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Quantum Theory & Bohr’s Model of the Atom

Ch. 4 - Electrons in Atoms. Quantum Theory & Bohr’s Model of the Atom. A. Quantum Theory. Planck (1900) Observed - emission of specific colors of light from hot objects Concluded - energy is emitted in small, specific amounts (quanta).

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Quantum Theory & Bohr’s Model of the Atom

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  1. Ch. 4 - Electrons in Atoms Quantum Theory & Bohr’s Model of the Atom

  2. A. Quantum Theory • Planck (1900) • Observed - emission of specific colors of light from hot objects • Concluded - energy is emitted in small, specific amounts (quanta) • Quantum - minimum amount of energy that can be lost or gained by an atom.

  3. Classical Theory Quantum Theory A. Quantum Theory • Planck (1900) vs.

  4. A. Quantum Theory • Einstein (1905) • Observed - photoelectric effect

  5. A. Quantum Theory • Einstein (1905) • Concluded - light has properties of both waves and particles “wave-particle duality” • Photon - particle of light that carries a quantum of energy

  6. A. Quantum Theory • The energy of a photon is proportional to its frequency of the light. E: energy (J, joules) h: Planck’s constant (6.626  10-34 J/Hz) : frequency (Hz) E = h

  7. A. Examples • EX 1: Find the energy of a red photon with a frequency of 4.57  1014 Hz. GIVEN: E = ?  = 4.57  1014 Hz h =6.626  10-34 J/Hz WORK: E = h E = (6.626  10-34 J/Hz) (4.57  1014 Hz) E = 3.03  10-19 J

  8. A. Examples • EX 2: Find the energy of a photon whose wavelength is 1.0  10-9 m. GIVEN: E = ? • = 1.0  10-9 m c = 3.00  108 m/s h =6.626  10-34 J/Hz WORK: E = h = hc/  λ = (6.626 ·10-34 J/Hz)(3.00 ·108 m/s) 1.0 x 10-9 m E = 2.0  10-16 J

  9. B. Bohr’s Model • Linked photon emission with an atom’s electrons (e-) • In Bohr’s model, e- exist only in orbits with specific amounts of energy called energy levels

  10. B. Bohr’s Model • Therefore… • e- can only gain or lose certain amounts of energy (quanta) • only certain photons are produced • each photon has a unique frequency, and therefore a unique color of light is seen

  11. e- B. Bohr’s Model excited state (high energy orbit; further from nucleus) electron “relaxes” ENERGY IN PHOTON OUT ground state (low energy orbit; closer to nucleus) Line Emission Spectrum produced

  12. Energy of photon depends on the difference in energy levels Bohr’s calculated energies matched the IR (Paschen), visible (Balmer), and UV (Lyman) lines for the H atom D. Bohr Model Hydrogen Emission Spectrum 6 5 4 3 2 1

  13. D. Other Elements • Each element has a unique bright-line emission spectrum. • “Atomic Fingerprint” Helium • Bohr’s calculations only worked for hydrogen! 

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