Question

Arrange each of the following sets of atoms and ions, in order of increasing size: \((\mathbf{a}) \mathrm{Se}^{2-}, \mathrm{Te}^{2-}, \mathrm{Se} ;(\mathbf{b}) \mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+};\) \((\mathbf{c}) \mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+} ;(\mathbf{d}) \mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}.\)

Short answer

The order of increasing size for each of the given sets is as follows: (a) Se < Te^2- < Se^2- (b) Fe^3+ < Co^3+ < Fe^2+ (c) Ti^4+ < Sc^3+ < Ca (d) Be^2+ < Ne < Na^+

Step-by-step solution

(a) Arrange Se^2-, Te^2-, and Se in order of increasing size

Firstly, consider the atomic number: Se (34) and Te (52). Se^2- and Te^2- have the same charge, which means they have the same number of electrons. Since Te has a higher atomic number, its increased number of protons result in a stronger attraction to the electrons, making Te^2- smaller than Se^2-. Now, compare Se^2- and Se. Se^2- has gained two extra electrons, which causes increased electron-electron repulsion and a subsequent expansion of the electron cloud. Therefore, Se is smaller than Se^2-. The final order of increasing size is Se < Te^2- < Se^2-.

(b) Arrange Co^3+, Fe^2+, and Fe^3+ in order of increasing size

Co^3+ (27) and Fe^2+ (26) are in the same period and close in atomic number. However, Co^3+ has a higher charge, which results in a greater effective nuclear charge experienced by its electrons, making it smaller than Fe^2+. Now, compare Fe^2+ and Fe^3+. Both have the same atomic number (26), but Fe^3+ has one less electron, leading to a greater effective nuclear charge for the remaining electrons. Thus, Fe^3+ is smaller than Fe^2+. The final order of increasing size is Fe^3+ < Co^3+ < Fe^2+.

(c) Arrange Ca, Ti^4+, and Sc^3+ in order of increasing size

Ca (20), Ti^4+ (22), and Sc^3+ (21) are in the same period. Since they are close in atomic number, we will focus on the effect of the charges on their sizes. The higher the charge in an ion, the greater the effective nuclear charge experienced by its electrons and therefore, the smaller the ion's size. Thus, the order of increasing size is Ti^4+ < Sc^3+ < Ca.

(d) Arrange Be^2+, Na^+, and Ne in order of increasing size

Be^2+ (4), Na^+ (11), and Ne (10) are in different periods, so the atomic number is an important factor here. Ions with a higher atomic number have more protons, which exerts a stronger attractive force on the electron cloud. Additionally, we must consider the charges on the ions, as a greater charge corresponds to a smaller ion size. Be^2+ has a higher charge than Na^+ and Ne, making it the smallest of these three species. In this specific case, though Ne has one less proton and one less electron than Na^+, their electron configurations result in a similar effective nuclear charge experienced by the outer electrons. Ne's configuration is complete, whereas Na^+ has lost its outermost electron. This makes Na^+ larger than Ne since its electron cloud becomes less tightly bound. The final order of increasing size is Be^2+ < Ne < Na^+.

Key concepts

Atom Comparison

When comparing atoms, such as selenium (Se) and tellurium (Te), we often look at their atomic numbers and electron configurations. The atomic number represents the number of protons in the nucleus, and as this number increases, so does the strength of the atom's ability to hold onto its electrons. This can make seemingly larger atoms, due to added protons, often appear smaller in size because their electron clouds are held more tightly.

• Atomic Number: More protons mean a stronger attraction on electrons.
• Electron Configuration: The distribution of electrons in shells affects size.

Therefore, even though tellurium is lower in the periodic table compared to selenium, its higher atomic number makes it smaller when comparing their respective ionic forms.

Ionic Size

The size of ions can vary significantly from their neutral atoms, mainly due to electron gain or loss. Adding electrons, as seen in anions like Se^2-, increases electron-electron repulsion, thus expanding the electron cloud and making the ion larger than its neutral counterpart. Conversely, cations, like Fe²⁺ and Co³⁺, have fewer electrons, which allows the remaining electrons to be pulled closer to the nucleus.

• Anions: Gain of electrons increases size.
• Cations: Loss of electrons decreases size due to stronger nuclear pull.

In summary, the ionic size is determined by the balance between added electron repulsion and the effective pull from the nucleus.

Electron Configuration

An atom's electron configuration describes how electrons are distributed among its atomic orbitals. For example, in neutral elements and their ions, changes in electron configuration lead to changes in size. Excising or adding electrons alters the balance of forces within an atom or ion, leading to shifts in their sizes. When an electron is removed to form cations such as Ti⁴⁺ and Fe³⁺, the energy levels may become adjusted.

• Stable Configurations: Noble gases, like Ne, tend to resist size change.
• Shielding: Electrons in inner shells offset charge on outer electrons.

These configurations and electron interactions define how tightly electrons are held, subsequently affecting the species' size.

Effective Nuclear Charge

Effective nuclear charge ( Z_{ ext{eff}} ) is the net positive charge experienced by an electron in a multi-electron atom. It considers the actual nuclear charge minus the shielding effect by inner electrons. A higher effective nuclear charge leads to stronger attractions between the nucleus and the electrons, thus reducing the overall size of an atom or ion. For example, moving from Fe²⁺ to Fe³⁺, the reduction in electron count increases Z_{ ext{eff}} .

• High Z_{ ext{eff}}: Smaller atoms/ions as electrons are held more tightly.
• Low Z_{ ext{eff}}: Larger atoms due to less effective nuclear pull.

Thus, understanding the effective nuclear charge is crucial in predicting the size differences between ions and their corresponding atoms.