Class 11 Chemistry — Ch 4 Structure of Atom

⚡ 4.1 Subatomic Particles

Dalton's atomic theory explained laws of chemical combination but failed to explain why substances like glass, when rubbed with silk, generate electricity. Discovery of subatomic particles in the late 19th and early 20th century broke this model.

Particle	Symbol	Charge	Mass (kg)	Mass (u)	Discoverer
Electron	e⁻	−1 (−1.6022×10⁻¹⁹ C)	9.109×10⁻³¹	≈ 0 u	J. J. Thomson (1897)
Proton	p	+1 (+1.6022×10⁻¹⁹ C)	1.672×10⁻²⁷	1 u	Rutherford (1919)
Neutron	n	0	1.674×10⁻²⁷	1 u	James Chadwick (1932)

Proton + Neutron are collectively called nucleons — present in the nucleus.
Electrons are present in the extranuclear (outer) region of the atom.
Cathode ray tube (CRT) experiment by J. J. Thomson identified electrons — particles 1837 times lighter than hydrogen.
Rutherford's α-particle scattering experiment (gold foil) proved the existence of a dense, positively charged nucleus.
Chadwick identified neutrons by bombarding beryllium with α-particles from polonium.

🔢 4.2 Atomic Number & Mass Number

Atomic Number (Z) = Number of protons = Number of electrons (in neutral atom)
Mass Number (A) = Number of protons (Z) + Number of neutrons (N)
∴ N = A − Z
Representation of a nuclide: ᴬ_Z X (A = mass number on top-left, Z = atomic number on bottom-left)

A = Z + N | N = A − Z | Z = Number of protons = Number of electrons

🔸 Solved Example: Find protons, electrons and neutrons in ⁴⁰₁₈Ar

A = 40, Z = 18
Protons = 18 | Electrons = 18 | Neutrons = A − Z = 40 − 18 = 22

⚗️ 4.3 Isotopes, Isobars & Isotones IMP

Isotopes: Same atomic number (Z), different mass number (A). Same chemical properties, different physical properties. Example: ¹²C, ¹³C, ¹⁴C (all have Z = 6)
Isobars: Same mass number (A), different atomic number (Z). Different elements, different chemical properties. Example: ¹⁴C (Z=6) and ¹⁴N (Z=7)
Isotones: Same number of neutrons (N), different atomic number. Example: ¹¹B (N=6) and ¹²C (N=6)

Type	Same	Different	Example
Isotopes	Z (protons)	A, N (neutrons)	¹H, ²H, ³H
Isobars	A (mass number)	Z, N	¹⁴C and ¹⁴N
Isotones	N (neutrons)	Z, A	¹¹B and ¹²C

🔸 Solved: Two isotopes of Cl — ³⁵Cl and ³⁷Cl exist in 3:1 ratio. Find average atomic mass.

Average mass = (3×35 + 1×37) / 4 = (105 + 37) / 4 = 142/4 = 35.5 u

🏛️ 4.4 Drawbacks of Rutherford's Model

Rutherford's nuclear model is like a miniature solar system — nucleus is the sun, electrons are planets.
Drawback 1 (Instability): According to Maxwell's electromagnetic theory, revolving charged particles (electrons) must continuously emit radiation, lose energy, spiral inward, and collapse into the nucleus. But real atoms are stable — contradiction!
Drawback 2 (No electron distribution): Rutherford's model did not describe where exactly electrons are and what their energies are.
These drawbacks were overcome by Bohr's atomic model.

🌊 4.5 Wave-Particle Duality of EM Radiation & Hydrogen Spectrum

Wave nature explains diffraction and interference of light.
Particle nature explains blackbody radiation and photoelectric effect.
Resolution: light has dual behaviour — wave when propagating, particle (photon) when interacting with matter.

EM Wave Parameters:

Wavelength (λ): distance between two consecutive crests/troughs. SI unit: metre (m).
Frequency (ν): number of waves passing a point per second. SI unit: Hertz (Hz or s⁻¹).
Wavenumber (ν̄): number of wavelengths per unit length. Unit: cm⁻¹. ν̄ = 1/λ
Amplitude (A): height of the crest. A² = intensity of radiation.
Speed of light (c) = 3.0 × 10⁸ m/s (in vacuum, same for all EM radiation)

c = νλ | ν̄ = 1/λ | E = hν (Planck's equation)

Planck's quantum theory (1900): Energy of EM radiation depends on frequency, not amplitude. Smallest energy unit = quantum. E = hν where h = 6.626 × 10⁻³⁴ J·s (Planck's constant).
Photoelectric effect (Einstein, 1905): EM radiation is a stream of photons, each of energy hν. A photon has zero rest mass.

