For each set of atoms and ions, pick the smallest one.
a. I, I+, I−
b. Be2+, Ca2+, Mg2+
c. Fe, Fe2+, Fe3+

Verified step by step guidance

1. <strong>Step 1:</strong> Understand the concept of atomic and ionic size. Generally, cations (positively charged ions) are smaller than their neutral atoms because they lose electrons, reducing electron-electron repulsion and allowing the remaining electrons to be pulled closer to the nucleus. Anions (negatively charged ions) are larger than their neutral atoms because they gain electrons, increasing electron-electron repulsion.
2. <strong>Step 2:</strong> Analyze set (a): I, I⁺, I⁻. Iodine (I) is a neutral atom. I⁺ is a cation, which means it has lost an electron, making it smaller than the neutral iodine atom. I⁻ is an anion, which means it has gained an electron, making it larger than the neutral iodine atom.
3. <strong>Step 3:</strong> Analyze set (b): Be²⁺, Ca²⁺, Mg²⁺. All are cations with a +2 charge, but they belong to different periods in the periodic table. As you move down a group in the periodic table, the size of the ions increases due to the addition of electron shells. Therefore, Be²⁺ is the smallest because it is in the second period, while Ca²⁺ is in the fourth period, and Mg²⁺ is in the third period.
4. <strong>Step 4:</strong> Analyze set (c): Fe, Fe²⁺, Fe³⁺. Iron (Fe) is a neutral atom. Fe²⁺ and Fe³⁺ are cations, with Fe³⁺ having lost more electrons than Fe²⁺. Therefore, Fe³⁺ is smaller than Fe²⁺ due to the greater positive charge pulling the remaining electrons closer to the nucleus.
5. <strong>Step 5:</strong> Compare the sizes within each set based on the analysis from the previous steps and identify the smallest atom or ion in each set.

Key Concepts

Atomic Radius

The atomic radius is the distance from the nucleus of an atom to the outermost shell of electrons. Generally, atomic size decreases across a period due to increased nuclear charge, which pulls electrons closer to the nucleus. Conversely, atomic size increases down a group as additional electron shells are added, resulting in a larger radius.

Ionic Radius

Ionic radius refers to the size of an ion in a crystal lattice. Cations (positively charged ions) are typically smaller than their neutral atoms because they lose electrons, reducing electron-electron repulsion and allowing the remaining electrons to be pulled closer to the nucleus. Anions (negatively charged ions) are larger than their neutral atoms due to the addition of electrons, which increases repulsion among electrons.

Effective Nuclear Charge (Z_eff)

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner-shell electrons that reduce the full nuclear charge felt by outer-shell electrons. A higher Z_eff leads to a stronger attraction between the nucleus and the outer electrons, resulting in a smaller atomic or ionic size.