Which metal in the first series of transition metals exhibits +1 oxidation state most frequently and why?

Exercises · 4.23

Q. Which metal in the first series of transition metals exhibits +1 oxidation state most frequently and why?

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Concept understanding — Lanthanide Contraction

Lanthanide Contraction: The Intuition

Imagine you are walking through a dense forest. With every step forward, you push through thick undergrowth. The deeper you go, the more tired you become — each step feels a little harder, and you find yourself hunching forward, your shoulders pulling inward. That inward pull is exactly what happens inside the lanthanide atoms.

The lanthanides are the 14 elements from cerium ( $Ce$ , atomic number 58) to lutetium ( $Lu$ , atomic number 71). As you move from one element to the next, you add one proton to the nucleus and one electron to the atom. The new electron goes into a 4f orbital — a set of orbitals that are shaped like clover leaves and sit deep inside the atom, close to the nucleus.

Here is the key: 4f orbitals are poorly shielded. They do not spread out far from the nucleus, and they do not block the nuclear charge from pulling on the outer electrons. So when you add a proton, the nucleus gets stronger, and the 4f electrons do almost nothing to stop that extra pull. The result? The entire electron cloud — especially the outermost electrons — gets pulled inward. The atom shrinks.

Note

Shielding is the ability of inner electrons to "block" the outer electrons from feeling the full positive charge of the nucleus. Electrons in s and p orbitals shield well; 4f electrons shield very poorly.

The Precise Statement

Lanthanide contraction is the steady and significant decrease in the atomic and ionic radii of the lanthanide elements as atomic number increases from 58 (Ce) to 71 (Lu).

\text{Atomic radius} \propto \frac{1}{Z_{\text{eff}}}

The total contraction across the entire series is about 15–20 picometers — roughly 10–15% of the initial radius. That is a substantial shrinkage for a single row of the periodic table.

Why It Matters

This contraction has two enormous consequences in chemistry:

Similarity of post-lanthanide elements: After lutetium, the next elements are hafnium ( $Hf$ , 72), tantalum ( $Ta$ , 73), and tungsten ( $W$ , 74). Because the lanthanide contraction has made the atoms so small, these elements have almost identical atomic and ionic radii to their counterparts directly above them in the periodic table — zirconium ( $Zr$ ), niobium ( $Nb$ ), and molybdenum ( $Mo$ ). This is why zirconium and hafnium are chemically almost inseparable — they are the same size.
Difficulty in separating lanthanides: All lanthanide ions ( $Ln^{3+}$ ) have nearly identical chemical properties because their radii change so gradually. Separating them requires hundreds of repeated steps (ion-exchange chromatography, solvent extraction) — a painstaking process that was a major challenge in early nuclear chemistry.

Watch out

A common mistake is to think lanthanide contraction means the atoms get smaller because the 4f orbitals are "full" or because of some repulsion effect. It is purely due to poor shielding of the 4f electrons, which lets the nuclear charge pull everything inward.

The Numbers (for reference)

Element	Atomic Number	Ionic Radius ( $Ln^{3+}$ , pm)
Ce	58	103.4
Pr	59	101.3
Nd	60	99.5

Why this formula?

Lanthanide Contraction: Why It Happens

The Lanthanide Contraction is the steady decrease in atomic and ionic radii of the lanthanide elements (Ce to Lu) as atomic number increases. The key observation: the radii shrink by about 1–2 pm per element, despite adding electrons to the 4f subshell.

The Core Question

Why does adding electrons not increase the size, but instead decrease it?

The Formula That Governs It

The effective nuclear charge ( $Z_{\text{eff}}$ ) experienced by an electron is:

Z_{\text{eff}} = Z - S

Where:

$Z$ = atomic number (protons in nucleus)
$S$ = shielding constant (screening by inner electrons)

The key formula for the trend in ionic radii ( $r$ ) across the lanthanides is:

r \propto \frac{n^2}{Z_{\text{eff}}}

Where $n$ is the principal quantum number of the outermost electron (here, $n=6$ for the 6s orbital).

The Derivation: Step by Step

1. What happens when you add a proton and an electron?

Each lanthanide adds:

+1 proton to the nucleus (increases $Z$ by 1)
+1 electron to the 4f subshell

2. The 4f orbital is "penetrating" but poorly shielding

The 4f orbital has a radial distribution that peaks close to the nucleus (inside the 5s and 5p shells).
However, 4f electrons are very poor at shielding the outer 6s electrons from the nuclear charge.

