Chapter 4 Arrangement of
Electrons in Atoms
4.1 The Development of a New
Atomic Model
Properties of Light
• Electromagnetic Radiation:
EM radiation are forms of energy which move
through space as waves
• There are many different types of EM waves
• visible light
• x-rays
• ultraviolet light
• infrared light
• radio waves
EM Waves
• Move at speed of light: 3.00 x 108 m/s
• Speed is equal to the frequency times the
wavelength c = v
• Frequency (v) is the number of waves passing
a given point in one second
• Wavelength () is the distance between
peaks of adjacent waves
• Speed of light is a constant, so v is also a
constant; v and  must be inversely
proportional
• Relationships between frequency and
wavelength
• λν=c, where λ is the wavelength (m), ν is
the frequency (s-1) and c is the speed of
light (m s-1).
Related Problems
• Problem #1: Calculate the frequency of
radiation with a wavelength of 442 nm.
• Problem #2: What is the frequency of
infrared radiation of wavelength 67.5
μm
• Problem #3: Calculate the frequency of
radiation with a wavelength of 4.55 x
10¯9 cm.
• Problem #4: What is the wavelength (in
nm) of EMR with a frequency of 4.95 x
1014 s¯1?
Light and Energy:
The Photoelectric Effect
• Electrons are emitted from a
metal when light shines on
the metal
• Incoming EM radiation from
the left ejects electrons,
depicted as flying off to the
right, from a substance.
• Radiant energy is
transferred in units (or
quanta) of energy called
photons
(Max Planck)
Photoelectric Effect
energy
p+
absorption
spectrum
no
e-
ground
state e-
When a specific or
quantized amount of
energy is exposed to
the atom, the electron
jumps from its “ground”
or original state to an
“excited” state
Photoelectric Effect
When the “excited”
electron returns to
lower energy levels,
it releases energy in
the form of light
energy
photon
p+
no
e-
emission
excited
state espectrum!
travels at the
speed of light
(3.00 x 108 m/s)
• A photon is a particle of energy having a
rest mass of zero and carrying a quantum
of energy
• A quantum is the minimum amount of
energy that can be lost or gained by an
atom
• Energy of a photon is directly
proportional to the frequency of
radiation
• E = hv (h is Planck’s constant,
6.62554 x 10 -34 J * sec)
Electromagnetic Spectrum
• Wavelength increases→
• Frequency decreases→
• Energy decreases→
Electromagnetic Spectrum
Wave-Particle Duality
• Energy travels through space as
waves, but can be thought of as a
stream of particles (Einstein)
• Each particle has 1 quantum of
energy.
Line Spectrums
• Ground State: The lowest energy state of an atom
• Excited State:
A state in which an atom has
a higher potential energy than in its ground state
example: Neon lights
Emissions
Spectrum
• Bright line spectrum: Light is given off by
excited atoms as they return to lower energy
states
• Light is given off in very definite wavelengths
• A spectroscope reveals lines of particular colorslight passed through a prism; specific frequencies
given off.
The Hydrogen Line Spectrum
• Definite frequency
• Definite wavelength
Bohr Model
e-
p+
Energy
levels
Niels Bohr
no
Electrons circle
around the nucleus
on their energy level
The Bohr Model of the Atom
• Electron Orbits, or Energy Levels
• Electrons can circle the nucleus only in allowed
paths or orbits
• The energy of the electron is greater when it
is in orbits farther from the nucleus
• The atom achieves the ground state when
atoms occupy the closest possible positions
around the nucleus
• Electromagnetic radiation is emitted when
electrons move closer to the nucleus.
The Bohr Atomic Model
Energy transitions
• Energies of atoms
are fixed and
definite quantities
• Energy transitions
occur in jumps of
discrete amounts of
energy
• Electrons only lose
energy when they
move to a lower
energy state
Related Problem
• Problem #1: How many Joules of
energy are contained in a photon with λ
= 550 nm? How many kJ/mol of energy
is this?
Shortcomings of the Bohr Model
• Doesn't work for atoms larger than
hydrogen
(more than one electron)
• Doesn't explain chemical behavior
Chapter 4 Arrangement of
Electrons in Atoms
4.2 The Quantum Model of the
Atom
Electrons as Waves and Particles
• Louis deBroglie (1924)
• Electrons have wavelike properties
• Consider the electron as a wave confined
to a space that can have only certain
frequencies
The Heisenberg
Uncertainty
Principle
"It is impossible to
determine simultaneously
both the position and
velocity of an electron or
any other particle.”
