Why does gadolinium have 4f⁷ 5d¹ instead of 4f⁸?

A half-filled 4f⁷ subshell — all seven f orbitals each holding one electron with parallel spins — gains extra stability through exchange energy. Promoting one electron to 5d¹ achieves this half-filled state, making [Xe] 4f⁷ 5d¹ 6s² lower in energy than the naive [Xe] 4f⁸ 6s². This is the lanthanide analogue of the chromium d⁵ exception.

What is the noble-gas shorthand for gadolinium?

The abbreviated notation is [Xe] 4f⁷ 5d¹ 6s², where [Xe] represents the filled xenon core (1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶, 54 electrons).

How many unpaired electrons does gadolinium have?

Gadolinium has eight unpaired electrons in its ground state: seven in the half-filled 4f⁷ subshell (one electron per orbital, all spin-up by Hund's rule) plus one in the 5d¹ orbital. This gives gadolinium the highest magnetic moment of any element.

Why is gadolinium used in MRI contrast agents?

Gadolinium's seven unpaired 4f electrons create a very large magnetic moment (7.94 Bohr magnetons). This strongly shortens the relaxation times (T1 and T2) of nearby water protons, brightening MRI images in the region where the contrast agent accumulates. Gadolinium chelates such as Gd-DTPA (gadopentetate dimeglumine) are used because free Gd³⁺ is toxic; chelation keeps it safe while preserving the magnetic effect.

What oxidation state does gadolinium typically form?

Gadolinium most commonly forms the +3 ion (Gd³⁺) by losing its 5d¹ and 6s² electrons. This leaves the stable [Xe] 4f⁷ half-filled core intact, further reinforcing why +3 dominates. +2 and +4 states are rare and exist only in specific compounds.

Is gadolinium a transition metal or lanthanide?

Gadolinium is a lanthanide (rare-earth element) in period 6, f-block. It sits between europium (Z=63) and terbium (Z=65). Unlike most lanthanides that have no 5d electrons, gadolinium has one 5d electron due to the half-filled 4f stabilization effect.

Gadolinium Electron Configuration

Name: Gadolinium Electron Configuration
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Author: Nham Vu

Reference tool for gadolinium's electron configuration ([Xe] 4f⁷ 5d¹ 6s²), orbital diagram, the half-filled 4f exception, and key properties including MRI contrast agent use.

Z = 64 Gd Gadolinium

Gadolinium — Electron Configuration

Atomic number 64 · Lanthanide · Period 6 · f-block · Exception: half-filled 4f⁷

[Xe] 4f⁷ 5d¹ 6s² 64 electrons 7 unpaired 4f + 1 unpaired 5d Highest magnetic moment

Half-filled 4f exception

The naive prediction is [Xe] 4f⁸ 6s². Gadolinium instead adopts [Xe] 4f⁷ 5d¹ 6s² because a completely half-filled 4f⁷ subshell — all seven orbitals singly occupied with parallel spins — gains extra stabilization through exchange energy. This is the lanthanide analogue of the chromium (3d⁵ 4s¹) and copper (3d¹⁰ 4s¹) exceptions in the d-block.

Subshell Breakdown

Subshell	Type	Electrons	Max Capacity	Notation
1s	s orbital, shell n=1	2	2	1s²
2s	s orbital, shell n=2	2	2	2s²
2p	p orbitals, shell n=2	6	6	2p⁶
3s	s orbital, shell n=3	2	2	3s²
3p	p orbitals, shell n=3	6	6	3p⁶
3d	d orbitals, shell n=3 (part of Xe core)	10	10	3d¹⁰
4s	s orbital, shell n=4	2	2	4s²
4p	p orbitals, shell n=4	6	6	4p⁶
4d	d orbitals, shell n=4 (part of Xe core)	10	10	4d¹⁰
5s	s orbital, shell n=5	2	2	5s²
5p	p orbitals, shell n=5 (completes Xe core)	6	6	5p⁶
4f	f orbitals, shell n=4 (half-filled — exception)	7	14	4f⁷
5d	d orbitals, shell n=5 (1 electron from 4f exception)	1	10	5d¹
6s	s orbital, shell n=6 (outermost)	2	2	6s²
Total		64

Full Configuration

1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f⁷ 5s² 5p⁶ 5d¹ 6s²

All subshells written explicitly; 64 electrons total.

Noble-Gas Shorthand

[Xe] 4f⁷ 5d¹ 6s²

[Xe] = xenon core, 54 electrons (1s² through 5p⁶).

