---
title: "A materials scientist screens four rock-salt ionic solids as simplified models for selecting a refractory ceramic. The ionic radii are shown in the table.  | Solid | Cation radius, \\(r_+\\) (\\(\\text{pm}\\)) | Anion radius, \\(r_-\\) (\\(\\text{pm}\\)) | |—|—:|—:| | \\(\\text{MgO}\\) | \\(72\\) | \\(140\\) | | \\(\\text{CaO}\\) | \\(100\\) | \\(140\\) | | \\(\\text{NaF}\\) | \\(102\\) | \\(133\\) | | \\(\\text{KBr}\\) | \\(138\\) | \\(196\\) |  Assume that all other lattice factors are comparable and that the expected melting point increases with the magnitude of the Coulombic attraction between adjacent ions, modeled by  \\[ |U|\\propto \\dfrac{|q_+q_-|}{r_++r_-} \\]  Which choice gives the expected melting-point order from greatest to least and best justifies the ranking?"
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url: "https://nerd-notes.com/ubq/120064/"
date_modified: "2026-08-21T08:41:07+00:00"
---

# A materials scientist screens four rock-salt ionic solids as simplified models for selecting a refractory ceramic. The ionic radii are shown in the table.

| Solid | Cation radius, \(r_+\) (\(\text{pm}\)) | Anion radius, \(r_-\) (\(\text{pm}\)) |
|—|—:|—:|
| \(\text{MgO}\) | \(72\) | \(140\) |
| \(\text{CaO}\) | \(100\) | \(140\) |
| \(\text{NaF}\) | \(102\) | \(133\) |
| \(\text{KBr}\) | \(138\) | \(196\) |

Assume that all other lattice factors are comparable and that the expected melting point increases with the magnitude of the Coulombic attraction between adjacent ions, modeled by

\[
|U|\propto \dfrac{|q_+q_-|}{r_++r_-}
\]

Which choice gives the expected melting-point order from greatest to least and best justifies the ranking?

A materials scientist screens four rock-salt ionic solids as simplified models for selecting a refractory ceramic. The ionic radii are shown in the table.

| Solid | Cation radius, \(r_+\) (\(\text{pm}\)) | Anion radius, \(r_-\) (\(\text{pm}\)) |
|---|---:|---:|
| \(\text{MgO}\) | \(72\) | \(140\) |
| \(\text{CaO}\) | \(100\) | \(140\) |
| \(\text{NaF}\) | \(102\) | \(133\) |
| \(\text{KBr}\) | \(138\) | \(196\) |

Assume that all other lattice factors are comparable and that the expected melting point increases with the magnitude of the Coulombic attraction between adjacent ions, modeled by

\[
|U|\propto \dfrac{|q_+q_-|}{r_++r_-}
\]

Which choice gives the expected melting-point order from greatest to least and best justifies the ranking?

- **A.** \(\text{MgO} > \text{CaO} > \text{KBr} > \text{NaF}\), because the larger charge product places the oxides first, the smaller separation places \(\text{MgO}\) above \(\text{CaO}\), and the greater polarizability of the ions in \(\text{KBr}\) places it above \(\text{NaF}\).
- **B.** \(\text{MgO} > \text{CaO} > \text{NaF} > \text{KBr}\), because the oxides have the larger value of \(|q_+q_-|\), and within each charge class a smaller value of \(r_++r_-\) produces stronger attraction.
- **C.** \(\text{CaO} > \text{MgO} > \text{KBr} > \text{NaF}\), because the oxides have the larger value of \(|q_+q_-|\), and within each charge class larger ionic radii produce stronger Coulombic attraction.
- **D.** \(\text{NaF} > \text{KBr} > \text{MgO} > \text{CaO}\), because a smaller value of \(|q_+q_-|\) produces stronger attraction, while a smaller value of \(r_++r_-\) strengthens attraction within each charge class.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120064/*