CBSE Class 11 Chemistry Chapter 2 Notes: Structure of Atom

Chapter Overview

Structure of Atom is the second chapter of CBSE Class 11 Chemistry and one of the most concept-heavy chapters in the syllabus. It traces the evolution of atomic models — from Thomson's plum pudding model to Rutherford's nuclear model, Bohr's quantized orbits, and finally the quantum mechanical model. You will learn about subatomic particles, quantum numbers, electronic configurations, and the dual nature of matter.

This chapter connects directly to periodic properties (Chapter 3) and chemical bonding (Chapter 4). Master the quantum numbers and electronic configurations, and those chapters become much easier.

1. Discovery of Subatomic Particles

1.1 Discovery of the Electron (Cathode Rays)

J.J. Thomson (1897) discovered the electron through cathode ray tube experiments:

• Cathode rays travel in straight lines from cathode to anode.
• They cause fluorescence on striking the glass wall.
• They are deflected by electric and magnetic fields — indicating they carry negative charge.
• The charge-to-mass ratio (e/m) of the electron was determined:

This ratio is independent of the gas in the tube and the electrode material, proving electrons are universal constituents of all atoms.

1.2 Charge on the Electron

Millikan's oil drop experiment (1909) measured the charge on a single electron:

Using e and e/m, the mass of the electron:

1.3 Discovery of the Proton

Goldstein (1886) discovered canal rays (positive rays) using a perforated cathode. The lightest positive particle was the proton:

1.4 Discovery of the Neutron

Chadwick (1932) discovered the neutron by bombarding beryllium with alpha particles:

2. Atomic Models

2.1 Thomson's Model (Plum Pudding / Raisin Bun Model, 1898)

• The atom is a sphere of positive charge with electrons embedded like seeds in a watermelon.
• Total positive charge equals total negative charge, making the atom neutral.
• Limitation: Could not explain the results of Rutherford's alpha scattering experiment.

2.2 Rutherford's Nuclear Model (1911)

Alpha scattering experiment:

• A beam of alpha particles (He²⁺) was directed at a thin gold foil.
• Most alpha particles passed through undeflected.
• Some were deflected at small angles.
• A very few (1 in 8000) were deflected by more than 90° — some bounced back.

Conclusions: 1. Most of the atom is empty space (most alpha particles passed through). 2. The positive charge and most of the mass are concentrated in a very small region called the nucleus. 3. The volume of the nucleus is negligible compared to the volume of the atom. 4. Electrons revolve around the nucleus in circular paths.

Limitations of Rutherford's model:

• According to classical electromagnetic theory, an accelerating charged particle (electron) must radiate energy. This would cause the electron to spiral into the nucleus, making atoms unstable.
• It could not explain the line spectrum of hydrogen.

2.3 Developments Leading to Bohr's Model

Electromagnetic radiation:

• Consists of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.
• Characterized by wavelength (λ), frequency (ν), and speed (c = 3 × 10⁸ m s⁻¹).

Electromagnetic spectrum:

Hydrogen spectrum: When hydrogen gas is excited in a discharge tube, it emits light that produces a line spectrum (not continuous). The lines appear in series:

Rydberg constant: R = 1.097 × 10⁷ m⁻¹

3. Bohr's Model of the Hydrogen Atom (1913)

Postulates

1. Quantized orbits: Electrons revolve in certain fixed circular paths called orbits (or stationary states) without radiating energy. 2. Energy quantization: Each orbit has a definite energy. An electron in an orbit does not radiate energy. 3. Quantum condition: The angular momentum of an electron in a permitted orbit is quantized:

4. Radiation condition: Energy is emitted or absorbed only when an electron jumps from one orbit to another:

Key Results of Bohr's Model

Radius of nth orbit:

Energy of nth orbit:

Velocity of electron in nth orbit:

Limitations of Bohr's model:

• Could not explain the spectrum of atoms with more than one electron (multi-electron atoms).
• Could not explain the fine structure of spectral lines (splitting due to spin).
• Could not explain the Zeeman effect (splitting in a magnetic field) and Stark effect (splitting in an electric field).
• Violates Heisenberg's uncertainty principle (assumes both position and momentum of an electron are known simultaneously).

4. Dual Nature of Matter and Radiation

de Broglie Wavelength (1924)

Louis de Broglie proposed that matter, like radiation, has a dual nature (wave-particle duality):

Key points:

• The de Broglie wavelength is significant only for particles with very small mass (like electrons). For macroscopic objects, the wavelength is negligibly small.
• Davisson and Germer (1927) experimentally confirmed de Broglie's hypothesis by observing electron diffraction.

Relation between de Broglie wavelength and kinetic energy:

Heisenberg's Uncertainty Principle (1927)

It is impossible to determine simultaneously the exact position and exact momentum (or velocity) of an electron.