Why?

The 4f orbital is diffuse and deeply buried — it does not effectively screen the outer electrons because:

Its shape (complex, multi-lobed) means it doesn't occupy the space between the nucleus and the 6s electrons efficiently.
The 4f electrons are inside the 5s/5p shells, so they don't block the nuclear pull on the 6s electrons.

3. The net effect on $Z_{\text{eff}}$

When you add one proton ( $\Delta Z = +1$ ) and one 4f electron ( $\Delta S \approx 0.85$ to 0.95), the change in effective nuclear charge is:

\Delta Z_{\text{eff}} \approx +1 - 0.85 = +0.15 \text{ to } +0.05

Result: $Z_{\text{eff}}$ increases slightly with each element.

4. How this shrinks the radius

From the formula $r \propto \frac{n^2}{Z_{\text{eff}}}$ :

$n$ (the principal quantum number of the 6s orbital) stays constant at 6.
$Z_{\text{eff}}$ increases.
Therefore, $r$ decreases. …

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The 3d transition metal that most frequently shows a +1 oxidation state is copper (Cu), because its $3d^{10}$ configuration (achieved after losing one electron) is exceptionally stable due to a completely filled d-subshell.

1. The core idea: stability of electronic configurations

The question asks about the first transition series — Sc through Zn. In this series, the common oxidation states are +2 and +3. A +1 state is rare because removing a single electron from a neutral atom usually leaves an unstable $d^n$ configuration that wants to lose another electron to become either half-filled ( $d^5$ ) or fully filled ( $d^{10}$ ).

The key is to look for an element where losing one electron gives a particularly stable electronic arrangement. That stability would make the +1 state more accessible than for other metals in the series.

2. Scanning the series

Let’s check the ground-state configurations of the neutral atoms and what happens after one electron is removed:

Element	Neutral atom config	After losing 1 e⁻ (M⁺)	Stability of M⁺
Sc	$3d^1 4s^2$	$3d^1 4s^1$	Unstable — wants to lose another e⁻
Ti	$3d^2 4s^2$	$3d^2 4s^1$	Unstable
V	$3d^3 4s^2$	$3d^3 4s^1$	Unstable
Cr	$3d^5 4s^1$	$3d^5$	Half-filled d⁵ — a stable-looking configuration, yet Cr(+1) chemistry is still rare: chromium's real chemistry is dominated by +2, +3 and +6
Mn	$3d^5 4s^2$	$3d^5 4s^1$	Unstable
Fe	$3d^6 4s^2$	$3d^6 4s^1$	Unstable
Co	$3d^7 4s^2$	$3d^7 4s^1$	Unstable
Ni	$3d^8 4s^2$	$3d^8 4s^1$	Unstable
Cu	$3d^{10} 4s^1$	$3d^{10}$	Fully filled d¹⁰ — extremely stable
Zn	$3d^{10} 4s^2$	$3d^{10} 4s^1$	Unstable — wants to lose the 4s¹ to become $d^{10}$

Watch out

A common mistake is to think that because Zn has a $d^{10}$ configuration in its neutral state, it should easily form Zn⁺. But Zn⁺ has a $d^{10}4s^1$ configuration — the 4s electron is loosely held and easily lost, so Zn⁺ is actually unstable and quickly becomes Zn²⁺ ( $d^{10}$ ). The stability comes from the final configuration after losing two electrons, not one.

3. Why copper stands out

Copper’s neutral atom has the configuration $3d^{10}4s^1$ . When it loses the single 4s electron, it becomes Cu⁺ with a $3d^{10}$ configuration — a completely filled d-subshell. This is an exceptionally stable arrangement because:

A filled d-subshell has spherical symmetry and maximum exchange energy.
There is no driving force to lose another electron (the next ionization energy is much higher). …

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Which First-Series Transition Metal Shows the +1 Oxidation State Most Frequently?

Method: Electronic Configuration Analysis

Step 1: Recall the general electronic configuration of first-row transition metals:

\text{[Ar]} \, 3d^{1-10} \, 4s^{1-2}

Step 2: Identify the condition for a stable +1 oxidation state.

A +1 state means losing the 4s electron(s) first (since 4s is higher in energy than 3d once occupied).
Stability of +1 state increases if the resulting $d^n$ configuration is half-filled or fully filled (exchange energy + stability).

