CH 6 (Cont'd)

Miles Eckles March 3, 2011
Chem 101 A Chapter 6
Last thoughts on Bohr’s Model
 Bohr’s model worked perfectly for explaining the spectra of atoms containing a single
electron (H, He+, etc.)
 Further refinements needed to explain other atoms
Wave Behavior of Matter
 DeBroglie suggested that electrons orbiting about a nucleus have a characteristic

wavelength and dubbed the wave characteristics of particles matter waves. The
wavelength of a matter wave:
 λ = h/mv
 photons have wave-like and matter-like behavior
The product of mass and velocity is momentum.
The Wavelength of a Baseball

Calculate the wavelength of a baseball thrown by Carlos Zambrano of the Chicago Cubs (fastball
v = 95 mph) Mass of the baseball is 143 g.
λ = h/mv
v = 95 mi x 1hr x 1.6093km x 1000m = 42m/s
hr 3600s mi km
λ = 6.63 x 10-34 J-s / (0.143kg)(42 m/s)

λ = 1.1 x 10-34 J-s2 kg-m2/s2
kg-m 1J
λ = 1.1 x 10-34m
 this value is awfully small; can’t perceive in the microscopic world.
The Uncertainty Principle
 States that it is inherently impossible for us to know simultaneously both the exact
momentum and exact location in space
 Fundamental limitation on knowing where any electron is; got to treat as wave and
particle
Quantum Mechanics
 Schrodinger developed equation to relate wave and particle nature of electrons,

opening up the field of quantum mechanics or wave mechanics.
 Wave functions (Ψ) are solutions to Schrodinger’s equations, but they have no physical
meaning Ψ2, however, represents a probability density of finding the electron.
 When wave functions is squared Ψ2 it gives us a physical 3-D representation of finding
an electron in a certain position
Orbitals and Quantum Numbers
 Orbitals are wave functions

o Each orbital has a characteristic energy and shape
 n – principal quantum number specifies orbital energy
o integer values 1, 2, 3…
 l –azimuthal quantum number specifies shape of orbital
o Integral values from 0 to n—1
 Example: if n = 1 : l =0
 Example 2: if n = 2 : l = 0, 1
 Example 3: if n = 3 : l = 0, 1, 2
 l =0 (s orbital), l = 1 (p), l = 2 (d), l = 3 (f)
o s = spherical , has 1 type
o p = p orbital (oblong dumbbells), has 3 types (px, py, pz)
o d = d orbital (clover leaves), 5 types (dxy, dxz,dyz,dz2, dx2- y2)
o f = f orbitals, 7 types
o Group 1 and Group 2 elements s orbitals
o Group 17 and 18 (gases) have p orbitals
 ml is the magnetic quantum number

o describes the orientation of the orbital in space
o can have integral values from -l to l, including 0
 can have only 3 values in this case
 All electrons in orbitals with same n are said to be in the same electron shell.
 All electrons in orbitals with same n and l are said to be in same subshell.
Effective nuclear charge
 Effective nuclear charge, Zeff’ equals the number of protons in the nucleus (Z) minus the
average number of electrons (S) between nucleus and electron in question.
 Zeff = Z — S
o Electrons in outer most shell are involved with other atoms
 The screening effect (positive charge felt by outer shell electrons ) is caused by inner
electrons shielding nuclear force from the outer electrons.
In General
 In many electron atom, for a given value of n, Zeff decreases with increasing value of l
 For many electron atom, for a given value of n, the energy of the orbital increases with
increasing l
 Orbitals with the same energy are said to be degenerate
Electronic Spin and Pauli Exclusion Principle
 The electron spin quantum number, ms, is observed in line spectra.

o Possible values are + ½ and – 1/2
o Represents how an electron might spin, either clockwise or counterclockwise
 Pauli excursion principle states that no two electrons in an atom can have the same set
of four quantum numbers n, l, ml, and ms.
Electron Configurations
 The way in which the electrons are distributed among the various orbitals of an atom is
called its electron configuration.
 The ground state is the most stable and lowest energy state of atom.
 Hund’s rule – for degenerate orbitals, the lowest energy is attained when the number of
electrons with same spin is maximized
Orbital Energy Levels in Multi Electron Systems
___ ___ ___ ___ ___ 3d
___ 4s
___ ___ ___ 3p
___ 3s
___ ___ ___ 2p
___ 2s
___ 1s
Arrow represents increase in Energy
Electron Configurations
 Write the orbital diagram for the ground state of sodium. The electron configuration is
[Ne]3s1.
________ Using the [Ne] abbreviation lets you

1s22s22p6 configuration of Ne is Na.
3s
Electronic Structures Examples
 What is the electron configuration of Li?
1s22s1 or [He]2s1
 What about Ti?
1s22s22p63s23p64s23d2 or [Ar]4s23d2
 What about Zn?
1s22s22p63s23p64s23d10 or [Ar]4s23d10
Core vs. Valence Electrons
 Core electrons are electrons in the inner shells, while outer shells are known as
valence electrons.
 Valence electrons are the ones that play the real roles in chemical behavior
Kinds of elements
 Transition Elements fill d orbitals.
 Lanthanide elements are filling the 4f orbitals.
 Actinide elements are filling the 5f orbitals.
 Main group elements are filling s and p orbitals.
o See Figure 6.28 for full electron configurations

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Miles Eckles March 3, 2011

Chem 101 A Chapter 6

Last thoughts on Bohr’s Model

Wave Behavior of Matter

 DeBroglie suggested that electrons orbiting about a nucleus have a characteristic

The product of mass and velocity is momentum.

The Wavelength of a Baseball

λ = 6.63 x 10-34 J-s / (0.143kg)(42 m/s)

The Uncertainty Principle

 Schrodinger developed equation to relate wave and particle nature of electrons,

Orbitals and Quantum Numbers

 Orbitals are wave functions

o Group 1 and Group 2 elements s orbitals

o Group 17 and 18 (gases) have p orbitals

 ml is the magnetic quantum number

Effective nuclear charge

Electronic Spin and Pauli Exclusion Principle

 The electron spin quantum number, ms, is observed in line spectra.

Orbital Energy Levels in Multi Electron Systems

___ ___ ___ ___ ___ 3d

___ ___ ___ 3p

___ ___ ___ 2p

________ Using the [Ne] abbreviation lets you

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_ _ _ _ ___ 3d

_ _ ___ 3p

_ _ ___ 2p