Write down the number of 3d electrons in each of the following ions: $Ti^{2+}$, $V^{2+}$, $Cr^{3+}$, $Mn^{2+}$, $Fe^{2+}$, $Fe^{3+}$, $Co^{2+}$, $Ni^{2+}$ and $Cu^{2+}$. Indicate how would you expect the five 3d orbitals to be occupied for these hydrated ions (octahedral).

Question

Accepted Answer

> [!TLDR]
> The number of 3d electrons in each ion is found by subtracting the ion charge from the neutral atom’s atomic number, then removing 4s electrons first. For hydrated octahedral complexes, the five 3d orbitals split into $t_{2g}$ (lower energy) and $e_g$ (higher energy) sets; electrons fill according to Hund’s rule and the ligand field strength (here, weak-field/high-spin for most first-row transition metal aqua ions).

## Concept and Intuition

To find the 3d electron count for a transition metal ion, you must remember the **Aufbau principle** for neutral atoms: for elements in the 3d series, the 4s orbital fills before 3d (e.g., $[Ar]4s^2 3d^x$). When forming a positive ion, **electrons are removed first from the 4s orbital**, not the 3d — this is a common mistake. So for $Ti^{2+}$, the neutral Ti has $[Ar]4s^2 3d^2$; removing two electrons takes both 4s electrons, leaving $3d^2$.

Once we know the 3d count, we consider the hydrated ion in an **octahedral crystal field**. Water is a weak-field ligand, so the splitting energy $\Delta_o$ is small. This means electrons fill all five orbitals singly before pairing (Hund’s rule) — the **high-spin** configuration. The five d orbitals split into a lower-energy triplet ($d_{xy}, d_{xz}, d_{yz}$ — called $t_{2g}$) and a higher-energy doublet ($d_{z^2}, d_{x^2-y^2}$ — called $e_g$). For weak fields, electrons occupy $t_{2g}$ first, then $e_g$, all with parallel spins as far as possible.

> [!WARNING]
> A classic error: for $Fe^{3+}$, students often write $3d^5$ but then pair electrons in $t_{2g}$ because they think of the free ion. In a weak octahedral field, $Fe^{3+}$ has all five orbitals singly occupied — a half-filled $t_{2g}^3 e_g^2$ configuration. Do not pair unless the ligand is strong (like CN⁻).

Let’s work through each ion step by step.

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### 1. $Ti^{2+}$ (Titanium, Z = 22)
Neutral Ti: $[Ar]4s^2 3d^2$. Remove 2 electrons → both from 4s.  
**3d electrons = 2**.  
In octahedral field: two electrons go i

Material Type	$\chi_m$	Behaviour	Example
Diamagnetic	Small and negative ( $\approx -10^{-5}$ )	Weakly repelled by a magnet; $\vec{M}$ opposes $\vec{H}$	Water, copper, bismuth
Paramagnetic	Small and positive ( $\approx 10^{-5}$ to $10^{-3}$ )	Weakly attracted; $\vec{M}$ aligns with $\vec{H}$	Aluminium, oxygen gas
Ferromagnetic	Large and positive ( $\gg 1$ )	Strongly attracted; $\vec{M}$ can be huge and persists even after $\vec{H}$ is removed	Iron, nickel, cobalt

Ion	3d $^n$	$t_{2g}$ occupancy	$e_g$ occupancy	Unpaired e $^-$
$Ti^{2+}$	2	↑ ↑	—	2
$V^{2+}$	3	↑ ↑ ↑	—	3

Ion	Atomic No.	Neutral configuration	Ion configuration	3d electrons ( $n$ )
$Ti^{2+}$	22	$[Ar]\,3d^2 4s^2$	$[Ar]\,3d^2$	2
$V^{2+}$	23	$[Ar]\,3d^3 4s^2$	$[Ar]\,3d^3$	3
$Cr^{3+}$	24	$[Ar]\,3d^5 4s^1$	$[Ar]\,3d^3$	3
$Mn^{2+}$	25	$[Ar]\,3d^5 4s^2$	$[Ar]\,3d^5$	5
$Fe^{2+}$	26	$[Ar]\,3d^6 4s^2$	$[Ar]\,3d^6$	6
$Fe^{3+}$	26	$[Ar]\,3d^6 4s^2$	$[Ar]\,3d^5$	5
$Co^{2+}$	27	$[Ar]\,3d^7 4s^2$	$[Ar]\,3d^7$	7
$Ni^{2+}$	28	$[Ar]\,3d^8 4s^2$	$[Ar]\,3d^8$	8
$Cu^{2+}$	29	$[Ar]\,3d^{10} 4s^1$	$[Ar]\,3d^9$	9

