br}^{-},\mathrm{Sr}^{2+}, \mathrm{Se}^{2-}\).

Analyze Nuclear Charge

Analyze the number of protons for each atom/ion. The number of protons in the nuclear core (atomic number) is greater for \(\mathrm{Rb}^{+}\) (37), \(\mathrm{Sr}^{2+}\) (38) and \(\mathrm{Y}^{3+}\) (39) than for \(\mathrm{Br}^{-}\) (35), and \(\mathrm{Se}^{2-}\) (34). Higher charge implies more attraction on the electron cloud.

Arrange based on Atomic Radii

The higher the nuclear charge, the more effective it is at holding the electrons closer to the nucleus, thereby reducing the radius of the atom. Therefore, among the isoelectrons, the one with the highest nuclear charge will be smallest and the one with the lowest nuclear charge will be biggest. This gives us the order as: \(\mathrm{Y}^{3+}< \mathrm{Sr}^{2+}< \mathrm{Rb}^{+}< \mathrm{Br}^{-}< \mathrm{Se}^{2-}\).

Reason the Order

The above order is deduced by examining the nuclear charge of each ion. Higher nuclear charge pulls electrons closer to the nucleus, hence the ion size decreases. On the other hand, lower nuclear charge allows electrons to be further from the nucleus, hence the ion size increases.

Key concepts

Understanding Ionic Radius

When comparing ionic radius, it's important to look at the size of ions that have an equal number of electrons; such ions are called isoelectronic. The radius of an ion is a measure of the size of the ion, generally measured by the distance between the nucleus and the outermost electrons. In general, when an atom loses electrons and becomes a cation, its radius decreases. Conversely, when an atom gains electrons and becomes an anion, its radius increases.

Isoelectronic species, like extit{Rb} extsuperscript{+}, extit{Y} extsuperscript{3+}, extit{Br} extsuperscript{-}, extit{Sr} extsuperscript{2+}, and extit{Se} extsuperscript{2-}, all have the same electron configuration as krypton. Yet, their ionic radii differ. This difference arises from the varying nuclear charge of each species, with larger positive charges leading to smaller ionic radii. Thus, the ionic radius order accounts for the differences in their sizes:

• Cations have smaller radii due to more protons pulling on the same number of electrons.
• Anions have larger radii since fewer protons attract an increased electron cloud.

Understanding these principles will help predict the sizes of ions.

Influence of Nuclear Charge

Nuclear charge plays a key role in determining the size of ions within isoelectronic species. It refers to the total charge of the nucleus, which is determined by the number of protons present in the atom's nucleus. Normally, a higher nuclear charge implies a greater ability to attract and hold electrons, making them be pulled closer to the nucleus.

For isoelectronic species, the one with the highest nuclear charge will have the smallest radius because the electron cloud is more effectively pulled inward. Conversely, a lower nuclear charge means less pull on the electron cloud, allowing electrons to be farther from the nucleus, resulting in a larger radius. For example:

• extit{Y} extsuperscript{3+} has the highest nuclear charge among the species in question, making its ionic radius the smallest.
• extit{Se} extsuperscript{2-} has the lowest nuclear charge, thus the largest ionic radius due to weaker attraction of the electrons.

Recognizing how nuclear charge influences the attraction between the nucleus and the electron cloud is vital for determining ionic size.

Role of Electron Configuration

Electron configuration describes the arrangement of electrons in an atom or ion, indicating where the electrons reside around the nucleus within the shells and subshells. For these isoelectronic species, they all share an electron configuration identical to that of krypton. This is ( 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ ).

Having the same electron configuration means these species have the same number of electrons distributed in identical subshells. However, differences arise from the nuclear charge.

Key points include:

• Same electron configuration indicates the same number of energy levels and subshells filled.
• The nuclear charge changes the arrangement by affecting how tightly the electrons are held.

This is why, despite having the same electron configuration, extit{Rb} extsuperscript{+}, extit{Y} extsuperscript{3+}, extit{Br} extsuperscript{-}, extit{Sr} extsuperscript{2+}, and extit{Se} extsuperscript{2-} differ in size. Understanding electron configuration helps us see how it provides a baseline for electron arrangement, while nuclear charge and resulting interactions create variation in ionic sizes.