Werner Heisenberg- 1927
• Electrons are located by their interactions with
photons
• Electrons and photons have similar energies
• Interaction between a photon and an electron knocks
the electron off of its course
The SchrØdinger
Wave Equation
• Proved quantization of electron
energies and is the basis for
Quantum Theory
• Quantum theory describes
mathematically the wave
properties
of electrons and other very small
particles
• Electrons do not move around the
nucleus in "planetary orbits"
????????
The SchrØdinger
Wave Equation
• Electrons exist in regions called orbitals
• An orbital is a three-dimensional region
around the nucleus that indicates the
probable location of an electron
• SchrØdinger equation for probability of
a single electron being found along a
single axis (x-axis)
Atomic Orbitals & Quantum Numbers
• Quantum Numbers specify the
properties of atomic orbitals and the
properties of the electrons in orbitals:
Principal Quantum Number (n)
Angular Momentum Quantum Number (l)
Magnetic Quantum Number (m)
Spin Quantum Number
Principal Quantum Number (n)
• Indicates the main energy levels
occupied by the electron
• Values of n are positive integers
• n = 1 is closest to the nucleus, and
lowest in energy
• The number of orbitals possible per
energy level (or "shell") is equal to n2
Quantum Theory
Energy
levels, n
en=1
p+
no
n=2
n=3
n=4
Angular Momentum Quantum Number (l)
•
•
•
•
Indicates the shape of the orbital
Number of orbital shapes = n
Possible values are l = 0, 1, 2, or 3
Shapes are designated s, p, d, f
• S shape is spherical
• P shape is a dumbbell, or figure 8
Magnetic Quantum Number (m)
• The orientation of the orbital around the
nucleus
• s orbitals have only one possible orientation,
m=0
• p orbitals have three possible,
m = +1, 0 or -1
• d orbitals have five possible,
m = -2, -1, 0, +1, or +2
• f orbitals have 7 possible orientations
Spin Quantum Number
• Indicates the fundamental spin states
of an electron in an orbital
• Two possible values for spin, +1/2, -1/2
• A single orbital can contain only two
electrons, which must have opposite
spins
Diagrams of the Orbitals
Summary of the Quantum
Numbers
Chapter 4 Arrangement of
Electrons in Atoms
4.3 Electron Configurations
Energy Levels
Energy Levels
(7)
Sublevels
(4)
s
1 orbital
p
3 orbitals
2 e-
d
5 orbitals
6 e-
f
7 orbitals
10 e-
14 e-
Writing Electron Configurations
Pauli
Exclusion
Principle
No two
electrons in
the same
atom can
have the
same set of
four quantum
numbers
Rules:
Hund's Rule
Orbitals of equal
energy are each
occupied by one
electron before
any orbital is
occupied by a
second electron,
and all electrons in
singly occupied
orbitals must have
the same spin
Aufbau
Principle
An electron
occupies the
lowestenergy
orbital that
can receive it
Orbital Notation (1 of 3)
• Unoccupied orbitals are represented by
a line, _____
• Lines are labeled with the principal
quantum number and the sublevel letter
• Arrows are used to represent electrons
• Arrows pointing up and down indicate
opposite spins:
Pauli Exclusion Principle
No two electrons in the
same atom can have the
same set of four quantum
numbers (occupy the same
space @ the same time)
Writing Electron
Configurations
1st
e-
2nd
e-
Hund's Rule
Orbitals of equal energy are
each occupied by one
electron before any orbital is
occupied by a second
electron, and all electrons in
singly occupied orbitals must
have the same spin
3rd
e-
4th
e-
Configuration Notation (2 of 3)
• The number of electrons in a sublevel is
indicated by adding a superscript to the
sublevel designation
• Hydrogen = 1s1
Aufbau Principle
2
• Helium =
1s
An electron occupies
the lowest-energy
• Lithium =
1s2 2s1
orbital that can receive
it
(Always start with n = 1
and work your way up)
1 2
3 4 5
6 7
8 9 1
0
1
1
Sublevel Blocks on
the Periodic Table
1 1 1
2 3 4
15 1 1
6 7
18
Fill-In the Periodic Table using Energy Levels & Sublevels
Orbital Filling Order
START
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
FINISH
Noble Gas Notation (3 of 3)
• The configuration begins with the
preceding noble gas’s symbol in
brackets and is followed by the rest of
the configuration for the particular
element.