Hydrogen Emission Spectrum — Series of Lines: IMP

Series	n₁	n₂	Spectral Region
Lyman	1	2, 3, …	Ultraviolet
Balmer	2	3, 4, …	Visible
Paschen	3	4, 5, …	Infrared
Brackett	4	5, 6, …	Infrared
Pfund	5	6, 7, …	Infrared

Rydberg Equation: ν̄ = 109677 [ 1/n₁² − 1/n₂² ] cm⁻¹ (Rydberg constant R_H = 109677 cm⁻¹)

🔵 4.6 Bohr's Model for Hydrogen Atom IMP

Postulates of Bohr's Theory:

Postulate 1: Electron revolves around nucleus in certain fixed circular paths (orbits) of fixed radius and energy — called stationary states or allowed energy states.
Postulate 2: Energy of electron in an orbit does not change with time. Electron jumps from lower to higher orbit by absorbing energy; emits radiation while moving from higher to lower orbit.
Postulate 3 (Bohr's Frequency Rule): Frequency of radiation absorbed/emitted = ΔE/h where ΔE = E₂ − E₁.
Postulate 4: Angular momentum of electron is quantized: mvr = n(h/2π), where n = 1, 2, 3…

Results of Bohr's Theory:

Radius of nth orbit: rₙ = n²a₀ (a₀ = 52.9 pm, Bohr radius)
Energy of nth orbit: Eₙ = −R_H (1/n²) where R_H = 2.18 × 10⁻¹⁸ J
For hydrogen-like species: Eₙ = −2.18×10⁻¹⁸ (Z²/n²) J | rₙ = 52.9(n²/Z) pm
Angular momentum: mvr = n × h/2π

Ground state (n=1): E₁ = −2.18 × 10⁻¹⁸ J (lowest energy, most stable)
Negative energy sign means electron energy in atom is lower than a free electron at rest (E = 0).
Bohr's theory applies to hydrogen and hydrogen-like species (one extranuclear electron): H, He⁺, Li²⁺, Be³⁺

🔸 Solved: Wavelength of photon emitted during transition from n=5 to n=2 in H-atom?

ν̄ = 109677 [1/2² − 1/5²] = 109677 [1/4 − 1/25] = 109677 × 21/100 = 23032.17 cm⁻¹
λ = 1/ν̄ = 4.34 × 10⁻⁵ cm = 434 nm (Balmer series, visible blue-violet light)

Limitations of Bohr's Model:

Could not explain finer details (fine structure) of hydrogen spectrum.
Could not explain spectra of multi-electron atoms.
Could not explain Zeeman effect (magnetic field) and Stark effect (electric field).
Could not explain ability of atoms to form chemical bonds.

🔬 4.7 Quantum Mechanical Model of Atom IMP

Two developments that led to this model:

de Broglie's dual behaviour of matter (1924): Matter (electrons) should exhibit both particle and wave properties. de Broglie relation: λ = h/mv = h/p
Heisenberg's Uncertainty Principle (1927): "It is impossible to simultaneously determine the exact position and exact momentum of an electron." Mathematically: Δx × Δpₓ ≥ h/4π

de Broglie: λ = h/mv = h/p
Heisenberg: Δx × Δpₓ ≥ h/4π (Δx = uncertainty in position, Δpₓ = uncertainty in momentum)

Quantum Mechanics (1926): developed by Werner Heisenberg and Erwin Schrödinger.
Schrödinger Wave Equation: Ĥψ = Eψ, where Ĥ = Hamiltonian operator, ψ = wave function, E = total energy.
ψ itself has no physical meaning. ψ² = probability density of finding electron at a point.

