Download Chapter 7: Quantum Mechanical Model of Atom

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.