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Difficulty: Very hardAtomic Models

Match each historical atomic model on the left with its defining postulate, experimental outcome, or theoretical limitation on the right.

  • Thomson's Plum Pudding ModelModeled electrons embedded in a diffuse positive charge sphere; disproved by large-angle α\alpha-particle backscattering.
  • Rutherford's Planetary ModelEstablished a dense positive nucleus in mostly empty space, but classically predicted orbital collapse due to continuous electromagnetic radiation.
  • Bohr's Quantized ModelPostulated stationary orbits with quantized angular momentum L=nh2πL = \frac{nh}{2\pi}, successfully predicting single-electron Rydberg spectral lines.
  • Sommerfeld's ExtensionIntroduced elliptical sub-shells and relativistic electron mass variations to explain fine-structure splitting of hydrogen spectral lines.

Answer

Thomson's model matches the diffuse positive sphere disproved by alpha particle backscattering; Rutherford's model matches the dense nucleus with classical radiation collapse limitations; Bohr's model matches quantized angular momentum in non-radiating orbits; Sommerfeld's extension matches elliptical sub-shells and relativistic adjustments for fine-structure splitting.
Each model directly maps to its defining theoretical contribution or failure mechanism: Thomson's diffuse charge sphere failed under α\alpha-particle scattering; Rutherford's nuclear atom suffered from classical radiation instability; Bohr's model introduced angular momentum quantization L=nℏL = n\hbar; and Sommerfeld's model extended orbits to ellipses with relativistic velocity corrections to account for fine structure.

Step-by-Step Solution

1
Analyze Thomson's Plum Pudding Model
Thomson proposed electrons embedded in a sea of positive charge. This continuous distribution could not account for α\alpha-particles rebounding at angles greater than 90∘90^\circ.
Identify the historical assumption and experimental contradiction for Thomson's model.
2
Analyze Rutherford's Planetary Model
Rutherford deduced a concentrated positive core (nucleus). However, according to Maxwellian electrodynamics, orbiting electrons accelerate continuously, radiating energy until collapsing into the nucleus.
Identify the primary theoretical failure of classical planetary electron orbits.
3
Analyze Bohr's Quantized Model
Bohr introduced the non-classical postulate that electrons exist in stable stationary states with angular momentum L=nh2πL = \frac{nh}{2\pi}, accurately yielding the Rydberg formula for hydrogen.
Recognize the quantum postulate resolving Rutherford's radiation collapse.
4
Analyze Sommerfeld's Extension
To explain fine spectral line splitting not accounted for by circular Bohr orbits, Sommerfeld introduced elliptical orbits with azimuthal quantum numbers and relativistic mass variation at high electron velocities.
Connect fine-structure spectral features to relativistic elliptical orbital modifications.

Key Concept

Development and Limitations of Historical Atomic Models
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Topics

Atomic Models

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