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Lesson 11.4 • Competency 11.4Complete Lesson
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Atomic Models and Line Emission Spectra

Study Rutherford’s nuclear model, Bohr’s postulates for hydrogen, angular momentum quantization mvr = nh/(2π), energy levels E_n = -13.6/n² eV, Rydberg formula 1/λ = R_H (1/n₁² - 1/n₂²), and spectral series (Lyman, Balmer, Paschen).

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • State Bohr’s postulates and explain how quantized stationary orbits overcome classical radiative collapse.
  • Calculate hydrogen energy levels E_n = -13.6 / n² eV, excitation energies, and ionization energy (13.6 eV).
  • Apply the Rydberg equation to determine transition wavelengths across Lyman, Balmer, and Paschen series.

Core Theory & Concepts

Classical physics predicted that an orbiting electron should continually accelerate, radiate away its energy as electromagnetic waves, and spiral into the nucleus within 10⁻¹¹ seconds. Furthermore, atoms emit discrete, sharp line spectra rather than continuous rainbows. In 1913, Niels Bohr resolved this paradox by quantizing electron orbits in the hydrogen atom.

Bohr Angular Momentum Quantization

Electrons orbit stably without radiating only when orbital angular momentum is an integral multiple of h / (2π): L = m_e v r = n h / (2π), n = 1, 2, 3...

L = m_e v r = \frac{n h}{2\pi}, \quad n = 1, 2, 3\dots

Hydrogen Energy Levels & Rydberg Formula

Energy of level n is E_n = -13.6 / n² eV. Photon emission during transitions yields 1/λ = R_H (1/n₁² - 1/n₂²), where R_H = 1.097 × 10⁷ m⁻¹.

\frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)

Common Misconceptions

Misconception

All spectral lines of hydrogen lie in the visible light spectrum.

Physical Clarification:Only the Balmer series (transitions ending at n=2) lies in the visible spectrum. Lyman series (n=1) is ultraviolet; Paschen (n=3), Brackett (n=4), and Pfund (n=5) lie entirely in infrared.

Syllabus Topic Outline

Competency 11.4
  • 1Rutherford alpha scattering experiment and nuclear atom model
  • 2Bohr’s stationary non-radiating orbit postulate
  • 3Orbital angular momentum quantization: L = mvr = nh / (2π)
  • 4Energy levels of hydrogen atom: E_n = -13.6 / n² eV
  • 5Line emission and absorption: ΔE = E_upper - E_lower = hf = hc/λ
  • 6Rydberg formula and spectral series: Lyman (UV), Balmer (Visible), Paschen (IR)