Complete Summary and Solutions for Atoms – NCERT Class XII Physics Part II, Chapter 12 – Atomic Models, Nuclear Structure, and Atomic Properties

Full Chapter Summary & Detailed Notes - Atoms Class 12 NCERT

Overview & Key Concepts

Chapter Goal: Understand atomic structure evolution: Thomson, Rutherford, Bohr models; spectra, quantization. Exam Focus: Models, derivations for energy/radius, spectra series; 2025 Updates: Quantum links, applications (lasers, LEDs). Fun Fact: Bohr model 1913. Core Idea: Quantized orbits explain spectra. Real-World: Hydrogen lamps, quantum tech. Expanded: All subtopics point-wise with evidence (e.g., Fig 12.1 scattering), examples (e.g., Balmer lines), debates (classical vs quantum).
Wider Scope: From atomic hypothesis to de Broglie; sources: Text, figures (12.1-12.8), examples.
Expanded Content: Include calculations, graphs; links (e.g., to waves Ch11); point-wise breakdown.

12.1 Introduction

Summary in Points: Atomic hypothesis by 19th C; Thomson 1897: Electrons in atoms. Neutral: Positive charge balances. Thomson model 1898: Plum pudding (uniform +ve with e- embedded). Fails: Later studies show different distribution. Blackbody: Continuous spectra solids/liquids; line spectra rarefied gases (individual atoms). Element-specific spectra; Balmer 1885: H lines formula. Rutherford: Alpha scattering probes structure.
Phenomena: Continuous vs discrete; hydrogen simplest.
Expanded: Evidence: Neon signs; debates: Plum pudding vs nuclear; real: Flame tests.

Conceptual Diagram: Plum Pudding Model

Uniform +ve sphere with e- like plums; vs actual nuclear.

12.2 Alpha-Particle Scattering & Rutherford’s Nuclear Model

Summary in Points: Geiger-Marsden 1911: Alpha beam on gold foil; most pass undeflected (0.14% >1° scatter, 1/8000 >90°). Rutherford: Large deflections imply concentrated +ve mass (nucleus). Size: Nucleus 10^{-15}-10^{-14}m; atom 10^{-10}m (empty space). Trajectory: Coulomb repulsion; impact parameter b small → large θ. Head-on: Rebounds.
Model: Nucleus (+ve, massive); e- orbit like planets. Limitations: Unstable (radiates), continuous spectra.
Expanded: Evidence: Fig 12.3 data vs theory; debates: Stability; real: Nuclear size estimates.

Diagram: Geiger-Marsden Setup

Alpha source, gold foil, ZnS screen; scattering angles.

12.3 Atomic Spectra

Summary in Points: Emission: Bright lines (excited gas); absorption: Dark lines (continuous through gas). H spectrum: Balmer series (visible). Fingerprint for elements.
Expanded: Evidence: Fig 12.5 H lines; debates: Continuous vs discrete; real: Spectroscopy ID.

12.4 Bohr Model of Hydrogen Atom

Summary in Points: Fixes Rutherford: Postulates - Stable orbits (no radiation), L=nh/2π, transitions emit hν=E_i-E_f. Radius r_n = n² h² ε_0 / (π m e²); E_n = -13.6 / n² eV. Ground n=1: -13.6 eV (ionization 13.6 eV).
Energy Levels: n=1 lowest; excited higher, closer spacing.
Expanded: Evidence: Matches ionization; debates: Semiclassical; real: H lamp spectra.

Diagram: Energy Levels

Horizontal lines n=1 to ∞; ionization at 0 eV.

12.5 Line Spectra of Hydrogen

Summary in Points: Transitions: hν = E_i - E_f; series (Lyman UV, Balmer visible, Paschen IR). Explains discrete lines.
Expanded: Evidence: Balmer formula; debates: Intensities; real: Astronomical spectra.

12.6 de Broglie’s Explanation of Bohr’s Quantisation

Summary in Points: Electron wave: Standing waves 2π r_n = n λ; λ=h/p → L= n h/2π. Explains quantization via waves.
Limitations: H only; no intensities; multi-e- fails.
Expanded: Evidence: Davisson-Germer; debates: Wave-particle; real: Electron diffraction.

Diagram: Standing Wave Orbit

Circular path with n=4 wavelengths fitting circumference.

Key Themes & Tips

Aspects: Models evolution, quantization, spectra.
Tip: Derive E_n, r_n; memorize series; differentiate models.

Project & Group Ideas

Model atomic spectra with discharge tube.
Debate: Classical vs quantum stability.
Simulate Rutherford scattering.

Key Definitions & Terms - Complete Glossary

All terms from chapter; detailed with examples, relevance. Expanded: 30+ terms grouped by subtopic; added advanced like "stationary state", "principal quantum number".

Plum Pudding Model

Thomson: Uniform +ve with embedded e-. Ex: Watermelon seeds. Relevance: Early uniform idea, failed scattering.

Nucleus

Rutherford: Tiny +ve massive core. Ex: Gold Z=79. Relevance: Atomic center.

Impact Parameter

Perp distance initial velocity to nucleus. Ex: Small b → large scatter. Relevance: Trajectory determinant.

Stationary State

Bohr: Stable orbit no radiation. Ex: n=1 ground. Relevance: Quantized energy.

Principal Quantum Number

n: Orbit label. Ex: n=1,2,... Relevance: Energy/radius scaler.

Quantization

Discrete values (L=nh/2π). Ex: Angular momentum. Relevance: Explains spectra.

Excited State

n>1, higher energy. Ex: n=2, -3.4 eV. Relevance: Transitions emit light.

Ionization Energy

Energy to remove e- (13.6 eV H). Ex: Ground state. Relevance: Binding measure.

Emission Line Spectrum

Bright lines on dark. Ex: H Balmer. Relevance: Atomic fingerprint.

Absorption Spectrum

Dark lines in continuous. Ex: Solar Fraunhofer. Relevance: Gas absorption.

de Broglie Wavelength

λ=h/p for particles. Ex: Electron waves. Relevance: Standing orbits.

Hydrogenic Atom

One e-, +Ze nucleus. Ex: He+. Relevance: Bohr applies.

Tip: Group by model (Thomson/Rutherford/Bohr); examples for recall. Depth: Debates (e.g., stability). Errors: Confuse n and l. Interlinks: To waves Ch11. Advanced: Balmer formula. Real-Life: LEDs. Graphs: E vs n. Coherent: Evidence → Interpretation. For easy learning: Flashcard per term with example.

Key Formulas - All Important Equations

List of all formulas from chapter; grouped, with units/explanations.

Formula	Description	Units/Example
F = (1/(4πε₀)) (2e)(Ze)/r²	Coulomb repulsion alpha-gold	N; r in m
d = (1/(4πε₀)) (2Ze²)/K	Closest approach	m; K kinetic energy
Fe = Fc: (1/(4πε₀)) e²/r² = m v² / r	Centripetal balance	For orbits
L = n h / 2π	Angular momentum quantization	J s; n integer
r_n = n² h² ε₀ / (π m e²)	Bohr radius	m; a₀=0.53 Å for n=1
E_n = - (m e⁴) / (8 ε₀² h² n²) = -13.6 / n² eV	Energy levels	eV
h ν = E_i - E_f	Photon emission	J; transitions
2π r_n = n λ	de Broglie standing wave	λ = h / (m v)

Tip: Memorize with derivations; practice n=1 values.

Derivations - Detailed Guide

Key derivations with steps; from PDF (e.g., Bohr radius, energy).

Bohr Radius r_n

Step 1: L = m v r = n h / 2π.
Step 2: Fe = Fc: k e² / r² = m v² / r (k=1/4πε₀).
Step 3: v = n h / (2π m r).
Step 4: Substitute: r_n = n² (h² ε₀) / (π m e²).
Depth: Quantization + balance.

Energy Levels E_n

Step 1: Total E = K + U = (1/2) m v² - k e² / r.
Step 2: From Fc: (1/2) m v² = (1/2) k e² / r.
Step 3: E = - (1/2) k e² / r.
Step 4: Substitute r_n: E_n = - (m (k e²)²) / (2 h² n²) = -13.6/n² eV.
Depth: Negative for bound.

de Broglie Quantization

Step 1: Standing wave: 2π r = n λ.
Step 2: λ = h / p = h / (m v).
Step 3: 2π r m v = n h.
Step 4: m v r = n h / 2π = L quantized.
Depth: Wave nature explains postulate.

Tip: Step proofs; examples apply. Depth: Assumptions (circular orbits).

Solved Examples from Textbook

All solved examples from the PDF with detailed explanations.

Example 12.1: In Rutherford’s nuclear model, nucleus ~10^{-15}m, electron orbit ~10^{-10}m. If solar system scaled to atom proportions, Earth orbit vs actual? (Earth r=1.5×10^{11}m, Sun r=7×10^8 m)

Simple Explanation: Compare emptiness.

Solution: Ratio r_e / r_n = 10^5. Scaled Earth r = 10^5 × 7×10^8 = 7×10^{13} m (>100× actual). Atom emptier than solar system.
Simple Way: Vast empty space.

Example 12.2: Distance closest approach 7.7 MeV alpha to Au nucleus?

Simple Explanation: Energy conservation to stop.

Solution: K = U at d: d = (1/4πε₀) (2 Z e²) / K. Z=79, K=1.23×10^{-12}J → d=3×10^{-14}m=30 fm. Actual nucleus smaller; no touch.
Simple Way: Potential equals kinetic.

Example 12.3: Orbital r, v for H ground state? Ionization 13.6 eV.

Simple Explanation: From E_n.

Solution: E=-13.6 eV=-2.2×10^{-18}J. r = [n² h² ε₀ / (π m e²)] n=1 → 5.3×10^{-11}m. v = e² / (2 ε₀ h) → 2.2×10^6 m/s.
Simple Way: Quantized formulas.

Example 12.4: Classical frequency revolving e- in H? r=5.3×10^{-11}m, v=2.2×10^6 m/s.

Simple Explanation: Orbital ν.

Solution: ν = v / (2π r) = 6.6×10^{15} Hz. Emitted light same classically (wrong).
Simple Way: Revolution rate.

Tip: All textbook examples covered with full details from PDF.

NCERT Textbook Exercise Questions & Solutions

All NCERT exercise questions with detailed solutions (12.1 to 12.9).

12.1 Choose correct: (a) Atom size Thomson vs Rutherford? (b) Ground state equilibrium? (c) Classical collapse? (d) Mass distribution? (e) +ve mass in?

Solution:

(a) No different. (b) Thomson stable, Rutherford net force. (c) Rutherford. (d) Thomson continuous, Rutherford non-uniform. (e) Rutherford.
Long Note: Model contrasts.

12.2 Alpha scattering on solid H foil? Expect?

Solution:

H Z=1 small repulsion; less scatter, more transmission than Au.
Long Note: Light nucleus recoils.

12.3 ΔE=2.3 eV transition frequency?

Solution:

ν = ΔE / h = 2.3×1.6×10^{-19} / (6.6×10^{-34}) ≈ 5.6×10^{14} Hz.
Long Note: Yellow light.

12.4 H ground KE, PE? E=-13.6 eV.

Solution:

KE = -E =13.6 eV; PE=2E=-27.2 eV (virial).
Long Note: |PE|=2 KE.

12.5 H ground to n=4: λ, ν photon?

Solution:

ΔE=13.6(1-1/16)=12.75 eV; ν=ΔE/h≈3.08×10^{15} Hz; λ=c/ν=97.3 nm (UV).
Long Note: Lyman series.

12.6 Bohr: v for n=1,2,3? Orbital periods.

Solution:

v_n = v_1 / n; v_1=2.2×10^6 m/s. T_n = T_1 n^3; T_1=1.5×10^{-16}s.
Long Note: Scales with n.

12.7 Innermost r=5.3×10^{-11}m; n=2,3?

Solution:

r_n = r_1 n²; n=2: 2.12×10^{-10}m; n=3: 4.77×10^{-10}m.
Long Note: Quadratic.

12.8 12.5 eV beam on H: Emitted series?

Solution:

Excites to n=3 (12.09 eV); emissions: n=3→2 (656 nm Balmer), 3→1,2→1 (Lyman).
Long Note: Below n=4 (12.75 eV).

12.9 Earth orbit quantum n? r=1.5×10^{11}m, v=3×10^4 m/s, m=6×10^{24}kg.

Solution:

n = L / (h/2π) = m v r / (h/2π) ≈ 2.5×10^{74}.
Long Note: Huge n, classical.

Tip: All 9 exercises covered with detailed point-wise solutions.

Lab Activities - Step-by-Step Guide

Related experiments (e.g., spectrometer for spectra, verify Bohr via discharge).

Activity 1: Observe H Emission Spectrum

Step-by-Step:

Step 1: H discharge tube + power supply.
Step 2: Spectrometer align.
Step 3: View lines, measure wavelengths.
Step 4: Identify Balmer (656 nm red).
Observation: Discrete lines.
Precaution: Dark room.

Activity 2: Verify Ionization Energy

Step-by-Step:

Step 1: Franck-Hertz setup (electrons on Hg).
Step 2: Vary voltage, measure current drops.
Step 3: Drops at 4.9 eV intervals.
Step 4: Extrapolate to ionization.
Observation: Quantized losses.
Precaution: Vacuum tube.

Note: PDF implies spectra observation; general for Bohr verification.

Key Concepts - In-Depth Exploration

Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls.

Atomic Models Evolution

Steps: 1. Thomson uniform, 2. Rutherford nuclear, 3. Bohr quantized. Ex: Scattering evidence. Pitfall: Forget Rutherford stability issue. Interlink: To radioactivity. Depth: Empty space.

Quantization Postulate

Steps: 1. Discrete L, 2. Stable orbits, 3. Photon emission. Ex: H lines. Pitfall: Confuse with continuous classical. Interlink: Planck Ch11. Depth: de Broglie explanation.

Line Spectra

Steps: 1. Excitation, 2. Transition, 3. hν=ΔE. Ex: Balmer visible. Pitfall: Mix emission/absorption. Interlink: Waves. Depth: Series formulas.

Advanced: Wave-particle duality. Pitfalls: n starts 1. Interlinks: Modern QM. Real: Quantum dots. Depth: 12 concepts. Examples: Numerical. Graphs: E-n. Errors: Sign of E. Tips: Derive all.

Interactive Quiz - Master Atoms

10 MCQs; 80%+ goal. Covers models, Bohr, spectra.

Quick Revision Notes & Mnemonics

Concise for all subtopics; mnemonics. Expanded to cover all subtopics for last-minute revision.

Introduction

Thomson: Plum pudding; Rutherford: Nuclear; Bohr: Quantized. Mnemonic: "Plum Nuclear Quantized Progress".

Alpha Scattering

Most undeflected; large θ rare → tiny nucleus. Mnemonic: "Few Bounce Back, Tiny Core".

Spectra

Emission bright lines; absorption dark. H: Lyman UV, Balmer vis. Mnemonic: "Lyman UltraViolet, Balmer Visible".

Bohr Postulates

1. Stable orbits; 2. L=nh/2π; 3. ΔE=hν. Mnemonic: "Stable, Quantized, Photon".

Formulas

r_n ∝ n²; E_n ∝ -1/n². Mnemonic: "Radius Squares Up, Energy Inverses Down".

de Broglie

2πr = nλ → Quantization. Mnemonic: "Wave Fits Circle Integer".

Limitations

H only; no intensities; multi-e- fails. Mnemonic: "Hydrogen Only, No Multi Intensity".

Overall Mnemonic: "Thomson Rutherford Bohr deBroglie Spectra" (TRBDS). Flashcards: One per model. Easy: Bullets, bold keys.

Key Processes & Diagrams - Step-by-Step

Expanded major; desc diags.

Process 1: Alpha Scattering

Step-by-Step:

Step 1: Collimated alpha beam.
Step 2: Hit foil, observe scintillations.
Step 3: Count vs angle.
Step 4: Large θ → repulsion from nucleus.
Step 5: Infer size.
Diagram Desc: Fig 12.2 setup with rotatable detector.

