---
title: "A materials scientist is choosing between zirconium and hafnium for a corrosion-resistant alloy. The ground-state electron configurations of the neutral atoms are shown.  | Atom | Atomic number, \\(Z\\) | Ground-state electron configuration | |——|———————-|————————————-| | \\(\\text{Zr}\\) | \\(40\\) | \\([\\text{Kr}]\\,4d^2 5s^2\\) | | \\(\\text{Hf}\\) | \\(72\\) | \\([\\text{Xe}]\\,4f^{14} 5d^2 6s^2\\) |  Across the intervening lanthanides, the \\(4f\\) subshell becomes filled as \\(Z\\) increases. A student initially predicts that \\(\\text{Hf}\\) has a substantially larger atomic radius because its outer electrons occupy the \\(n=6\\) shell rather than the \\(n=5\\) shell. After accounting for the relative penetration and shielding ability of electrons in \\(s\\), \\(d\\), and \\(f\\) subshells, which outcome for the atomic radii is most likely, and what accounts for it?"
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url: "https://nerd-notes.com/ubq/120084/"
date_modified: "2026-08-21T08:41:21+00:00"
---

# A materials scientist is choosing between zirconium and hafnium for a corrosion-resistant alloy. The ground-state electron configurations of the neutral atoms are shown.

| Atom | Atomic number, \(Z\) | Ground-state electron configuration |
|——|———————-|————————————-|
| \(\text{Zr}\) | \(40\) | \([\text{Kr}]\,4d^2 5s^2\) |
| \(\text{Hf}\) | \(72\) | \([\text{Xe}]\,4f^{14} 5d^2 6s^2\) |

Across the intervening lanthanides, the \(4f\) subshell becomes filled as \(Z\) increases. A student initially predicts that \(\text{Hf}\) has a substantially larger atomic radius because its outer electrons occupy the \(n=6\) shell rather than the \(n=5\) shell. After accounting for the relative penetration and shielding ability of electrons in \(s\), \(d\), and \(f\) subshells, which outcome for the atomic radii is most likely, and what accounts for it?

A materials scientist is choosing between zirconium and hafnium for a corrosion-resistant alloy. The ground-state electron configurations of the neutral atoms are shown.

| Atom | Atomic number, \(Z\) | Ground-state electron configuration |
|------|----------------------|-------------------------------------|
| \(\text{Zr}\) | \(40\) | \([\text{Kr}]\,4d^2 5s^2\) |
| \(\text{Hf}\) | \(72\) | \([\text{Xe}]\,4f^{14} 5d^2 6s^2\) |

Across the intervening lanthanides, the \(4f\) subshell becomes filled as \(Z\) increases. A student initially predicts that \(\text{Hf}\) has a substantially larger atomic radius because its outer electrons occupy the \(n=6\) shell rather than the \(n=5\) shell. After accounting for the relative penetration and shielding ability of electrons in \(s\), \(d\), and \(f\) subshells, which outcome for the atomic radii is most likely, and what accounts for it?

- **A.** \(r_{\text{Hf}} \approx r_{\text{Zr}}\), because the \(4f\) electrons incompletely shield the increasing nuclear charge, causing contraction of the outer orbitals that largely offsets the expected increase from occupying the \(n=6\) shell.
- **B.** \(r_{\text{Hf}} \approx r_{\text{Zr}}\), because both atoms have \(4\) valence electrons, and atoms with equal numbers of valence electrons have approximately equal radii.
- **C.** \(r_{\text{Hf}} > r_{\text{Zr}}\), because the \(4f\) electrons completely shield the additional nuclear charge, allowing the larger \(n=6\) shell to determine the radius.
- **D.** \(r_{\text{Hf}} < r_{\text{Zr}}\) by a large amount, because the \(4f\) electrons provide essentially no shielding from the additional nuclear charge.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120084/*