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Chapter 7: Quantum Mechanical Model of Atom

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Title: Chapter 7: Quantum Mechanical Model of Atom


1
Chapter 7 Quantum Mechanical Model of Atom
  • CHE 123 General Chemistry I
  • Dr. Jerome Williams, Ph.D.
  • Saint Leo University

2
Overview
  • Bohr Model of Hydrogen Atom
  • Quantum Mechanical Model of Atom
  • Quantum Numbers

3
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.

10
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, ?.

14
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)

15
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.

16
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

17
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
20
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

21
Quantum Numbers
  • Spin Quantum Number (ms)
  • The Pauli Exclusion Principle states that no two
    electrons can have the same four quantum numbers.
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