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Chapter 7: Quantum Mechanical Model of Atom

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Chapter 7: Quantum Mechanical Model of Atom

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    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.

    4. Chapter 7, Figure 7.11 The Bohr Model and Emission SpectraChapter 7, Figure 7.11 The Bohr Model and Emission Spectra

    5. 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) ]

    6. Chapter 7, Unnumbered Figure, Page 297Chapter 7, Unnumbered Figure, Page 297

    7. Chapter 7, Figure 7.20 Excitation and RadiationChapter 7, Figure 7.20 Excitation and Radiation

    8. Chapter 7, Figure 7.21 Hydrogen Energy Transitions and Radiation Chapter 7, Figure 7.21 Hydrogen Energy Transitions and Radiation

    9. 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.

    11. Chapter 7, Figure 7.16 The Concept of Trajectory Chapter 7, Figure 7.16 The Concept of Trajectory

    12. Chapter 7, Figure 7.17 Trajectory versus Probability Chapter 7, Figure 7.17 Trajectory versus Probability

    13. Chapter 7, Figure 7.18 Trajectory of a Macroscopic Object Chapter 7, Figure 7.18 Trajectory of a Macroscopic Object

    14. Chapter 7, Figure 7.19 The Quantum-Mechanical Strike Zone Chapter 7, Figure 7.19 The Quantum-Mechanical Strike Zone

    15. 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, ?.

    16. 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)

    17. 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.

    18. 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

    19. Chapter 7, Unnumbered Table, Page 298Chapter 7, Unnumbered Table, Page 298

    20. 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 of: l = 0 giving ml = 0 l = 1 giving ml = –1, 0, +1 l = 2 giving ml = –2, –1, 0, 1, 2, and so on…...

    21. Chapter 7, Unnumbered Figure, Page 298 Chapter 7, Unnumbered Figure, Page 298

    22. Quantum Numbers

    23. Quantum Numbers Why can’t 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

    24. 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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