Shell Fill Summary

Shell 1 (n=1) — 1s² 2 / 2 electrons (100%)

Shell 2 (n=2) — 2s² 2p⁶ 8 / 8 electrons (100%)

Shell 3 (n=3) — 3s² 3p⁶ 3d¹⁰ 18 / 18 electrons (100%)

Shell 4 (n=4) — 4s² 4p⁶ 4d¹⁰ 4f⁷ 25 / 32 electrons (78%)

Shell 5 (n=5) — 5s² 5p⁶ 5d¹ 9 / 50 electrons (18%)

Shell 6 (n=6) — 6s² 2 / 72 electrons (3%)

Shell 4 holds 25 of its 32-electron maximum (4f stops at 7 due to the half-filled exception). Shell 5 has only 9 electrons — the 5d subshell receives just one electron before 4f filling resumes in heavier lanthanides.

The Xenon Core — [Xe]

The first 54 electrons of gadolinium match the complete electron configuration of xenon (Z=54):

[Xe] = 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶

The remaining 10 electrons — 4f⁷ 5d¹ 6s² — govern gadolinium's chemistry, magnetic properties, and oxidation states.

Orbital Box Diagram — Valence Region

The xenon core (1s² through 5p⁶, 54 electrons) is shown in compact form. The valence subshells 4f, 5d, and 6s are shown in detail.

[Xe]

core: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶

54 electrons, all paired — xenon configuration

7 electrons — all 7 orbitals singly occupied (half-filled, maximum exchange energy)

1 electron in first 5d orbital; orbitals 2–5 empty

2 electrons (paired) — outermost shell

Each box = one orbital. Opposing arrows = paired electrons (+½ and −½ spin). Single up arrow = unpaired electron. Colored border = partially filled subshell.

Gadolinium has 8 unpaired electrons total: 7 from 4f⁷ and 1 from 5d¹. This gives it the highest effective magnetic moment of any element (7.94 Bohr magnetons from the 4f contribution).

Quantum Numbers — Valence Electrons (post-[Xe])

Electron #	n	l	mₗ	mₛ	Subshell
55	4	3	-3	+½	4f
56	4	3	-2	+½	4f
57	4	3	-1	+½	4f
58	4	3	0	+½	4f
59	4	3	1	+½	4f
60	4	3	2	+½	4f
61	4	3	3	+½	4f
62	5	2	-2	+½	5d
63	6	0	0	+½	6s
64	6	0	0	−½	6s

Electrons 1–54 fill the xenon core (not shown). n = principal quantum number; l = azimuthal (3→f); mₗ = magnetic (−3 to +3 for f); mₛ = spin. All seven 4f electrons have parallel spin (+½) per Hund's rule, maximizing exchange energy.

Summary

Reference tool for gadolinium's electron configuration ([Xe] 4f⁷ 5d¹ 6s²), orbital diagram, the half-filled 4f exception, and key properties including MRI contrast agent use.

How it works

The Aufbau principle fills orbitals from lowest to highest energy, placing the xenon core (1s² through 5p⁶) first.
After the xenon core, electrons fill 4f orbitals — but gadolinium stops at 4f⁷ rather than the expected 4f⁸.
A half-filled 4f⁷ subshell (seven singly-occupied orbitals, all spin-up) gains extra stability from exchange energy between electrons of the same spin.
Promoting one electron to 5d¹ instead of pairing in 4f gives the configuration [Xe] 4f⁷ 5d¹ 6s², maximizing this exchange stabilization.
This is the lanthanide analogue of the chromium (3d⁵ 4s¹) and copper (3d¹⁰ 4s¹) exceptions seen in d-block elements.
The seven unpaired 4f electrons produce gadolinium's exceptionally high magnetic moment (7.94 Bohr magnetons), the highest of any element.

Use cases

Quick reference for chemistry homework or exam review on lanthanide electron configurations.
Understand why gadolinium is a special case — half-filled 4f⁷ stability drives the exception.
Visualize how 4f, 5d, and 6s subshells fill across the lanthanide series.
Explain why gadolinium is used in MRI contrast agents due to its seven unpaired electrons.
Compare gadolinium to adjacent lanthanides (europium, terbium) to see 4f-filling trends.
Teaching aid for exchange energy and half-filled subshell stabilization in advanced chemistry.
Understand gadolinium's +3 oxidation state from its valence electron configuration.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu