For each of the following groups, place the atoms and/or...

For each of the following groups, place the atoms and/or ions in order of decreasing size. a. $\mathrm{Cu}, \mathrm{Cu}^{+}, \mathrm{Cu}^{2+}$ b. $\mathrm{Ni}^{2+}, \mathrm{Pd}^{2+}, \mathrm{Pt}^{2+}$ c. $\mathrm{O}, \mathrm{O}^{-}, \mathrm{O}^{2-}$ d. $\mathrm{La}^{3+}, \mathrm{Eu}^{3+}, \mathrm{Gd}^{3+}, \mathrm{Yb}^{3+}$ e. $\mathrm{Te}^{2-}, \mathrm{I}^{-}, \mathrm{Cs}^{+}, \mathrm{Ba}^{2+}, \mathrm{La}^{3+}$

For each of the following groups, place the atoms and/or ions in order of decreasing size.
a. $\mathrm{Cu}, \mathrm{Cu}^{+}, \mathrm{Cu}^{2+}$
b. $\mathrm{Ni}^{2+}, \mathrm{Pd}^{2+}, \mathrm{Pt}^{2+}$
c. $\mathrm{O}, \mathrm{O}^{-}, \mathrm{O}^{2-}$
d. $\mathrm{La}^{3+}, \mathrm{Eu}^{3+}, \mathrm{Gd}^{3+}, \mathrm{Yb}^{3+}$
e. $\mathrm{Te}^{2-}, \mathrm{I}^{-}, \mathrm{Cs}^{+}, \mathrm{Ba}^{2+}, \mathrm{La}^{3+}$

Key Concepts

Atomic and Ionic Radii

This concept refers to the size of atoms and ions, which is determined by the distance from the nucleus to the outermost electron cloud. In atoms and ions, factors such as electron-electron repulsions, the number of electron shells, and the magnitude of the effective nuclear charge play a major role in determining the overall size. When comparing species, a higher positive charge typically leads to a smaller radius due to the stronger pull of the nucleus on the electrons, whereas an extra electron (or electrons) tends to increase the size due to enhanced repulsions.

Effective Nuclear Charge

Effective nuclear charge (Zeff) represents the net positive charge experienced by an electron after accounting for the shielding effect of other electrons. It is a crucial concept in explaining trends in atomic and ionic sizes; as Zeff increases, electrons are held more tightly by the nucleus, resulting in a smaller radius. Conversely, lower effective nuclear charge allows electrons to spread further from the nucleus, increasing the size of the atom or ion.

Isoelectronic Series

An isoelectronic series comprises atoms and ions that have the same number of electrons. Within this series, the size of the species primarily depends on the nuclear charge. A species with a higher nuclear charge will have a smaller radius, as the increased positive charge pulls the electron cloud closer to the nucleus. This concept helps explain why ions with the same electron configuration can vary in size based solely on their differing nuclear charges.

Periodic Trends

Periodic trends refer to the systematic changes in properties such as atomic and ionic sizes, ionization energies, and electronegativities across the periodic table. For atomic and ionic radii, trends include a decrease in size across a period (due to increasing nuclear charge with similar shielding) and an increase in size down a group (due to additional electron shells). These trends are foundational for predicting how the sizes of different species compare.

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