Bohr Model of the Atom p. 97 103

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Bohr Model of the Atom(p. 97 - 103)

• Ch. 4 - Electrons in Atoms

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A. EM Spectrum
c ??
c speed of light (3.00 ? 108 m/s) ? wavelength
(m, nm, etc.) ? frequency (Hz)
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B. 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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B. Quantum Theory

• Planck (1900)

vs.
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B. Quantum Theory

• Einstein (1905)
• Observed - photoelectric effect

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B. 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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B. Quantum Theory

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

E h?

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

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C. Line-Emission Spectrum
excited state
ENERGY IN
PHOTON OUT
ground state
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D. Bohr Model

• e- exist only in orbits with specific amounts of
  energy called energy levels
• Therefore
• e- can only gain or lose certain amounts of
  energy (quanta)
• only certain photons are produced

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D. Bohr Model

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

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3
2
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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! ?

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E. Examples

• EX 1 Find the frequency of a photon with a
  wavelength of 434 nm.

GIVEN ? ? ? 434 nm 4.34 ? 10-7 m c
3.00 ? 108 m/s
? 6.91 ? 1014 Hz
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E. Examples

• EX 2 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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E. Examples

• EX 3 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 Js

WORK E h? hc/ ? ? (6.626 10-34 J/Hz)(3.00
108 m/s) 1.0 x 10-9 J E 2.0 ? 10-16 J