Question

Which one in each pair has the larger radius? Explain. (a) \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) (b) a potassium atom or a potassium ion (c) a sodium ion or a chloride ion (d) a strontium atom or an iodine atom (e) a rubidium ion or a strontium ion

Short answer

\(\mathrm{Fe}^{2+}\) has a larger radius than \(\mathrm{Fe}^{3+}\); a potassium atom has a larger radius than a potassium ion; a chloride ion has a larger radius than a sodium ion; a strontium atom has a larger radius than an iodine atom; a rubidium ion has a larger radius than a strontium ion.

Step-by-step solution

Define atomic and ionic radii

Atomic radius is the distance from the center of the nucleus to the edge of the electron cloud. Ionic radius is the size of an ion in a crystal lattice. Cations typically have a smaller radius compared to their neutral atoms due to loss of electron(s), leading to a reduced electron cloud and greater effective nuclear charge pulling the remaining electrons closer. Anions have a larger radius due to the addition of electron(s), resulting in increased electron-electron repulsion.

Compare \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\)

Since \(\mathrm{Fe}^{3+}\) has lost an additional electron compared to \(\mathrm{Fe}^{2+}\), it has a higher positive charge and a smaller ionic radius due to increased nuclear charge pulling the electrons closer. Therefore, \(\mathrm{Fe}^{2+}\) has the larger radius.

Compare a strontium atom or an iodine atom

Strontium (Sr) is an alkaline earth metal with a larger atomic radius than iodine (I), which is a halogen. Metals tend to have larger atomic radii than nonmetals in the same period due to lesser effective nuclear charge experienced by the outer electrons. Therefore, a strontium atom has a larger radius than an iodine atom.

Compare a rubidium ion or a strontium ion

Rubidium ion (\(\mathrm{Rb}^+\)) has one more electron shell compared to strontium ion (\(\mathrm{Sr}^{2+}\)), even though both have lost electrons to form cations. The presence of an additional electron shell in rubidium makes its radius larger than that of the strontium ion. Therefore, a rubidium ion has a larger radius than a strontium ion.

Key concepts

Cations and Anions

Understanding the size differences between cations and anions is crucial when comparing atomic and ionic radii. A cation is an atom that has lost one or more electrons, resulting in a net positive charge. The loss of negatively charged electrons means that the remaining electrons experience a greater effective nuclear charge, as there are now fewer electrons to shield the attractive force from the nucleus. This causes the electron cloud to 'shrink,' making cations smaller than their corresponding neutral atoms.

Conversely, an anion is an atom that has gained one or more electrons, leading to a net negative charge. The additional electrons increase the electron-electron repulsion within the cloud, causing it to expand. Therefore, anions are larger than their neutral counterparts. When comparing ionic sizes, the number of electrons lost or gained as well as the overall charge of the ions are key factors in determining their relative sizes.

Effective Nuclear Charge

The concept of effective nuclear charge (ENC) helps us to rationalize the size of atoms and ions. ENC is the net positive charge experienced by an electron in a multi-electron atom. The more protons in the nucleus, the higher the nuclear charge; however, not all electrons feel this full charge due to shielding by other electrons. ENC increases across a period on the periodic table as the number of protons increases but shielding effects do not similarly rise, meaning outer electrons feel a stronger pull toward the nucleus. This pull results in smaller atomic radii as one moves from left to right across a period. On the contrary, in the case of anions, where the number of electrons has increased while the number of protons remains the same, the ENC felt by each additional electron is less, which thus contributes to an increase in size compared to the neutral atom.

Electron-Electron Repulsion

Electron-electron repulsion is a key force in determining the spatial arrangement of electrons around the nucleus. The principle is straightforward: electrons carry the same negative charge, so they repel each other. This repulsive force must be considered particularly when atoms gain electrons to become anions. As the density of electrons increases in an atom or ion, so does the repulsion between them, pushing them further apart and increasing the size of the electron cloud. This is apparent in anions, which are typically larger than their neutral atoms because the added electrons increase repulsion throughout the electron cloud. The balance between electron-electron repulsion and the pull of the nucleus (effective nuclear charge) ultimately shapes the size of atoms and ions.

Periodic Trends in Atomic Radius

The atomic radius of elements displays distinct trends on the periodic table, which can be largely explained by the concepts of effective nuclear charge and electron-electron repulsion. One key trend is that atomic radii decrease from left to right across a period. This is due to a steady increase in effective nuclear charge, which draws the electron cloud closer to the nucleus, resulting in a smaller atomic radius.

Another trend observed is that atomic radii increase down a group. Each additional electron shell is further from the nucleus and increases the size of the atom. Even though each shell may add more electrons which results in greater electron-electron repulsion, the outer electrons are still shielded by the inner shells and the increased distance from the nucleus means the pull they feel is weaker. This results in larger atomic radii as we move down a group. These periodic trends are paramount when predicting the relative sizes of atoms and deducing the behavior of elements in chemical reactions.