Atomic Models

Why This Matters

The evolution of atomic models represents one of the most important conceptual journeys in physics—and it's exactly the kind of progression AP Physics 2 loves to test. You're not just memorizing who proposed what; you're being tested on why each model failed, what experimental evidence drove scientists to revise their understanding, and how quantization fundamentally changed our picture of matter. The Bohr model, in particular, is a major focus because it directly connects to energy level transitions, photon emission and absorption, and the mathematical relationships you'll need for calculations involving hydrogen spectra.

Understanding these models also builds your foundation for interpreting spectral lines, applying the de Broglie wavelength, and recognizing when classical physics breaks down. Don't just memorize the timeline—know what problem each model solved, what it couldn't explain, and how the Bohr model's quantization conditions lead to $E_n = -\frac{13.6 \text{ eV}}{n^2}$. That equation, and the reasoning behind it, will appear on your exam.

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Classical Models: The Pre-Quantum Era

These early models attempted to explain atomic structure using classical physics concepts. Each failed in specific ways that revealed the limitations of classical thinking and pointed toward quantum mechanics.

Dalton's Atomic Model

• Atoms as indivisible spheres—proposed that all matter consists of tiny, indestructible particles that cannot be broken down further
• Element identity determined by identical atoms; different elements have atoms with different masses and properties
• Chemical reactions involve rearrangement of atoms, not creation or destruction—conservation of mass at the atomic level

Thomson's "Plum Pudding" Model

• First subatomic particle discovery—identified electrons as negatively charged components embedded within atoms
• Positive charge distributed uniformly throughout the atom like a "pudding," with electrons scattered like plums to balance the charge
• Electrical neutrality maintained by equal amounts of positive and negative charge; no concentrated nucleus proposed

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The Nuclear Revolution: Rutherford's Discovery

Rutherford's gold foil experiment provided the critical evidence that atoms have internal structure radically different from Thomson's model. The unexpected scattering of alpha particles revealed a concentrated positive core.

Rutherford's Nuclear Model

• Gold foil experiment results—most alpha particles passed through, but some deflected at large angles, indicating a small, dense, positively charged nucleus
• Nuclear concentration of mass—nearly all atomic mass located in the tiny nucleus, with electrons orbiting in the surrounding space
• Mostly empty space—atoms are primarily vacuum; this explains why most particles pass through matter undeflected

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The Bohr Model: Quantization Enters Physics

The Bohr model is the most heavily tested atomic model on AP Physics 2. It introduced quantized energy levels to explain why atoms emit light at discrete wavelengths rather than a continuous spectrum.

Bohr's Atomic Model

• Quantized energy levels—electrons can only occupy specific orbits with energies given by $E_n = -\frac{13.6 \text{ eV}}{n^2}$ for hydrogen, where $n$ is the principal quantum number
• Photon emission and absorption—when electrons transition between levels, they emit or absorb photons with energy $\Delta E = h\nu$, directly explaining atomic spectral lines
• Quantized angular momentum—electron orbital angular momentum restricted to $L = n\frac{h}{2\pi}$, which can be understood through the de Broglie standing wave condition $2\pi r = n\lambda$

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Beyond Bohr: The Quantum Mechanical Model

While the quantum mechanical model goes beyond typical AP Physics 2 calculations, understanding why the Bohr model is incomplete helps you recognize its limitations and the conceptual shift toward probability-based descriptions.

Quantum Mechanical Model (Electron Cloud Model)

• Wave-particle duality—electrons behave as waves described by the de Broglie wavelength $\lambda = \frac{h}{p}$, leading to probability distributions rather than fixed orbits
• Orbitals replace orbits—electrons exist in three-dimensional probability clouds; an orbital describes where an electron is likely to be found, not a definite path
• Heisenberg uncertainty principle—the exact position and momentum of an electron cannot be simultaneously known with arbitrary precision, fundamentally limiting classical descriptions

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Quick Reference Table

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Self-Check Questions

1. What experimental evidence led Rutherford to reject Thomson's "plum pudding" model, and what did the results reveal about atomic structure?

2. In the Bohr model, an electron transitions from $n = 3$ to $n = 1$. Which spectral series does this belong to, and how would you calculate the photon's wavelength using the Rydberg formula?

3. Compare and contrast Rutherford's and Bohr's models: both have electrons orbiting a nucleus, so what critical problem did Bohr solve that Rutherford's model could not address?

4. Why does the Bohr model successfully predict hydrogen's spectral lines but fail for helium and heavier atoms? What conceptual limitation does this reveal?

5. How does the de Broglie standing wave condition $2\pi r = n\lambda$ provide a physical justification for Bohr's quantization of angular momentum?