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.

5. Bohr Model of Hydrogen Atom Energy levels evaluated using the following equation E = -2.178 x 10 -18 J (Z 2 / n 2 ) ΔE = E (final) – E (initial) = -2.178 x 10 -18 J [ (1 / n final 2 – 1 / n inital 2 ) ]

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.

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 (m l )

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

20. Quantum Numbers Magnetic Quantum Number (m l ): Defines the spatial orientation of the orbital. For orbital of angular-momentum quantum number, l, the value of m l has integer values from –l to +l. This gives a spatial orientation of: l = 0 giving m l = 0 l = 1 giving m l = –1, 0, +1 l = 2 giving m l = –2, –1, 0, 1, 2, and so on…...

22. Quantum Numbers

23. Why can’t an electron have the following quantum numbers? – (a) n = 2, l = 2, m l = 1(b) n = 3, l = 0, m l = 3 – (c) n = 5, l = –2, m l = 1 Give orbital notations for electrons with the following quantum numbers: – (a) n = 2, l = 1, m l = 1(b) n = 4, l = 3, m l = –2 – (c) n = 3, l = 2, m l = –1

24. Quantum Numbers Spin Quantum Number (m s ): The Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers.