### energy levels

```Electrons in Atoms
What do you know about a wave?
Electromagnetic spectrum
Visible light: all that can be seen by the human eye
***Blue flames have a shorter wavelength than yellow flames
***Blue flames are higher in energy and hotter!
The rest can’t be seen, but is still considered light
Graphing Direct and Inverse Proportions
Direct Proportion:
Inverse Proportion:
Y
Y
X
X
Frequency and Wavelength
Relationships Between Energy, Wavelength and Frequency of
Waves:
Energy and Frequency:
Wavelength and Frequency:
Direct
ν
E
Inverse
ν
Energy and Wavelength:
Inverse
λ
E
λ
Problems:
1. If the wavelength of a wave doubles, and its energy and
speed don’t change, what will happen to its frequency?
2λ → ½ υ
The frequency (υ) will be cut in half.
2. If the frequency of a wave triples, what happens to the energy
needed for the wave?
3υ → 3E
You will need THREE times the energy
3. A student modifies the wavelength of a wave by changing
the energy. If the energy is cut in half, what must have
happened to the wavelength?
½ E → 2λ
Light has two components:
Wavelength: in (m)
Frequency: in (1/s)
λ=
Energy: in (J)
E = hυ or
ν=
c = speed of light (3 x 108 m/s)
h = Planck’s constant (6.6 x 10-34 Js)
1 x 109 nm = 1 m
Or
1nm = 1.0 × 10-9 m
λ ↑ ν↓
E↓
λ ↓ ν ↑ E↑
Energy WS problems
1. Find the energy of a wave if its frequency is
2.2 x 1016 1/sec
E = hυ
E = (6.6 x 10-34 Js) x (2.2 x 1016 1/sec)
E = 1.45 x 10-17 J
6. Find the wavelength of light if its energy is 2.8 x 10-19J.
What color light would you see?
Use E = hυ to find υ:
2.8 x 10-19J = (6.6 x 10-34 Js) x υ
υ = 4.24 x 1014 1/s
Then solve for wavelength:
=
=
= 7.07 x 10-7 m = 707 nm Red color
#6 (using one equation)
E=
=
Review: Neil Bohr
Confined electrons to energy levels
Energy (light)
being released
when e- jump from
excited state to
ground state.
Quantum leaps:
Atomic emission spectrum:
 Each element has a unique line-emission spectrum
Emission spectrum of Hydrogen and Iron:
Drawing Bohr’s atom:
Energy levels
# of e-
1
2
2
8
3
18
4
32
Present Day Model
 Electrons are located in an orbital
 Orbitals- regions around a nucleus that correspond to
specific energy levels
 Orbitals are also called electron clouds
 Don’t know the exact position of the electron- creates fuzzy
image
Electron cloud
Quantum Numbers
 Quantum Mechanical Model - present day model of
the atom
Electrons do NOT orbit nucleus in circular pattern
How can we keep track of the electrons?
Four Quantum numbers - defines region in which
electrons can be found
1. Energy Level
The fixed energies an electron can have are called energy levels.
electron’s energy & distance from the nucleus ↑
{analogy is floors in apartment building}
n= 1, 1st energy level,
1st floor
+
n= 2, 2nd energy level,
2nd floor
Think of the atom as an apartment building with
each floor representing an energy level
2. Sublevel
 Represent the sublevels of the main energy level
{analogy is apartments on a floor}
 Type or shape of orbital: s, p, d, f
S - orbital
Size: 1S < 2S < 3S
p - orbital
d - orbital
3. Orbital
 subset of the sublevels
 probability map of finding an electron.
 Indicates numbers and orientations of orbitals around
nucleus {analogy is rooms in an apartment}
# of orbitals includes:
one s orbital
three p orbitals
five d orbitals
seven f orbitals
4. Spin
 indicates the orientation of an electron’s magnetic field
relative to an outside magnetic field
+
1
1
or 
or (  or  )
2
2
• A single orbital can hold a maximum of 2 electrons, which
must have opposite spins {analogy is roommates in a room}
S: 1 orbital
Max e- = 2
P:3 diff. orbitals
Max e- = 6
D:5 diff. orbitals
Max e- = 10
f: 7 diff. orbitals
Max e- = 14
Aufbau principle
states that electrons fill orbitals that have the lowest energy
first(e.g. 1s before 2s).
Overlapping Orbitals
Electron Configuration
• arrangement of the electrons around the nucleus
• Based on the quantum model of the atom
# of electrons
1
H
=
1s
1
1st energy level
n=1
Orbital Notation
1H
Sublevel
Hund’s Rule
 states that 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.
Pauli exclusion principle
 Maximum 2 electrons can occupy a single orbital and
they must have opposite spins ( or ).
 No 2 atoms in the same atom can have the same 4
quantum numbers
Electrons in orbitals can be represented by arrows in boxes
Give the full electron configuration for. . .
Li
1s22s1
Na
1s22s22p63s1
K
1s22s22p63s23p64s1
The electrons in the outer most shell are
called the valence electrons. Electrons in the
inner shells are core electrons.
Electron Configuration
Example: sulfur has sixteen electrons.