Ion	$n$	$t_{2g}$ occupancy	$e_g$ occupancy	Unpaired electrons
$Ti^{2+}$	2	$\uparrow \uparrow$	—	2
$V^{2+}$	3	$\uparrow \uparrow \uparrow$	—	3
$Cr^{3+}$	3	$\uparrow \uparrow \uparrow$	—	3
$Mn^{2+}$	5	$\uparrow \uparrow \uparrow$	$\uparrow \uparrow$	5
$Fe^{2+}$	6	$\uparrow \downarrow \uparrow \uparrow$	$\uparrow \uparrow$	4
$Fe^{3+}$	5	$\uparrow \uparrow \uparrow$	$\uparrow \uparrow$	5
$Co^{2+}$	7	$\uparrow \downarrow \uparrow \downarrow \uparrow$	$\uparrow \uparrow$	3
$Ni^{2+}$	8	$\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow$	$\uparrow \uparrow$	2
$Cu^{2+}$	9	$\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow$	$\uparrow \downarrow \uparrow$	1

Ion	Neutral config	Ion config	Number of 3d electrons
$Ti^{2+}$	$[Ar] 3d^2 4s^2$	$[Ar] 3d^2$	2
$V^{2+}$	$[Ar] 3d^3 4s^2$	$[Ar] 3d^3$	3
$Cr^{3+}$	$[Ar] 3d^5 4s^1$	$[Ar] 3d^3$	3
$Mn^{2+}$	$[Ar] 3d^5 4s^2$	$[Ar] 3d^5$	5
$Fe^{2+}$	$[Ar] 3d^6 4s^2$	$[Ar] 3d^6$	6
$Fe^{3+}$	$[Ar] 3d^6 4s^2$	$[Ar] 3d^5$	5
$Co^{2+}$	$[Ar] 3d^7 4s^2$	$[Ar] 3d^7$	7
$Ni^{2+}$	$[Ar] 3d^8 4s^2$	$[Ar] 3d^8$	8
$Cu^{2+}$	$[Ar] 3d^{10} 4s^1$	$[Ar] 3d^9$	9

$d^n$	Occupancy (five orbitals: $d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}, d_{z^2}$ )
$d^2$	$\uparrow$ $\uparrow$ _ _ _
$d^3$	$\uparrow$ $\uparrow$ $\uparrow$ _ _
$d^4$	$\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$ _
$d^5$	$\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$
$d^6$	$\uparrow\downarrow$ $\uparrow$ $\uparrow$ $\uparrow$ $\uparrow$
$d^7$	$\uparrow\downarrow$ $\uparrow\downarrow$ $\uparrow$ $\uparrow$ $\uparrow$
$d^8$	$\uparrow\downarrow$ $\uparrow\downarrow$ $\uparrow\downarrow$ $\uparrow$ $\uparrow$
$d^9$	$\uparrow\downarrow$ $\uparrow\downarrow$ $\uparrow\downarrow$ $\uparrow\downarrow$ $\uparrow$

Concept and Intuition

1. Ti2+Ti^{2+}Ti2+ (Titanium, Z = 22)

2. V2+V^{2+}V2+ (Vanadium, Z = 23)

3. Cr3+Cr^{3+}Cr3+ (Chromium, Z = 24)

4. Mn2+Mn^{2+}Mn2+ (Manganese, Z = 25)

5. Fe2+Fe^{2+}Fe2+ (Iron, Z = 26)

6. Fe3+Fe^{3+}Fe3+ (Iron, Z = 26)

7. Co2+Co^{2+}Co2+ (Cobalt, Z = 27)

8. Ni2+Ni^{2+}Ni2+ (Nickel, Z = 28)

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1. $Ti^{2+}$ (Titanium, Z = 22)

2. $V^{2+}$ (Vanadium, Z = 23)

3. $Cr^{3+}$ (Chromium, Z = 24)

4. $Mn^{2+}$ (Manganese, Z = 25)

5. $Fe^{2+}$ (Iron, Z = 26)

6. $Fe^{3+}$ (Iron, Z = 26)

7. $Co^{2+}$ (Cobalt, Z = 27)

8. $Ni^{2+}$ (Nickel, Z = 28)

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