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Chapter 4
Electrons in Atoms
Section 4.2
Development of the Atom
 Originally
described as the smallest
particles of matter
 Discoveries
of electrons, protons, and
neutrons destroyed the idea of an
indivisible atom
Development of the Atom
 Where
are the electrons?
 Niels
Bohr developed a model for the
hydrogen atom
Electrons are in definite fixed orbits
• Energy levels
Development of the Atom
The amount of energy
the electron possess
depends on its distance
from the nucleus.
The further away from
the nucleus the more
energy the electron
possess.
Development of the Atom
 Bohr’s
Model worked perfectly for
hydrogen but failed with any atom
that had more than one electron
 Back
to the drawing board…
Schrodinger Wave Equation
 Electrons
have dual wave-particle
nature
 Developed an equation that treated
electrons like waves
 Only waves of specific energies, and
therefore frequencies, provided
solutions to the equation.
Heisenberg Uncertainty
Principle
 There
is a fundamental limitation to
how precisely both the position and
the momentum of an electron can be
known.
 Together with Schrodinger’s wave
equation a new model of the atom
was developed.
The Quantum Mechanical
Model
Quantum Mechanics describes the
motion of small particles confined to a
tiny region of space.
 The exact position of an electron at
any given instant is not specified
 The exact path that the electron takes
can not be specified

 Its
The Quantum Mechanical
Model
all about
probability!
 The electron is found
inside a blurry
“electron cloud”
 An area where there is
a chance of finding an
electron.
The Quantum Mechanical
Model
 The
electron does not travel around the
nucleus in neat orbits of fixed energy like
Bohr proposed.
 The exist in certain regions called orbitals.
 An orbital is a 3-D region around the
nucleus that indicates the probable location
of an electron.
Atomic Orbitals
 Atomic
orbitals
have different
shapes and
sizes.
 More
to come!
Atomic Orbitals and Quantum
Numbers
 According
to Bohr, electrons of
increasing energy occupy orbits
farther and farther from the nucleus
 Schrodinger’s equation also accounts
for quantized energies for electrons
Atomic Orbitals and Quantum
Numbers
 Electrons
energy level is not the only
characteristic of an orbital that is
indicated by solving Schrodinger’s
Eq.
 Quantum numbers specify the
properties of atomic orbitals and the
properties of electrons in orbitals
Atomic Orbitals and Quantum
Numbers
 The
first three quantum numbers
result from solutions to Schrodinger’s
equation.
 They indicate the main energy level,
the shape and orientation of an
orbital.
 The fourth indicates the spin direction
of an electron.
Principal Quantum Number
 indicates
the main energy level
occupied by the electron.
 Positive
integers 1,2,3,…
 Symbol
n
 Larger
n = more energy
Principal Quantum Numbers
 Within
each energy level the complex
math of Schrödinger's equation
describes several shapes.
 These are called atomic orbitals
 regions where there is a high probability
of finding an electron.
 The total number of orbital’s that exist
in a main energy level is equal to n2
Angular Momentum Quantum
Number
 indicates
 Symbol
 Except
the shape of the orbital.
l
at E1, n = 1, orbitals of
different shapes (sublevels) exist for
a given value of n.
Angular Momentum Quantum
Number
 The
number of orbital shapes
possible is equal to n.
= 0, 1, 2, … n-1 (all positive
integers)
l
Shapes of Orbitals
n
=1 l=0
one orbital
s
n
= 2 l = 0, 1
two orbitals
s, p
n
= 3 l = 0, 1, 2 three orbitals s, p, d
S orbitals
 One
s orbital for every energy level
 Spherical
shaped
 Each
s orbital can hold 2 electrons
 Called the 1s, 2s, 3s, etc.. orbitals.
P orbitals
 Start
at the second energy level
 3 different directions
 3 different shapes (dumbell)
 Each can hold 2 electrons
P Orbitals
All three
p-orbitals
D orbitals
 Start
at the third energy level
 5 different shapes
 Each can hold 2 electrons
F orbitals
 Start
at the fourth energy level
 Have seven different shapes
 2 electrons per shape
F orbitals
Summary
# of
Max
shapes electrons
Starts at
energy level
s
1
2
1
p
3
6
2
d
5
10
3
f
7
14
4
Magnetic Quantum Number
 the
orientation of the orbital in 3-D
space. (x, y, z)
 symbol ml
 the values of ml range from – l to + l
 Ex: n=1
l=0
ml=0
n=2
l=0, 1
ml= -1,0, 1
n=3
l= 0, 1, 2 ml= ?
Spin Quantum Number
 electrons
are not stationary particles,
they spin
 symbol ms
 they can only spin in two directions,
clockwise and counterclockwise
(designations we have assigned
them)
 the values of ms are +1/2 or – 1/2
The Address of an Electron
 No
two electrons have the same 4
quantum numbers.

what I know from the quantum numbers
of an electron:
 Ex:
 1,
0, 0, +1/2
The Address of an Electron
= 1  first principal energy level,
 l = 0  s orbital,
 m l = 0  encompasses all axis, x, y,& z
 ms = + ½  spinning clockwise
n
 Try
this one
 3, 1, -1, -1/2
3, 1, -1, -1/2
= 3  third principal energy level,
 l = 1  one of the p orbitals,
 m l = -1  specifically the px orbital
 ms = - ½  spinning counterclockwise
n