Four Quantum Numbers: IMP

Quantum Number	Symbol	Values	Describes
Principal	n	1, 2, 3, 4 …	Shell / size / energy of orbit
Azimuthal	l	0 to (n−1)	Subshell / shape of orbital
Magnetic	m_l	−l to +l	Orientation of orbital in space
Spin	m_s	+½ or −½	Spin of electron (↑ or ↓)

Subshells and Orbital Shapes:

l = 0 → s subshell (1 orbital) — spherical shape
l = 1 → p subshell (3 orbitals: p_x, p_y, p_z) — dumbbell shape
l = 2 → d subshell (5 orbitals: d_xy, d_yz, d_xz, d_x²-y², d_z²) — double dumbbell / cloverleaf
l = 3 → f subshell (7 orbitals) — complex shape
Number of orbitals in shell n = n²; maximum electrons in shell = 2n²

Aufbau Principle — Rules for filling electrons:

Increasing energy order (n+l rule): Lower (n+l) = lower energy. If same (n+l), lower n has lower energy. Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p …
Pauli's Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers. Maximum 2 electrons per orbital with opposite spins.
Hund's Rule of Maximum Multiplicity: Electrons fill each orbital of a subshell singly first (each with same spin), then pairing begins. Half-filled and fully-filled sets of degenerate orbitals have extra stability.

Special Cases — Cr and Cu:

Chromium (Z=24): Expected [Ar] 4s² 3d⁴ → Actual [Ar] 4s¹ 3d⁵ (half-filled 3d has extra stability)
Copper (Z=29): Expected [Ar] 4s² 3d⁹ → Actual [Ar] 4s¹ 3d¹⁰ (fully-filled 3d has extra stability)

Isoelectronic Species:

Atoms/ions with same number of electrons are called isoelectronic.
Example: Na⁺, Mg²⁺, Al³⁺, Ne, F⁻, O²⁻ — all have 10 electrons, config: 1s² 2s² 2p⁶
K⁺, Ar, Ca²⁺, Cl⁻ — all have 18 electrons, config: 1s² 2s² 2p⁶ 3s² 3p⁶

📋 Quick Reference — All Key Formulas

Mass NumberA = Z + N

Speed of Lightc = νλ = 3×10⁸ m/s

Planck's EnergyE = hν; h = 6.626×10⁻³⁴ J·s

Rydberg Equationν̄ = 109677[1/n₁²−1/n₂²] cm⁻¹

Bohr Radiusrₙ = n² × 52.9 pm

Bohr EnergyEₙ = −2.18×10⁻¹⁸/n² J

Angular Momentummvr = nh/2π

de Broglieλ = h/mv = h/p

HeisenbergΔx·Δp ≥ h/4π

Max e⁻ in shell2n² (K=2, L=8, M=18, N=32)

Orbitals in shelln² (K=1, L=4, M=9, N=16)

Orbitals in subshell2l+1 (s=1, p=3, d=5, f=7)

✅ Important 2-Mark Questions & Answers

Q1. What are isotopes? Give two examples.

Atoms of the same element having the same atomic number (Z) but different mass numbers (A) are called isotopes. They have the same chemical properties but different physical properties.
Examples: (1) ¹²C and ¹⁴C (both Z=6) (2) ¹H (protium) and ²H (deuterium) (both Z=1)

Q2. Define isobars and give one example.

Atoms of different elements having the same mass number (A) but different atomic numbers (Z) are called isobars. They are different elements with different chemical properties.
Example: ¹⁴C (Z=6) and ¹⁴N (Z=7) — both have A=14.

Q3. State Heisenberg's Uncertainty Principle.

It is impossible to determine simultaneously the exact position and the exact momentum (or velocity) of an electron. Mathematically: Δx × Δpₓ ≥ h/4π, where Δx = uncertainty in position and Δpₓ = uncertainty in momentum.

Q4. What is the significance of ψ² in quantum mechanics?

ψ (wave function) itself has no physical meaning. ψ² at any point in an atom represents the probability density of finding the electron at that point. Higher the ψ², higher the probability of finding the electron there.

Q5. State Pauli's exclusion principle.

No two electrons in the same atom can have the same set of all four quantum numbers (n, l, m_l, m_s). This means an orbital can accommodate at most two electrons, and they must have opposite spins (+½ and −½).

Q6. What is de Broglie's relation? What does it mean?

de Broglie proposed that matter, like light, exhibits dual behaviour. The wavelength of a material particle is: λ = h/mv = h/p. This means electrons (and all matter) have both particle properties (momentum) and wave properties (wavelength).

