Chapter 5: Arrangement of
Electrons in Atoms
Niels Bohr (1885 – 1962)
– Danish Physicist
 Improved Rutherford’s work by
saying electrons do not lose
energy as they emit light, so
they will stay in orbit
 Stated there are definite levels
and the electrons follow set
paths without gaining or losing
energy (Planetary Model 1913)
Niels Bohr (1885 – 1962)
– Danish Physicist
 Each level has a
specific amount of
energy associated
with it
 The electrons can
only jump levels if
they gain or lose that
specific amount of
energy
Energy Levels
 In the ground state, electrons are at their lowest,
most stable energy levels.
 In the excited state, electrons require a specific
amount of energy to move to a higher energy level.
Max Planck (1858 – 1947)
– German Physicist
 Proposed Planck’s Theory
which says that energy is given
off in specific energy amounts
called quanta which is based on
the particle nature of light.
 Each quantum of energy
corresponds to the different
energy levels for electrons.
 Proposed the equation: E=hf,
E = energy
h = Planck’s constant
(6.626 x 10−34 J∙s)
f = frequency
Photoelectric Effect
When light
shines on the
surface of a
metal, the
metal surface
emits electrons
Louis de Broglie (1892 – 1987)
– French Physicist
 Suggested that if waves
can have a particle nature,
particles can have a wave
nature, known as the
“wave-particle duality”
principle
 Wondered why the positive
nucleus and negative
electrons do not attract.
 Proposed that electrons
moved so fast (speed of
light) that they had
properties of waves
instead of particles.
The Study of Waves
Wave: a progressive disturbance propagated from
point to point in a medium or space without
progress or advance by the points themselves
Mechanical Waves
Mechanical
wave: a wave
that requires an
energy source
and an elastic
material medium
to travel.
Electromagnetic Waves
 a wave that does not require a material medium to
travel
 it propagates by electric and magnetic fields
Transverse Waves
Transverse wave: displacement of the medium is
perpendicular to the direction of propagation of
the wave.
Longitudinal Waves
Longitudinal waves: displacement of the medium is
parallel to the direction of propagation of the wave
(also called compressional waves)
Properties of Waves
 Wavelength (λ): The
 Amplitude (A): The
distance between any part
maximum displacement of a
of the wave (peak) and the
vibrating particle from its
nearest part that is in phase equilibrium position.
with it (another peak).
Standard unit is meters (m).
Standard unit is meters
 Velocity (v): the distance a
(m).
wave travels in a given time.
Standard unit is meters per
 Frequency (f ): The
second (m/s).
number of peaks which
 Energy (E): The energy of
pass a given point each
a single photon of radiation
second. Standard unit is
of a given frequency.
cycles per second which is a Standard unit is joules (J).
hertz (Hz).
Equations
c=λf
c = speed of light
(m/s)
E=hf
E = energy (J)
λ = wavelength (m)
h = Planck’s constant
−34
(6.626x10
J∙s)
f = frequency (Hz)
f = frequency (Hz)
Transverse Wave
Werner Heisenberg (1901 – 1976)
– German Physicist
 “Heisenberg uncertainty
principle”:
states that the position and
momentum of an electron cannot
simultaneously be measured and
known.
 The arrangement of electrons is
discussed in terms of the
probability of finding an
electron in a certain location.
Erwin Schrödinger (1887 – 1961)
– Austrian Physicist
 Studied the wave nature of
the electron and developed
mathematical equations to
describe their wave-like
behavior.
 The most probable location of
the electrons can be found
and the plot of this probability
is called the charge cloud
model.
the four quantum numbers
 Principal Quantum Number (n)
 Angular Momentum Quantum
Number (l )
 Refers to the energy levels in the
atom which is the distance from
the nucleus and designated with a
positive whole number
(n=1,2,3,4,5,6,7)
 Wavelength of emitted photon is
determined by the “energy jump”
between energy levels
 Energy levels (or shells) means
electrons are contained in an area
where the probability of finding the
electron is 90%
 Refers to the sublevel (within an
energy level) which is one or more
“partitions” each with a slightly
different energy. (l = 0,1,2,3)
 The types of sublevels:
l
l
l
l
=
=
=
=
0
1
2
3
(s sublevel)
(p sublevel)
(d sublevel)
(f sublevel)
the four quantum numbers
 Magnetic Quantum Number (m)
Refers to the orientation in space of the electrons in a sublevel
Can have any whole number value from – l to + l which will tell
how many orbitals are in a sublevel.
A maximum of 2 electrons per orbital.
Sublevel
s
p
d
f
# of Orbitals
Total # of electrons
the four quantum numbers
Spin Quantum Number (s) +
1
2
or –
1
2
Refers to the spin of the electron.
Pauli Exclusion Principle: if two electrons
occupy the same orbital, they must have
opposite spin.
Half-filled orbital:
_____
Filled orbital:
_____
Permissible Values of Quantum Numbers for
Atomic Orbitals
n
1
l
0
m
0
Orbital
1s
# of Subshells
1
#of Orbitals
1
Max # of Electrons
2
2
0
1
0
-1,0,1
2s
2p
2
1
3
2
6
3
0
1
2
0
-1,0,1
-2,-1,0,1,2
3s
3p
3d
3
1
3
5
2
6
10
4
0
0
4s
1
-1,0,1
4p
2
-2,-1,0,1,2
4d
3 -3,-2,-1,0,1,2,3 4f
4
1
3
5
7
2
6
10
14
Electron Orbitals
Distribution of Electrons for Different Elements
(Electron Configuration)
 Electrons will occupy the lowest energy levels and
sublevels first.
 Notation:
Principal Quantum
Number, n (energy
level)
2p
Type of Orbital
(sublevel)
Number of
electrons
2
y
Orientation of
Orbital
Aufbau principle
 Aufbau principle: an electron occupies the lowest-energy
orbital that can receive it
Hund’s Rule
 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 state
Give the long notation electron
configuration for:
O
O2–
Ca
Ca2+
Ag
Give the long notation electron
configuration for:
O
1s22s22p4
O2–
1s22s22p6
Ca
1s22s22p63s23p64s2
Ca2+
1s22s22p63s23p6
Ag
1s22s22p63s23p64s23d104p65s24d9
Give the short notation
(noble gas notation)
O
O2–
Ca
Ca2+
Ag
Give the short notation
(noble gas notation)
O
[He]2s22p4
O2–
[He]2s22p6
Ca
[Ne]4s2
Ca2+
[Ne]
Ag
[Kr]5s24d9
Orbital Diagrams
Usually only done for the outer shell
electrons, which always includes the s and p
orbitals.
Give the orbital diagrams
(arrow notation)
O
____
2s
____ ____ ____
2p
O2–
____
2s
____ ____ ____
2p
Give the orbital diagrams
(arrow notation)
Ca
____
4s
Ca2+ ____
4s
Ag
____
5s
Electron Dot Diagrams
Shows the outer shell or valence electrons for elements.
Give the electron dot diagrams
O
O2–
Ca
Ca2+
Ag