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Chapter 7: Quantum Mechanical Model of Atom CHE 123: General Chemistry I Dr. Jerome Williams, Ph.D. Saint Leo University Overview • Bohr Model of Hydrogen Atom • Quantum Mechanical Model of Atom • Quantum Numbers 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. Bohr Model of Hydrogen Atom • Energy levels evaluated using the following equation • E = -2.178 x 10-18 J (Z2 / n2) • ΔE = E (final) – E (initial) = -2.178 x 10-18 J [ (1 / nfinal2 – 1 / ninital2) ] Quantum Mechanical Model of Atom • Erwin Schrödinger - proposed quantum mechanical model of atom, which focuses on wavelike properties of electrons. 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. 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, . 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) 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. Quantum Numbers • Angular-Momentum Quantum Number (l): Defines the threedimensional 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 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…... Quantum Numbers 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 – (c) n = 3, l = 2, ml = –1 (b) n = 4, l = 3, ml = –2 Quantum Numbers • Spin Quantum Number (ms): • The Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers.