Atoms and Atomic Structure — NEET Physics Notes

This topic covers the evolution of atomic models, Bohr’s theory of the hydrogen atom, spectral series, and fundamental atomic structure — an important but manageable portion of NEET Physics.

Quick Revision

• Rutherford’s Experiment: Alpha particle scattering → nuclear model of atom
• Bohr’s Postulates: Stationary orbits, angular momentum quantisation, frequency condition
• Hydrogen Spectrum: Lyman, Balmer, Paschen, Brackett, Pfund series
• Rydberg Formula: 1/λ = R(1/n₁² − 1/n₂²), R = 1.097 × 10⁷ m⁻¹
• Energy Levels: En = −13.6/n² eV for hydrogen
• de Broglie Hypothesis: λ = h/p — matter waves
• Atomic Nucleus: protons + neutrons, radius R = R₀A^(1/3)

Standard Study

Rutherford’s Atomic Model

• Gold foil experiment: most alpha particles passed through → atom is mostly empty
• Few particles deflected at large angles → presence of a dense positively charged nucleus
• Limitations: Cannot explain stability of atoms, nor the hydrogen spectrum

Thomson’s Plum Pudding Model

• Positive sphere with electrons embedded like plums in pudding
• Disproved by Rutherford’s experiment

Bohr’s Atomic Model

Postulates:

1. Electrons revolve in discrete circular orbits (stationary states) — do not radiate energy
2. Angular momentum is quantised: mvr = nh/2π
3. Radiation is emitted/absorbed when electrons transition between orbits: E = hν = E₂ − E₁

Successes:

• Explains hydrogen spectrum perfectly
• Explains ionisation energy of hydrogen
• Explains spectral series (Lyman, Balmer, etc.)

Limitations:

• Cannot explain fine spectral lines (Zeeman effect)
• Cannot explain spectral intensity variations
• Fails for multi-electron atoms

Energy Levels and Spectral Series

Hydrogen Spectrum Series:

Series	Transition (nᵢ → n_f)	Region
Lyman	nᵢ ≥ 2 → n_f = 1	UV
Balmer	nᵢ ≥ 3 → n_f = 2	Visible
Paschen	nᵢ ≥ 4 → n_f = 3	IR
Brackett	nᵢ ≥ 5 → n_f = 4	IR
Pfund	nᵢ ≥ 6 → n_f = 5	IR

Ionisation Energy of Hydrogen: 13.6 eV (ground state) Ionisation Potential: 13.6 V (first ionisation potential)

Hydrogen-like Atoms

• Species with one electron: He⁺, Li²⁺, Be³⁺
• Formula: En = −13.6 Z²/n² eV
• Radius: r = 0.529 n²/Z Å

de Broglie’s Matter Waves

• λ = h/mv = h/√(2mE)
• Applied to electron orbits: for stable orbits, circumference = nλ
• This gives the quantisation condition: mvr = nh/2π

X-rays

• Produced when high-speed electrons strike metal target
• Continuous spectrum (bremsstrahlung) + characteristic spectrum
• Duane-Hunt law: λ_min = hc/eV
• Moseley’s law: ν ∝ (Z − σ)² — frequency increases with atomic number

Deep Study

Velocity and Frequency in Bohr Orbits

• Orbital velocity: vₙ = (ke²Z)/nh = 2.18 × 10⁶ Z/n m/s
• Orbital radius: rₙ = (n²h²)/(4π²mke²Z) = 0.529 n²/Z Å
• Time period: Tₙ = (2πrₙ)/vₙ ∝ n³
• Frequency of revolution: fₙ = 1/Tₙ ∝ 1/n³

Frequency of Emitted Radiation

• ν = (me⁴)/(8ε₀²h³) × (Z²) × (1/n_f² − 1/n_i²)
• Rydberg constant for hydrogen: R = me⁴/(8ε₀²h³c) = 1.097 × 10⁷ m⁻¹

Shortest Wavelength in Hydrogen Spectrum

• Maximum energy transition: n = ∞ to n = 1
• λ_min = 1/R = 912 Å (Lyman series limit)

Atomic Radius and Nucleus Size

• Atomic radius: ~10⁻¹⁰ m (angstrom)
• Nuclear radius: ~10⁻¹⁵ m (femtometer)
• Nuclear radius formula: R = R₀A^(1/3), where R₀ ≈ 1.2 × 10⁻¹⁵ m

Bohr’s Correspondence Principle

• Quantum mechanics gives same results as classical physics for large quantum numbers (n → ∞)

Exam Tips

1. Bohr model applies ONLY to hydrogen and hydrogen-like atoms (one electron)
2. Ionisation energy: 13.6 eV for H, 54.4 eV for He⁺ (13.6 × 2²)
3. Lyman series is in UV region — Balmer series has some lines in visible range
4. For H-like atoms: energy depends on Z² and 1/n²
5. de Broglie wavelength for electron in nth orbit: λ = (2πrₙ)/n
6. Rutherford scattering: most particles go through, few deflect — nucleus is small and dense
7. Remember: 1 Å = 10⁻¹⁰ m, 1 fm = 10⁻¹⁵ m

Common Pitfalls

• Applying Bohr model to multi-electron atoms (it doesn’t work)
• Confusing spectral series and their wavelength ranges
• Forgetting to square Z when calculating energy for hydrogen-like ions
• Confusing frequency ν with wave number (1/λ)
• Not knowing that the Balmer series is the one visible in the visible spectrum

Suggested Study Order

1. Thomson and Rutherford models — experimental evidence
2. Bohr’s postulates and derivation
3. Energy levels and spectral series
4. Hydrogen-like atoms (extension of Bohr model)
5. de Broglie hypothesis and matter waves
6. X-rays and Moseley’s law
7. Nuclear size and structure