• [Ne] 3s23p5
Terms
• Highest occupied energy level:
The electron containing energy level
with the highest principal quantum
number
• Inner shell electrons:
Electrons that are not in the highest
energy level
• Octet Rule:
Highest energy level s and p electrons
are filled (8 electrons)
Octet Rule
• Characteristic of noble gases, Group 18
• Exceptions: Hydrogen & Helium
• Noble gas configuration:
Outer main energy level fully occupied,
usually (except for He) by eight
electrons
This configuration has extra stability
Survey of the Periodic Table
Elements of the Fourth Period
• Irregularity of Chromium
• Expected:
• Actual:
1s22s22p63s23p64s23d4
1s22s22p63s23p64s13d5
Rule:
Sublevels are most stable
when they are either half or
completely filled. Electrons
will shift to different energy
levels to accommodate this
stability whenever possible.
Survey of the Periodic Table
• Several transition and rare-earth
elements borrow from smaller sublevels
in order to half fill larger sublevels
i.e. d borrows 1 e- from s
• This accounts for some of the
unexpected electron configurations
found within the transition elements.
Magnetic Fields & Electrons
• Paramagnetic:
When an atom has unpaired electrons,
it will be attracted into a magnetic
field
Ex: 1s22s22p2
• Dimagnetic:
When an atom has only paired
electrons, it will be slightly repelled by
a magnetic field
Ex: 1s22s22p63s2
Electron Configuration & the Periodic
Table
• d-block elements (transition metals)group #3-#12 elements in which 5 “d”
orbitals are being filled in the energy
level equal to the period # minus 1.
– They are metals that have typical metallic
properties.
Practice problems
1-
What is the period, group, & block of the
element [Ar] 4s23d8 ?
period 4
group 10
d block
2What is the electron configuration
of the element in group 12 of the fifth
period?
[Kr] 5s24d10
Electron Configuration & the Periodic
Table
• f-block elements- are the two rows at the
bottom of the periodic table that represent 7
“f” orbitals being filled in the energy level that
is equal to the period number minus 2
– lanthanides- elements # 58-71 that are also
called the rare earth elements
– actinides- elements #90-103 that are all
radioactive
• elements 93(neptunium) through 103
(lawrencium) are all man-made and do not
occur naturally
Practice problem
For each of the following identify the block,
period, group, group name, element name,
element type, and relative reactivity.
1a-
1b-
[He]2s22p5
p-block, period 2, group 17, halogen,
fluorine (F), nonmetal, & highly reactive
[Ar]3d104s1
d-block, period 4, group 11, transition
metal, copper (Cu), metal, & low reactivity
Electron Configuration & Periodic
Properties
• atomic radius- one-half the distance
between the nuclei of identical atoms that are
bonded together.
– As you go across a period, the positive charge of
the nucleus increases across a period, the pull
exerted on the electron cloud increases and the
atomic radius of the elements decreases across
the period.
– As you move down a group, each successive element
adds an energy level so the atomic radii increase
down a group.
Electron Configuration & Periodic
Properties
• ion- an atom or group of atoms that
has a positive or negative charge
ionization- any process that results in
the formation of an ion
• ionization energy- the amount of
energy required to remove one electron
from a neutral atom of an element
– ionization energies of the main group
elements increase across a period
– ionization energies of the main group
elements usually decrease down a group
Electron Configuration & Periodic
Properties
• electron affinity- the energy change
that occurs when an electron is acquired
by a neutral atom
• cation- an ion with a positive charge
due to the loss of electrons
• anion- an ion with a negative charge
due to the gain of electrons
Electron Configuration & Periodic
Properties
• valence electrons- the electrons
available to be gained, lost, or shared by
atoms in the formation of chemical
bonds to make compounds
• electronegativity- a measure of the
ability of an atom in a chemical
compound to attract electrons from
another atom in the compound
– electronegativity tends to increase across a
period and either decrease or remain the
same down a group
– fluorine (F) is the most electronegative of
the elements.