---
title: "A materials student models two solid alloys of a hypothetical metal \\(M\\), which has an atomic radius of \\(140\\text{ pm}\\) and a molar mass of \\(56\\text{ g/mol}\\). In the model, a solute is predicted to occupy a substitutional site when \\(0.85\\leq \\dfrac{r_{\\text{solute}}}{r_M}\\leq 1.15\\), whereas a solute can fit into an ideal octahedral interstitial site when \\(\\dfrac{r_{\\text{solute}}}{r_M}\\leq 0.414\\).  | Alloy | Composition | Solute radius | Solute molar mass | |——-|————-|—————|——————-| | \\(P\\) | Replace \\(1\\) of every \\(10\\) atoms of \\(M\\) with \\(X\\) | \\(133\\text{ pm}\\) | \\(52\\text{ g/mol}\\) | | \\(Q\\) | Add \\(1\\) atom of \\(Y\\) for every \\(10\\) atoms of \\(M\\) | \\(56\\text{ pm}\\) | \\(16\\text{ g/mol}\\) |  Measurements indicate that the two alloys have the same volume per \\(10\\) original host-lattice sites. All other microstructural features that affect malleability are held constant. Which row correctly compares the density and malleability of the two alloys?"
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url: "https://nerd-notes.com/ubq/120055/"
date_modified: "2026-08-21T08:41:01+00:00"
---

# A materials student models two solid alloys of a hypothetical metal \(M\), which has an atomic radius of \(140\text{ pm}\) and a molar mass of \(56\text{ g/mol}\). In the model, a solute is predicted to occupy a substitutional site when \(0.85\leq \dfrac{r_{\text{solute}}}{r_M}\leq 1.15\), whereas a solute can fit into an ideal octahedral interstitial site when \(\dfrac{r_{\text{solute}}}{r_M}\leq 0.414\).

| Alloy | Composition | Solute radius | Solute molar mass |
|——-|————-|—————|——————-|
| \(P\) | Replace \(1\) of every \(10\) atoms of \(M\) with \(X\) | \(133\text{ pm}\) | \(52\text{ g/mol}\) |
| \(Q\) | Add \(1\) atom of \(Y\) for every \(10\) atoms of \(M\) | \(56\text{ pm}\) | \(16\text{ g/mol}\) |

Measurements indicate that the two alloys have the same volume per \(10\) original host-lattice sites. All other microstructural features that affect malleability are held constant. Which row correctly compares the density and malleability of the two alloys?

A materials student models two solid alloys of a hypothetical metal \(M\), which has an atomic radius of \(140\text{ pm}\) and a molar mass of \(56\text{ g/mol}\). In the model, a solute is predicted to occupy a substitutional site when \(0.85\leq \dfrac{r_{\text{solute}}}{r_M}\leq 1.15\), whereas a solute can fit into an ideal octahedral interstitial site when \(\dfrac{r_{\text{solute}}}{r_M}\leq 0.414\).

| Alloy | Composition | Solute radius | Solute molar mass |
|-------|-------------|---------------|-------------------|
| \(P\) | Replace \(1\) of every \(10\) atoms of \(M\) with \(X\) | \(133\text{ pm}\) | \(52\text{ g/mol}\) |
| \(Q\) | Add \(1\) atom of \(Y\) for every \(10\) atoms of \(M\) | \(56\text{ pm}\) | \(16\text{ g/mol}\) |

Measurements indicate that the two alloys have the same volume per \(10\) original host-lattice sites. All other microstructural features that affect malleability are held constant. Which row correctly compares the density and malleability of the two alloys?

- **A.** Density: \(\rho_Q<\rho_P\) | Malleability: alloy \(Q\) is less malleable than alloy \(P\)
- **B.** Density: \(\rho_Q=\rho_P\) | Malleability: alloy \(Q\) is less malleable than alloy \(P\)
- **C.** Density: \(\rho_Q>\rho_P\) | Malleability: alloy \(Q\) is less malleable than alloy \(P\)
- **D.** Density: \(\rho_Q>\rho_P\) | Malleability: alloy \(Q\) is more malleable than alloy \(P\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120055/*