Chapter 7: Quantum Mechanical Model of Atom

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Chapter 7 Quantum Mechanical Model of Atom

• CHE 123 General Chemistry I
• Dr. Jerome Williams, Ph.D.
• Saint Leo University

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Overview

• Bohr Model of Hydrogen Atom
• Quantum Mechanical Model of Atom
• Quantum Numbers

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Bohr Model of Hydrogen Atom

• Niels Bohr - described atom as electrons circling
  around a nucleus and concluded that electrons
  have specific energy levels.
• Limited only to Hydrogen atom or Hydrogen like
  ion.

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Bohr Model of Hydrogen Atom

• Energy levels evaluated using the following
  equation
• E -2.178 x 10-18 J (Z2 / n2)
• ?E E (final) E (initial) -2.178 x 10-18 J
  (1 / nfinal2 1 / ninital2)

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Quantum Mechanical Model of Atom

• Erwin Schrödinger - proposed quantum mechanical
  model of atom, which focuses on wavelike
  properties of electrons.

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Quantum Mechanical Model of Atom

• Werner Heisenberg - showed that it is impossible
  to know (or measure) precisely both the position
  and velocity (or the momentum) at the same time.
• The simple act of seeing an electron would
  change its energy and therefore its position.

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Quantum Mechanical Model of Atom

• Erwin Schrödinger - developed a compromise which
  calculates both the energy of an electron and the
  probability of finding an electron at any point
  in the molecule.
• This is accomplished by solving the Schrödinger
  equation, resulting in the wave function, ?.

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Quantum Numbers

• Wave functions describe the behavior of
  electrons.
• Each wave function contains three variables
  called quantum numbers
• Principal Quantum Number (n)
• Angular-Momentum Quantum Number (l)
• Magnetic Quantum Number (ml)

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Quantum Numbers

• Principal Quantum Number (n) Defines the size
  and energy level of the orbital. n 1, 2, 3,
  ???
• As n increases, the electrons get farther from
  the nucleus.
• As n increases, the electrons energy increases.
• Each value of n is generally called a shell.

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Quantum Numbers

• Angular-Momentum Quantum Number (l) Defines the
  three-dimensional shape of the orbital.
• For an orbital of principal quantum number n, the
  value of l can have an integer value from 0 to n
  1.
• This gives the subshell notation l 0 s -
  orbital l 1 p - orbital l 2 d -
  orbital l 3 f - orbital l 4 g - orbital

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Quantum Numbers

• Magnetic Quantum Number (ml) Defines the spatial
  orientation of the orbital.
• For orbital of angular-momentum quantum number,
  l, the value of ml has integer values from l to
  l.
• This gives a spatial orientation ofl 0 giving
  ml 0 l 1 giving ml 1, 0, 1l 2 giving
  ml 2, 1, 0, 1, 2, and so on...

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Quantum Numbers
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Quantum Numbers

• Why cant an electron have the following quantum
  numbers?
• (a) n 2, l 2, ml 1 (b) n 3, l 0, ml
  3
• (c) n 5, l 2, ml 1
• Give orbital notations for electrons with the
  following quantum numbers
• (a) n 2, l 1, ml 1 (b) n 4, l 3, ml
  2
• (c) n 3, l 2, ml 1

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Quantum Numbers

• Spin Quantum Number (ms)
• The Pauli Exclusion Principle states that no two
  electrons can have the same four quantum numbers.