Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
This chapter explains the quantum mechanical description of electrons in atoms. Understanding quantum numbers, orbital shapes, and filling rules is essential for electronic configurations, which directly underpin periodicity and bonding. NEET carries 2–3 questions from this chapter every year.
Key Concepts and Definitions
- Orbital: A region in space where the probability of finding an electron is maximum (≥90%)
- Principal quantum number (n): Defines energy level; n = 1, 2, 3, …
- Azimuthal quantum number (l): Defines subshell shape; l = 0 (s), 1 (p), 2 (d), 3 (f)
- Magnetic quantum number (mₗ): Defines orbital orientation; mₗ = −l to +l
- Spin quantum number (mₛ): +½ or −½
- Degenerate orbitals: Orbitals with equal energy (e.g., 2px, 2py, 2pz)
- Shielding effect: Inner electrons reduce nuclear attraction felt by outer electrons
Formulae
| Concept | Rule / Formula |
|---|---|
| Number of orbitals in shell n | n² |
| Max electrons in shell n | 2n² |
| Values of l for given n | 0, 1, 2, … (n−1) |
| Values of mₗ for given l | −l, …, 0, …, +l |
| Orbitals in subshell l | 2l + 1 |
| Electrons in subshell l | 2(2l + 1) |
Quantum Numbers — Summary Table
| n | l | Subshell | mₗ values | Max electrons |
|---|---|---|---|---|
| 1 | 0 | 1s | 0 | 2 |
| 2 | 0,1 | 2s, 2p | 0; −1,0,+1 | 2, 6 |
| 3 | 0,1,2 | 3s, 3p, 3d | 0; −1,0,+1; −2,−1,0,+1,+2 | 2, 6, 10 |
| 4 | 0,1,2,3 | 4s, 4p, 4d, 4f | — | 2, 6, 10, 14 |
Three Filling Rules
1. Aufbau Principle: Fill from lowest to highest energy. Use the (n + l) rule — lower sum fills first; equal sum, lower n fills first.
2. Hund's Rule: In degenerate orbitals, electrons enter singly with parallel spin before pairing.
3. Pauli Exclusion Principle: Maximum two electrons per orbital, with opposite spins.
Electronic Configurations — Key Examples
| Element | Z | Configuration |
|---|---|---|
| Na | 11 | 1s² 2s² 2p⁶ 3s¹ |
| Cl | 17 | 1s² 2s² 2p⁶ 3s² 3p⁵ |
| Ca | 20 | [Ar] 4s² |
| Cr | 24 | [Ar] 3d⁵ 4s¹ (exception) |
| Cu | 29 | [Ar] 3d¹⁰ 4s¹ (exception) |
Note: Cr and Cu have exceptional configurations due to extra stability of half-filled and fully-filled d orbitals.
Important Questions
One Mark (5)
- How many orbitals are present in the third shell?
- What is the maximum number of electrons in the 4f subshell?
- Define degenerate orbitals.
- State Pauli exclusion principle.
- Write the electronic configuration of Fe (Z = 26).
Short Answer 3-mark (3)
- Explain Hund's rule with the example of nitrogen (Z = 7).
- What are quantum numbers? List all four with their possible values.
- Why does chromium have the configuration [Ar] 3d⁵ 4s¹ instead of [Ar] 3d⁴ 4s²?
Long Answer 5-mark (2)
- State and explain the three rules for filling electrons in orbitals. Write the electronic configurations of Na, Cl, and Fe.
- Describe the shapes of s, p, and d orbitals. Explain the significance of quantum numbers in defining an electron's state.
Common Mistakes
- Writing 3d before 4s in the Aufbau order — remember (n + l) rule.
- Forgetting exceptions: Cr and Cu.
- Confusing mₗ range: it goes from −l to +l, including 0.
- Placing two electrons with same spin in one orbital (violates Pauli).
Board Exam Tips
- Electronic configuration questions appear every year — know them for the first 30 elements.
- Exceptions (Cr, Cu) are favourite NEET MCQ traps.
- Shapes of s, p, d orbitals are frequently asked as 3-mark questions.
- Practise writing box orbital diagrams to show Hund's rule visually.
Revision Checklist
- [ ] All four quantum numbers and their ranges memorised
- [ ] Aufbau order written from memory (up to 5p)
- [ ] Hund's rule explained with N, O, F examples
- [ ] Exceptions Cr and Cu noted with reason
- [ ] Electronic configurations of Z = 1 to 30 practised