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Quantization of Energy

Specific Orbit Radii. Quantization of Energy. r=a B =0.529 Å (Bohr radius). Most negative. Bohr Frequency Condition:. n = 1 is ground state (most negative energy) n> 1 is an excited state. Absorption vs. Emission. Bohr Model Calculation— Predicts Correctly the Spectrum of Hydrogen.

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Quantization of Energy

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  1. Specific Orbit Radii Quantization of Energy r=aB=0.529 Å (Bohr radius) Most negative Bohr Frequency Condition: n = 1 is ground state (most negative energy) n> 1 is an excited state

  2. Absorption vs. Emission

  3. Bohr Model Calculation—Predicts Correctly the Spectrum of Hydrogen Emission: Energy is Lost _ n =6 n =1 UV light

  4. n =2 n =1 Absorption: Energy is Gained + n = (here energy is zero) n =1

  5. Balmer and Lyman Series Balmer Series: Any n to n = 2 (Visible) Lyman Series: Any n to n = 1 (UV)

  6. The Bohr Model Failed to Predict the Emission Lines for Multi-electron Atoms A NEW PHYSICS WAS NEEDED: The BIRTH of QUANTUM MECHANICS

  7. Heisenberg Uncertainty Principle There is a fundamental limitation as to how precisely we can know the position and the momentum of a particle at a given time In other words: the position and the momentum of a particle cannot be simultaneously determined to arbitrarily high precision

  8. Thought Experiment Illustrating Heisenberg Uncertainty Principle Assume: Microscope-- Possibility 1: • photon: very energetic NO HIT NO OBSERVATION e Possibility 2: HIT therefore OBSERVATION BUT—CHANGE In Momentum and Position E electron e e Momentum changes Position OK The higher the accuracy in the knowledge of the position (more energetic light, lower wavelength) the higher the uncertainty in the knowledge of the velocity (or linear momentum).

  9. “In this way, quantum theory reminds us, as Bohr has put it, of the old wisdom that when searching for harmony in life one must never forget that in the drama of existence we are ourselves both players and spectators. It is understandable that in our scientific relation to nature our own activity becomes very important when we have to deal with parts of nature into which we can penetrate only by using the most elaborate tools.” Heisenberg, from “Physics and Philosophy”

  10. STANDING WAVES: The electron as a Standing Wave bound to the nucleus— node: zero magnitude of displacement L=n (/2)

  11. Erwin Schrödinger— In 1926 wrote a wave equation known as the Schrödinger Equation The electron as a Standing Wave bound to the nucleus— He used the classical wave equation and de Broglie relationship of wave-particle duality and obtained a Wave Equation for the electron in the atom

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