Significance: This principle means that Bohr's concept of definite orbits is not physically meaningful. We can only talk about the probability of finding an electron in a region of space.

5. Quantum Mechanical Model of the Atom

The quantum mechanical model uses Schrodinger's wave equation to describe electrons as probability clouds (orbitals) rather than fixed orbits.

5.1 Quantum Numbers

Each electron in an atom is described by four quantum numbers:

Subshell notation:

Total orbitals in shell n = n² Total electrons in shell n = 2n²

5.2 Shapes of Orbitals

• s orbitals: Spherically symmetric; probability depends only on distance from nucleus. 1s has no node; 2s has 1 radial node; ns has (n-1) radial nodes.
• p orbitals: Dumbbell-shaped; three orientations (px, py, pz). Each p orbital has a nodal plane passing through the nucleus.
• d orbitals: Five orientations. Four are clover-shaped (dxy, dyz, dxz, dx²-y²); one is doughnut-shaped (dz²). Two nodal planes each.
• f orbitals: Seven orientations, complex shapes with three nodal planes.

Node: A point/surface where the probability of finding the electron is zero.

• Total nodes = n - 1
• Radial nodes = n - l - 1
• Angular nodes = l

5.3 Rules for Filling Electrons in Orbitals

Aufbau Principle: Electrons fill orbitals in order of increasing energy. The order is:

Energy of an orbital ≈ n + l (lower n+l fills first; if n+l is equal, lower n fills first).

Hund's Rule of Maximum Multiplicity: In degenerate orbitals (same energy), electrons occupy singly with parallel spins before pairing.

• Correct: N (Z=7): 1s² 2s² 2pₓ¹ 2pᵧ¹ 2pz¹ (three unpaired electrons)
• Incorrect: pairing electrons in the same orbital before each has one

Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. This means each orbital can hold a maximum of 2 electrons, with opposite spins.

5.4 Electronic Configuration of Elements

Electronic configurations of the first 30 elements:

Exceptions to the Aufbau principle:

• Cr (Z=24): [Ar] 3d⁵ 4s¹ (not 3d⁴ 4s²) — half-filled d-subshell is more stable
• Cu (Z=29): [Ar] 3d¹⁰ 4s¹ (not 3d⁹ 4s²) — completely filled d-subshell is more stable

6. Stability of Half-Filled and Fully-Filled Orbitals

Half-filled (d⁵) and fully-filled (d¹⁰) subshells have extra stability due to: 1. Symmetry: Half-filled and fully-filled orbitals have symmetrical distribution of electrons, which lowers energy. 2. Exchange energy: Electrons with parallel spins in degenerate orbitals can exchange positions. The number of exchanges (and thus exchange energy stabilization) is maximum for half-filled configurations.

7. Important Definitions

8. Common Mistakes to Avoid

1. Confusing orbit with orbital — An orbit is a 2D path (Bohr model); an orbital is a 3D probability cloud (quantum mechanical model). 2. Writing electronic configurations without considering exceptions — Cr is [Ar] 3d⁵ 4s¹, not 3d⁴ 4s²; Cu is [Ar] 3d¹⁰ 4s¹, not 3d⁹ 4s². 3. Forgetting that 4s fills before 3d — The filling order follows n+l rule, so 4s (n+l=4) fills before 3d (n+l=5). 4. Writing ml values incorrectly — ml ranges from -l to +l, not 0 to l. For p orbital (l=1): ml = -1, 0, +1. 5. Counting nodes incorrectly — Total nodes = n-1, radial nodes = n-l-1, angular nodes = l. For 3p: total = 2, radial = 1, angular = 1. 6. Applying Bohr's model to multi-electron atoms — Bohr's model only works for hydrogen-like species (H, He⁺, Li²⁺). 7. Confusing spectral series — Lyman (UV, n₁=1), Balmer (visible, n₁=2), Paschen (IR, n₁=3). Memorize these. 8. Writing quantum numbers for electrons that violate Pauli's principle — Two electrons in the same orbital must have opposite spins (ms = +½ and -½).

9. Exam Tips

• For quantum number questions: First determine n, then l (0 to n-1), then ml (-l to +l), then ms (±½). Always check that the set is valid.
• For electronic configuration questions: Use noble gas abbreviation for elements beyond Ne. Watch for Cr and Cu exceptions.
• For Bohr model numericals: Use Eₙ = -13.6/n² eV for energy levels. The negative sign indicates the electron is bound to the nucleus.
• For de Broglie wavelength problems: Remember λ = h/mv. Convert mass to kg and velocity to m s⁻¹ before calculating.
• Common 1-mark questions: Define each quantum number, state Pauli exclusion principle, name the spectral series, give the charge and mass of an electron.
• Common 3-mark questions: Write electronic configurations of given elements (including exceptions), explain Bohr's postulates, differentiate between orbit and orbital.
• Common 5-mark questions: Explain Rutherford's experiment and conclusions, derive Bohr's quantization condition, write electronic configurations of first 20 elements with exceptions.

10. Quick Revision Notes

• Electron: e/m = 1.758820 × 10¹¹ C kg⁻¹; e = 1.602 × 10⁻¹⁹ C; mₑ = 9.109 × 10⁻³¹ kg
• Proton mass ≈ 1836 × electron mass; neutron mass ≈ proton mass
• Thomson model: positive sphere with embedded electrons; could not explain alpha scattering
• Rutherford model: dense positive nucleus + orbiting electrons; could not explain stability or line spectra
• Bohr model: quantized orbits; Eₙ = -13.6/n² eV; applies only to H-like species
• Hydrogen spectrum: Lyman (UV), Balmer (visible), Paschen (IR), Brackett (IR), Pfund (IR)
• de Broglie: λ = h/mv; confirmed by Davisson-Germer experiment
• Heisenberg: Δx × Δp ≥ h/4π
• Quantum numbers: n (shell), l (subshell), ml (orientation), ms (spin)
• Orbital capacity: s=2, p=6, d=10, f=14; Shell capacity: 2n²
• Nodes: total = n-1, radial = n-l-1, angular = l
• Filling order: Aufbau (n+l rule), Hund's rule, Pauli exclusion principle
• Exceptions: Cr [Ar]3d⁵4s¹, Cu [Ar]3d¹⁰4s¹
• Stability: half-filled (d⁵) and fully-filled (d¹⁰) subshells are extra stable

11. Practice Questions

1. Write the four quantum numbers for the 19th electron of potassium (Z=19). 2. How many radial nodes and angular nodes does a 4d orbital have? 3. Calculate the de Broglie wavelength of an electron moving at 1% of the speed of light. (mₑ = 9.1 × 10⁻³¹ kg, c = 3 × 10⁸ m s⁻¹) 4. What is the energy required to remove an electron from the n=2 level of a hydrogen atom? 5. Write the electronic configuration of Cr (Z=24) and explain why it is an exception. 6. Which quantum number determines (a) the size of the orbital (b) the shape of the orbital (c) the orientation of the orbital? 7. Calculate the number of electrons in the 3rd shell of an atom using the 2n² rule. 8. State Heisenberg's uncertainty principle and its significance. 9. An electron is in a 3d orbital. What are the possible values of (a) n (b) l (c) ml? 10. Write the electronic configurations of Fe²⁺ and Cu⁺.

Quick Answers to Practice Questions

1. 19th electron: n=4, l=0, ml=0, ms=+½ (it is the 4s¹ electron) 2. 4d: radial nodes = 4-2-1 = 1; angular nodes = l = 2 3. v = 3 × 10⁶ m s⁻¹; λ = 6.626 × 10⁻³⁴ / (9.1 × 10⁻³¹ × 3 × 10⁶) = 2.426 × 10⁻¹⁰ m = 2.426 Å 4. E₂ = -13.6/4 = -3.4 eV; Energy required = 3.4 eV 5. Cr: [Ar] 3d⁵ 4s¹ — half-filled d-subshell (3d⁵) gives extra stability due to symmetrical distribution and exchange energy 6. (a) Principal quantum number (n) (b) Azimuthal quantum number (l) (c) Magnetic quantum number (ml) 7. 2n² = 2(3)² = 18 electrons 8. It is impossible to simultaneously determine the exact position and exact momentum of an electron. Significance: We cannot define definite paths (orbits) for electrons; we can only describe probability regions (orbitals). 9. 3d orbital: n=3, l=2, ml = -2, -1, 0, +1, +2 10. Fe²⁺ (24 electrons): [Ar] 3d⁶; Cu⁺ (28 electrons): [Ar] 3d¹⁰

12. Final Revision Checklist

Before the exam, make sure you can:

• Describe Thomson's, Rutherford's, and Bohr's atomic models with their limitations
• Explain the alpha scattering experiment and its conclusions
• Write and interpret the four quantum numbers (n, l, ml, ms)
• Draw the shapes of s and p orbitals and describe d orbital shapes
• Write electronic configurations for elements 1-30, including Cr and Cu exceptions
• Calculate de Broglie wavelength and apply the uncertainty principle
• Identify spectral series (Lyman, Balmer, Paschen) and their regions
• Calculate energy, radius, and velocity for Bohr orbits
• Differentiate between orbit and orbital, isotopes and isobars
• Explain the stability of half-filled and fully-filled subshells