Bohr and Quantum Mechanical Model

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Bohr and Quantum Mechanical Model

• Mrs. Kay
• Chem 11A

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Those who are not shocked when they first come
across quantum theory cannot possibly have
understood it. (Niels Bohr on Quantum Physics)
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Wavelengths and energy

• Understand that different wavelengths of
  electromagnetic radiation have different
  energies.
• cv?
• cvelocity of wave
• v(nu) frequency of wave
• ?(lambda) wavelength

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• Bohr also postulated that an atom would not emit
  radiation while it was in one of its stable
  states but rather only when it made a transition
  between states.
• The frequency of the radiation emitted would be
  equal to the difference in energy between those
  states divided by Planck's constant.

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• E2-E1 hv
• h6.626 x 10-34 Js Planks constant
• E energy of the emitted light (photon)
• v frequency of the photon of light
• This results in a unique emission spectra for
  each element, like a fingerprint.
• electron could "jump" from one allowed energy
  state to another by absorbing/emitting photons of
  radiant energy of certain specific frequencies.
• Energy must then be absorbed in order to "jump"
  to another energy state, and similarly, energy
  must be emitted to "jump" to a lower state.
• The frequency, v, of this radiant energy
  corresponds exactly to the energy difference
  between the two states.

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• In the Bohr model, the electron is in a defined
  orbit
• Schrödinger model uses probability distributions
  for a given energy level of the electron.

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Orbitals and quantum numbers

• Solving Schrödinger's equation leads to wave
  functions called orbitals
• They have a characteristic energy and shape
  (distribution).

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• The lowest energy orbital of the hydrogen atom
  has an energy of -2.18 x 1018 J and the shape in
  the above figure. Note that in the Bohr model we
  had the same energy for the electron in the
  ground state, but that it was described as being
  in a defined orbit.

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• The Bohr model used a single quantum number (n)
  to describe an orbit, the Schrödinger model uses
  three quantum numbers n, l and ml to describe an
  orbital

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The principle quantum number 'n'

• Has integral values of 1, 2, 3, etc.
• As n increases the electron density is further
  away from the nucleus
• As n increases the electron has a higher energy
  and is less tightly bound to the nucleus

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The azimuthal or orbital (second) quantum number
'l'

• Has integral values from 0 to (n-1) for each
  value of n
• Instead of being listed as a numerical value,
  typically 'l' is referred to by a letter ('s'0,
  'p'1, 'd'2, 'f'3)
• Defines the shape of the orbital

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The magnetic (third) quantum number 'ml'

• Has integral values between 'l' and -'l',
  including 0
• Describes the orientation of the orbital in space
  

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For example, the electron orbitals with a
principle quantum number of 3
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• the third electron shell (i.e. 'n'3) consists of
  the 3s, 3p and 3d subshells (each with a
  different shape)
• The 3s subshell contains 1 orbital, the 3p
  subshell contains 3 orbitals and the 3d subshell
  contains 5 orbitals. (within each subshell, the
  different orbitals have different orientations in
  space)
• Thus, the third electron shell is comprised of
  nine distinctly different orbitals, although each
  orbital has the same energy (that associated with
  the third electron shell) Note remember, this is
  for hydrogen only.

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Practice

• What are the possible values of l and ml for an
  electron with the principle quantum number n4?
• If l0, ml0
• If l1, ml -1, 0, 1
• If l2, ml -2,-1,0,1, 2
• If l3, ml -3, -2, -1, 0, 1, 2, 3

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Problem 2

• Can an electron have the quantum numbers n2, l2
  and ml2?
• No, because l cannot be greater than n-1, so l
  may only be 0 or 1.
• ml cannot be 2 either because it can never be
  greater than l

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• In order to explain the line spectrum of
  hydrogen, Bohr made one more addition to his
  model. He assumed that the electron could "jump"
  from one allowed energy state to another by
  absorbing/emitting photons of radiant energy of
  certain specific frequencies. Energy must then be
  absorbed in order to "jump" to another energy
  state, and similarly, energy must be emitted to
  "jump" to a lower state. The frequency, v, of
  this radiant energy corresponds exactly to the
  energy difference between the two states.
  Therefore, if an electron "jumps" from an initial
  state with energy Ei to a final state of energy
  Ef, then the following equality will hold
  (delta) E Ef - E i hvTo sum it up, what
  Bohr's model of the hydrogen atom states is that
  only the specific frequencies of light that
  satisfy the above equation can be absorbed or
  emitted by the atom.