Step 3: Check each metal systematically:

Metal	Ground state config	M⁺ configuration (Table 4.2)	Stability of +1
Sc	$3d^1 4s^2$	$3d^1 4s^1$	Unstable
Ti	$3d^2 4s^2$	$3d^2 4s^1$	Unstable
V	$3d^3 4s^2$	$3d^3 4s^1$	Unstable
Cr	$3d^5 4s^1$	$3d^5$	Half-filled — yet +1 chemistry still rare
Mn	$3d^5 4s^2$	$3d^5 4s^1$	Unstable (a 4s electron remains; +1 is not a notable Mn state)
Fe	$3d^6 4s^2$	$3d^6 4s^1$	Unstable
Co	$3d^7 4s^2$	$3d^7 4s^1$	Unstable
Ni	$3d^8 4s^2$	$3d^8 4s^1$	Unstable
Cu	$3d^{10} 4s^1$	$3d^{10}$	Fully filled → very stable
Zn	$3d^{10} 4s^2$	$3d^{10} 4s^1$	Unstable (loses the remaining 4s electron to give Zn²⁺)

Step 4: Identify the most frequent +1 state.

Only copper loses a single electron to land directly on a stable configuration: Cu⁺ = $3d^{10}$ . Every other 3d metal's M⁺ ion still carries an easily-lost 4s electron — and even Cr⁺, though it is $d^5$ , has only rare +1 chemistry. …

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Common Mistakes: The +1 Oxidation State in the First Transition Series

The Question

Which metal in the first series of transition metals exhibits +1 oxidation state most frequently and why?

Correct answer: Copper (Cu) — due to its stable $3d^{10}$ configuration in the +1 state.

🚩 Mistake #1: Assuming the +1 state is common across the whole series

What students do wrong:

Because +2 is common for nearly every 3d metal, students assume +1 must also be reasonably common and pick a metal almost at random.

Why it's wrong:

The +1 state needs the special case where losing just ONE electron leaves a stable configuration. Table 4.2's M⁺ row shows that for almost every 3d metal, the M⁺ ion still carries an easily-lost 4s electron ( $3d^n 4s^1$ ) — only Cu⁺ lands directly on the stable $3d^{10}$ .

How to avoid:

Check the M⁺ configuration, not the atom's: only Cu ( $3d^{10}4s^1$ → Cu⁺ $3d^{10}$ ) reaches a full d-subshell by losing a single electron.

🚩 Mistake #2: Picking Zinc (Zn) because of $3d^{10}$

What students do wrong:

Zn has $3d^{10}4s^2$ and loses two electrons to form $Zn^{2+}$ (also $3d^{10}$ ). Students think Zn should show +1.

Why it's wrong:

Zn never shows +1 in stable compounds.
$Zn^{+}$ would be $3d^{10}4s^1$ — an unstable, unpaired 4s electron.
Zn prefers +2 because removing both 4s electrons gives a completely filled d-subshell ( $3d^{10}$ ).

How to avoid:

Remember: Zn is not a true transition metal by IUPAC definition (it has a full d-subshell in both atom and common ion).
For +1 stability, look for half-filled or fully-filled d-subshell after losing one electron, not before.

🚩 Mistake #3: Choosing Chromium (Cr) because of $3d^5$ stability

What students do wrong:

Cr has $3d^5 4s^1$ (half-filled d-subshell). Students think losing one electron gives $Cr^+$ with $3d^5$ — very stable.

Why it's misleading:

$Cr^+$ does exist, but $Cr^{3+}$ is far more common.
The question asks "most frequently" — Cr shows +1 only in a few complexes, not as a general trend.

How to avoid:

Compare actual oxidation state frequencies:
- Cu: +1 common in oxides ( $Cu_2O$ ), halides ( $CuCl$ ), many complexes.
- Cr: +1 is rare; +3 and +6 dominate.
"Most frequently" means most often encountered in stable compounds, not just theoretically possible.

🚩 Mistake #4: Forgetting the $3d^{10}$ special stability for Cu

What students do wrong:

Students know Cu has $3d^{10}4s^1$ configuration, but don't connect it to +1 stability.

The correct reasoning:

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Q.Which metal in the first series of transition metals exhibits +1 oxidation state most frequently and why?

1. The core idea: stability of electronic configurations

2. Scanning the series

3. Why copper stands out

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