Q7. Name the four quantum numbers and what each describes.

(1) Principal quantum number (n): identifies shell, size and energy. (2) Azimuthal quantum number (l): identifies subshell and shape of orbital. (3) Magnetic quantum number (m_l): identifies orientation of orbital. (4) Spin quantum number (m_s): identifies spin state of electron (+½ or −½).

Q8. Give two drawbacks of Rutherford's atomic model.

(1) Instability: According to Maxwell's theory, revolving electrons should radiate energy continuously, slow down, spiral into the nucleus and the atom should collapse. But real atoms are stable. (2) No electron distribution: The model did not describe how electrons are distributed around the nucleus or their energies.

Q9. What is Hund's rule of maximum multiplicity?

Pairing of electrons in orbitals belonging to the same subshell (degenerate orbitals) does not occur unless each orbital has got one electron. Electrons enter each orbital singly with the same spin before any pairing takes place. Half-filled and fully-filled subshells have extra stability.

Q10. What are isoelectronic species? Give an example.

Atoms and ions having the same number of electrons are called isoelectronic species. They have the same electronic configuration.
Example: Na⁺ (10 e⁻), Mg²⁺ (10 e⁻), Al³⁺ (10 e⁻), Ne (10 e⁻), O²⁻ (10 e⁻) — all isoelectronic with configuration 1s² 2s² 2p⁶.

✅ Important 3-Mark Questions & Answers

Q1. State the four postulates of Bohr's atomic model.

(1) Electrons revolve around the nucleus in fixed circular paths of fixed radius and energy called stationary states or allowed energy states, arranged concentrically in increasing order of energy.
(2) Energy of an electron in an orbit does not change with time. It absorbs energy to jump to a higher orbit and emits radiation when it falls to a lower orbit. Energy change is not continuous.
(3) Bohr's Frequency Rule: Frequency of radiation absorbed/emitted = ΔE/h = (E₂ − E₁)/h.
(4) Angular momentum of electron is quantized: mvr = n × h/2π, where n = 1, 2, 3...

Q2. Explain the Aufbau principle with its three bases.

Aufbau (German for "building up") principle states that electrons are filled in orbitals in the ground state of an atom in increasing order of energy. It is based on:
(i) Increasing order of orbital energies (decided by n+l rule): 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p …
(ii) Pauli's exclusion principle: maximum 2 electrons per orbital, with opposite spins.
(iii) Hund's rule: electrons fill each orbital of a subshell singly before pairing.

Q3. Explain anomalous electronic configurations of Cr and Cu.

Chromium (Z=24): Expected config: [Ar] 4s² 3d⁴. But 3d is not half-filled in this case. Due to interelectronic repulsion, one 4s electron shifts to 3d, making both half-filled: Actual config = [Ar] 4s¹ 3d⁵. Half-filled orbitals have extra stability due to symmetrical distribution and maximum exchange energy.

Copper (Z=29): Expected config: [Ar] 4s² 3d⁹. Neither half-filled nor fully-filled 3d. Due to repulsion, one 4s electron shifts to 3d, making it fully-filled: Actual config = [Ar] 4s¹ 3d¹⁰. Fully-filled 3d has extra stability.

Q4. Explain wave-particle duality of electromagnetic radiation with examples.

Electromagnetic radiation exhibits two types of behaviour depending on the context:
Wave nature: Explains phenomena like diffraction and interference of light. Parameters: wavelength (λ), frequency (ν), amplitude (A). Relation: c = νλ.
Particle nature: Explains blackbody radiation and photoelectric effect. Light is considered a stream of particles called photons, each having energy E = hν (Planck). Einstein used this to explain photoelectric effect.
Since both natures are needed to explain all observations, light has dual behaviour. It behaves as a wave when propagating and as a particle when interacting with matter.

Q5. Write the electronic configuration of Fe, Fe²⁺, Fe³⁺.

Fe (Z=26): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s² or [Ar] 4s² 3d⁶
Fe²⁺ (removes 2 electrons from 4s first): [Ar] 3d⁶
Fe³⁺ (removes 3 electrons — 2 from 4s, 1 from 3d): [Ar] 3d⁵
Note: Fe³⁺ has extra stability due to half-filled 3d⁵ configuration.

⚛️ Chapter 4 — Structure of Atom