Quantum Theory

1
Quantum Theory Bohrs Model of the Atom

• Ch. 4 - Electrons in Atoms

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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.

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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

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A. Quantum Theory

• The energy of a photon is proportional to its
  frequency of the light.

E h?

• E energy (J, joules)
• h Plancks constant (6.626 ? 10-34 J/Hz)
• ? frequency (Hz)

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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
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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/ ? ? (6.626 10-34 J/Hz)(3.00
108 m/s) 1.0 x 10-9 m E 2.0 ? 10-16 J
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B. Bohrs Model

• Linked photon emission with an atoms electrons
  (e-)
• In Bohrs model, e- exist only in orbits with
  specific amounts of energy called energy levels

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B. Bohrs 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

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B. Bohrs 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
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D. Bohr Model
Hydrogen Emission Spectrum

• Energy of photon depends on the difference in
  energy levels
• Bohrs calculated energies matched the IR
  (Paschen), visible (Balmer), and UV (Lyman) lines
  for the H atom

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D. Other Elements

• Each element has a unique bright-line emission
  spectrum.
• Atomic Fingerprint

Helium

• Bohrs calculations only worked for hydrogen! ?