Why Half-Filled Subshells Are Extra Stable? 🔥 | JEE Main Concept Explained

 

❓ Question

The extra stability of half-filled subshells is due to which of the following factors?

Options:
(A) Symmetrical distribution of electrons
(B) Smaller Coulombic repulsion energy
(C) Presence of electrons with same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electrons by one another

---

🖼️ Question Image

---

✍️ Short Solution

We often see exceptions in electronic configurations, like:

$$\text{Cr: } [\text{Ar}]\,3d^5\,4s^1 \quad \text{instead of } [\text{Ar}]\,3d^4\,4s^2$$
$$\text{Cu: } [\text{Ar}]\,3d^{10}\,4s^1 \quad \text{instead of } [\text{Ar}]\,3d^9\,4s^2$$

This happens because half-filled (d⁵) and fully-filled (d¹⁰) subshells are more stable than uneven ones.
Let’s understand why.

---

🔹 Step 1 — Symmetrical distribution of electrons

In a half-filled subshell, electrons are distributed symmetrically among all available orbitals.
Example: 3d⁵ means each of the five d orbitals has one electron → maximum symmetry.

✅ This symmetry gives stability because it minimizes electronic repulsion and balances charge distribution.
→ Option (A) is correct.

---

🔹 Step 2 — Exchange energy concept

Electrons with the same spin in different degenerate orbitals can exchange their positions without changing energy.
This exchange leads to extra stabilization, known as exchange energy.

The number of possible exchanges increases when more orbitals have unpaired, same-spin electrons — like in half-filled (d⁵) configurations.

✅ Larger exchange energy ⇒ greater stability.
→ Option (D) is correct.

---

🔹 Step 3 — Role of same-spin electrons

In half-filled subshells, all electrons have parallel spins (Hund’s rule).
This causes a lower electron-electron repulsion and increases the exchange stabilization.

✅ This is related to Option (C), which explains the spin contribution to stability.

---

🧮 Image Solution

---

✅ Conclusion & Video Solution

✅ Correct Options:

$$\boxed{{\displaystyle (A),(C),(D)}}$$

Key idea:
The extra stability of half-filled (and fully-filled) subshells arises from symmetry and exchange energy, both of which reduce overall system energy.

---

📘 Concept Recap

• Hund’s Rule ensures maximum number of unpaired electrons with parallel spins.

• Exchange energy (Eₑₓ) ∝ number of possible electron exchanges → more unpaired electrons → more stability.

• Symmetry = lower repulsion + uniform charge distribution.

$$\boxed{\text{Extra stability of half-filled subshells is due to (A), (C), and (D)}}$$