Atomic Models

• Rutherford model — nuclear atom, limitations due to classical radiation.
• Bohr model postulates for hydrogen: stationary orbits, angular momentum quantization, transition radiation.
• Energy levels E_n = −13.6/n² eV and Rydberg formula for spectral lines.
• Radius r_n ∝ n²/Z and velocity v_n ∝ Z/n for hydrogen-like species.
• Successes and failures of Bohr model — NCERT + JEE spectral line problems.

Level 1 — Foundations

Verbal: Atomic models describe how electrons occupy atoms. Bohr's model quantizes electron orbits in hydrogen, explaining discrete spectral lines.

Rutherford: Small dense nucleus; electrons orbit classically — predicts unstable atom (radiation problem).

Bohr postulates (H atom):

1. Electrons revolve in certain discrete orbits without radiating.
2. L = mvr = nh/(2π), n = 1, 2, 3…
3. Transition between orbits emits/absorbs photon hν = ΔE.

Ground state: n = 1, E₁ = −13.6 eV for hydrogen.

Level 2 — JEE / NEET depth

Energy levels: E_n = −(13.6 eV) Z²/n² for hydrogen-like ion (single electron).

Radius: r_n = (0.529 Å) n²/Z — Bohr radius a₀ ≈ 0.529 Å for H, n=1.

Series (H spectrum):

Rydberg: 1/λ = R(1/n_f² − 1/n_i²), R ≈ 1.097×10⁷ m⁻¹.

Limitations: Fails for multi-electron fine structure; superseded by quantum mechanics but formulas remain exam-critical.

Ionization energy: Energy to remove electron from ground state = 13.6 eV (H).

Excitation: Electron jumps to higher n by absorbing photon of exact ΔE (or collision energy).

Balmer series wavelength

Electron drops n=3 → n=2 in hydrogen. Find λ.

Step 1 — 1/λ = R(1/4 − 1/9) = R(5/36).
Step 2 — λ = 36/(5R) = 36/(5 × 1.097×10⁷) ≈ 656 nm.
Step 3 — Red H-alpha line in visible spectrum.
Step 4 — ΔE = hc/λ ≈ 1.89 eV between levels.

Energy of ionized hydrogen electron

How much energy to remove electron from n=2 state?

Step 1 — E_2 = −13.6/4 = −3.4 eV.
Step 2 — Ionization from n=2 → n=∞: need +3.4 eV.
Step 3 — Less than ground-state ionization (13.6 eV) — excited states easier to ionize.
Step 4 — Subsequent photon energies follow Rydberg for transitions to n=2 etc.

• State Bohr's three postulates.
• Write E_n for hydrogen.
• Which series lies in visible region?
• Find radius ratio r_3 : r_1.
• Stretch: Derive v₁ for electron in first Bohr orbit of hydrogen.

NCERT Chapter 12 link: Bohr model quantises angular momentum for hydrogen only — do not over-apply to multi-electron atoms without Z correction. Energy levels En = −13.6 Z²/n² eV for hydrogen-like species.

Exam connections: Rydberg formula for spectral lines — identify series by final n (Lyman n=1, Balmer n=2). Calculate radius, velocity, energy for n=1 ground state comparisons. Limitations of Bohr model (fine structure, Zeeman) — one-line each for descriptive questions.

Study strategy: Draw energy level diagram with transitions as arrows — downward emission, upward absorption. Remember negative total energy means bound state. Ionisation energy equals negative of level energy.

When studying Atomic Models within Modern Physics, start by listing every formula and definition on one page without looking at the textbook. Compare your list to NCERT — missing items indicate gaps to fix immediately. Work through at least two NCERT Examples for this section with steps written in full; examiners award method marks even when arithmetic slips.

For board exams (CBSE), long answers benefit from a clear structure: definition → explanation → diagram or formula → example → brief conclusion. Underline key terms. For JEE Main and NEET, prioritise conceptual traps and quick calculation paths; timed mixed quizzes of 10 questions after revision simulate exam pressure.

Cross-topic link: Calculus-based derivations assume differentiation comfort; units and dimensional analysis prevent numerical errors.

Spaced revision: Review this note at 1 day, 3 days, and 7 days after first study. Attempt the Quick check questions closed-book, then open the Practice tab for graded reinforcement. Maintain an error log — repeated mistake patterns reveal whether the issue is concept, formula recall, or careless reading.

Diagram and terminology drill: For Physics, redraw key figures from memory and define every labelled part in one sentence. Vocabulary precision prevents mark loss in descriptive answers — use NCERT terms exactly as printed in the textbook.

Revision tip: Link this topic to adjacent Class 12 chapters before attempting mixed practice.

Open the Practice tab for graded questions on Atomic Models.