Process 2: Electron Transition

Step-by-Step:

Step 1: Absorb photon, excite n_i → n_f.
Step 2: Drop back, emit hν=ΔE.
Step 3: Line at specific λ.
Step 4: Series for fixed n_f.
Step 5: Spectrum observed.
Diagram Desc: Energy ladder with arrows.

Tip: Label diags; analogies (orbits as planets, waves as string).

Complete Summary and Solutions for Atoms – NCERT Class XII Physics Part II, Chapter 12 – Atomic Models, Nuclear Structure, and Atomic Properties

Detailed summary and explanation of Chapter 12 'Atoms' from the NCERT Class XII Physics Part II textbook, covering atomic models, structure of the nucleus, isotopes, isobars, and atomic properties, along with solved NCERT questions and answers.

Atoms

Full Chapter Summary & Detailed Notes - Atoms Class 12 NCERT

Overview & Key Concepts

12.1 Introduction

Conceptual Diagram: Plum Pudding Model

12.2 Alpha-Particle Scattering & Rutherford’s Nuclear Model

Diagram: Geiger-Marsden Setup

12.3 Atomic Spectra

12.4 Bohr Model of Hydrogen Atom

Diagram: Energy Levels

12.5 Line Spectra of Hydrogen

12.6 de Broglie’s Explanation of Bohr’s Quantisation

Diagram: Standing Wave Orbit

Key Themes & Tips

Project & Group Ideas

Key Definitions & Terms - Complete Glossary

Plum Pudding Model

Nucleus

Impact Parameter

Stationary State

Principal Quantum Number

Quantization

Excited State

Ionization Energy

Emission Line Spectrum

Absorption Spectrum

de Broglie Wavelength

Hydrogenic Atom

Key Formulas - All Important Equations

Derivations - Detailed Guide

Bohr Radius r_n

Energy Levels E_n

de Broglie Quantization

Solved Examples from Textbook

Example 12.1: In Rutherford’s nuclear model, nucleus ~10^{-15}m, electron orbit ~10^{-10}m. If solar system scaled to atom proportions, Earth orbit vs actual? (Earth r=1.5×10^{11}m, Sun r=7×10^8 m)

Example 12.2: Distance closest approach 7.7 MeV alpha to Au nucleus?

Example 12.3: Orbital r, v for H ground state? Ionization 13.6 eV.

Example 12.4: Classical frequency revolving e- in H? r=5.3×10^{-11}m, v=2.2×10^6 m/s.

NCERT Textbook Exercise Questions & Solutions

12.1 Choose correct: (a) Atom size Thomson vs Rutherford? (b) Ground state equilibrium? (c) Classical collapse? (d) Mass distribution? (e) +ve mass in?

12.2 Alpha scattering on solid H foil? Expect?

12.3 ΔE=2.3 eV transition frequency?

12.4 H ground KE, PE? E=-13.6 eV.

12.5 H ground to n=4: λ, ν photon?

12.6 Bohr: v for n=1,2,3? Orbital periods.

12.7 Innermost r=5.3×10^{-11}m; n=2,3?

12.8 12.5 eV beam on H: Emitted series?

12.9 Earth orbit quantum n? r=1.5×10^{11}m, v=3×10^4 m/s, m=6×10^{24}kg.

Lab Activities - Step-by-Step Guide

Activity 1: Observe H Emission Spectrum

Activity 2: Verify Ionization Energy

Key Concepts - In-Depth Exploration

Atomic Models Evolution

Quantization Postulate

Line Spectra

Interactive Quiz - Master Atoms

Quick Revision Notes & Mnemonics

Introduction

Alpha Scattering

Spectra

Bohr Postulates

Formulas

de Broglie

Limitations

Key Processes & Diagrams - Step-by-Step

Process 1: Alpha Scattering

Process 2: Electron Transition

Related Previous Year Questions with Hints

PYQ 1: State Bohr postulates. (CBSE 2020)

PYQ 2: Derive E_n for H. (JEE Main 2019)

PYQ 3: Why Rutherford unstable? (NEET 2018)

PYQ 4: de Broglie explain Bohr 2nd postulate? (CBSE 2017)

PYQ 5: Balmer series wavelengths? (JEE Advanced 2016)

PYQ 30: Limitations Bohr model? (CBSE 2013)

Group Discussions