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The Quantum Model.notebook
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The Quantum Model
Unit D: Lesson 5
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Summary of the Bohr ModelAbsorption (nf > ni). • electron "jumps" to a higher energy level, it must
absorb energy. • dark lines correspond to specific photon
wavelengths needed for an electron to jump from lower to higher energy levels
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• Emission (nf < ni).
• electron "falls" to a lower orbit, energy is emitted.
• Emission lines correspond to specific photon wavelengths emitted when an electron jumps from higher to lower energy levels.
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• Eg) In an atom, an electron goes from the first orbital E = -24.0 eV to the 5th orbital. A photon with wavelength of 5.40 x 10-8m is absorbed. What is the energy of the 5th orbital for this atom?
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Quantum Model of the Atom• Recall de Broglie - particles have wave
properties because they have momentum
Particle: p = mv Photon:
∴ de Broglie’s wavelength is
• de Broglie predicted that electrons travel in a wave-like pattern
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• de Broglie model suggests that the electrons travel in a standing wave pattern
• orbitals exist only where the standing wave produces constructive interference (the circumference of the wave must be a whole multiple of one wavelength)
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• If the wave doesn’t fit, it will add destructively to itself and collapse. If the wave fits the radius, the electron is very stable. It exists as a circular standing wave
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circumference of the orbit = whole number of wavelengths
• NOTE: the number of standing wavelengths corresponds to the orbit number
• n =1 means 1 wavelength
• n = 2 means 2 wavelengths and so on
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• the standing wave is how electrons can occupy an orbit without giving off energy
• the atom only has specific energy levels indicating that the energies of the electrons are quantized
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Contemporary Model• the electron stops being a particle orbiting the
nucleus at a certain point
• Instead, an electron’s mass and charge can be thought of as “spread out” as a standing wave around the nucleus.
• The electron is not really at any one position as a particle, it's everywhere as a wave.
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Electron Cloud Model• The electrons have become a “cloud” of electrons.
• This is essentially the model used today.
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Example:• Determine the de Broglie wavelength for the
electron in the 2nd Bohr orbit for hydrogen where the energy level is 3.40 eV.
Solution:
1. Convert energy into joules
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Solution:2. Recognize that de Broglie’s wavelength requires velocity so calculate velocity from energy using
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Solution:3. Solve for wavelength
Remember this formula is not on the formula sheet.
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Eg. 2 Find the λ of an electron that was accelerated by a potential difference of 500V.
1. Determine energy.
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2. Determine velocity.
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3. Determine wavelength
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Warning:
• Do not find energy using Ek=1/2mv2 and then use E = hc/λ to find wavelength – it implies the mass ‘stops’ and changes its energy into EMR.
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Assignment: • Workbook p. 300 #1b,2-7, 8a