Its electron configuration is written as
1s22s22p63s23p4
Shorthand Notation:
It can also be written as follows by using the previous
noble gas:
[Ne]3s23p4
Write the electron configuration for an atom whose atomic
number is 20.
atomic number = number of protons =
number of electrons = 20
According to the aufbau principle, the order of orbital filling is
1s,2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.
Or
refer to the periodic table
1s22s22p63s23p64s2
Abbreviated as follows:
[Ar]4s2
Try These
1. Try writing out the electron configuration for Potassium.
2. Write the electron Configuration for an atom with an
atomic number 20.
3. Write an electron configuration for an atom of an element
whose atomic number is 8.
4. Write an electron configuration for an atom of an element
whose atomic number is 53.
1. K = 1s22s22p63s23p64s1
2. Ca = [Ar]4s2
3. O = 1s22s22p4
4. I = [Kr] 5s2 4d105p5
What is the correct electron
configuration of a sulfur atom?
A. 1s22s22p43s23p6
B. 1s22s22p63s23p3
C. 1s22s22p63s23p4
D. 1s22s22p63s63p2
Drawing Molecules using Lewis Electron-Dot Structures
 Lewis structure: shows how the valence electrons are arranged
among the atoms in the molecule
 Valence electrons are represented by dots
 Nuclei and electrons of the inner energy level (if any) are
represented by the symbol of the element
Exceptional Electron Configurations
Cr 1s22s22p63s23p63d44s2
Cu 1s22s22p63s23p63d94s2
• The correct electron configurations are as follows:
Cr 1s22s22p63s23p63d54s1
Cu 1s22s22p63s23p63d104s1
• These arrangements give chromium a half-filled d sublevel and
copper a filled d sublevel.
Some actual electron configurations differ from those
assigned using the aufbau principle because although
half-filled sublevels are not as stable as filled sublevels,
they are more stable than other configurations.
How are the quantum mechanical
model and the Bohr model alike?
How are they different?
Like the Bohr model, the quantum mechanical model restricts the
energy of electrons to certain values. Unlike the Bohr model, the
quantum mechanical model does not specify an exact path the
electron takes around the nucleus.
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Calculate the maximum number of
electrons in the 5th principal energy
level (n = 5).
The maximum number of electrons that can occupy a principal energy
level is given by the formula 2n2. If n = 5, 2n2 = 50.
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How does Electron Configuration relate to the Periodic Table?
10
6
2
14
Explain why the correct electron
configuration of oxygen is 1s22s22p4
and not 1s22s22p33s1.
The 2p orbitals are lower in energy than
the 3s orbital, so they will be completely
filled before any electrons will be found
in the 3s orbital.
Frequency and Wavlength
 Light has two components:
Energy Levels in Atoms
The rungs on this ladder are somewhat like
the energy levels in Bohr’s model of the
atom.
• A person on a ladder
cannot stand between the
rungs. Similarly, the
electrons in an atom
cannot exist between
energy levels.
Energy Levels in Atoms
The rungs on this ladder are somewhat like
the energy levels in Bohr’s model of the
atom.
• The energy levels in atoms
are unequally spaced, like the
The higher energy levels are
closer together.
Light and Atomic Emission Spectra
A prism separates light into the colors it
contains. White light produces a rainbow
of colors.
Screen
Light
bulb
Slit
Prism
Light and Atomic Emission Spectra
Light from a helium lamp produces discrete lines.
Screen
Helium
lamp
Slit
Prism
Spectrum: wavelengths of visible light that are separated
when a beam of light passes through a prism; range of
Hydrogen’s Line-Emission Spectrum
Spectrum: wavelengths of visible light that are separated
when a beam of light passes through a prism; range of
An Explanation of Atomic Spectra
The three groups of lines in the hydrogen
spectrum correspond to the transition of
electrons from higher energy levels to lower
energy levels.
p orbitals are dumbbell-shaped
s orbitals are spherical
s
1 orientaion
Max e- = 2
p
3 orientaion
3 diff. orbitals
Max e- = 6
D
5 orientaion
5 diff. orbitals
Max e- = 10
f
7 orientaion
7 diff. orbitals
Max e- = 14
Quantum Mechanics
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states
that it is impossible to know both the velocity
and the position of a particle at the same time.
• This limitation is critical when dealing with
small particles such as electrons.
• But it does not matter for ordinary-sized objects
such as cars or airplanes.
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Reserved.
Quantum Mechanics
•
To locate an electron, you might strike it with a photon.
•
The electron has such a small mass that striking it with a photon affects its
motion in a way that cannot be predicted accurately.
•
The very act of measuring the position of the electron changes its velocity,
making its velocity uncertain.
Before collision:
A photon strikes
an electron
during an attempt
to observe the
electron’s
position.
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Reserved.
After collision:
The impact
changes the
electron’s velocity,
making it
uncertain.
Amplitude: the height of a wave’s crest
Wavelength ( ,lambda): distance between adjacent crests of a wave
Frequency (, nu): #of wave cycles to pass a given point per unit of time.
Electromagnetic spectrum
E=hν
Speed of light: 3  108 m/s in a vacuum.
Frequency and Wavelength
 Light has two components: wavelength (λ – read lambda) and
 Frequency and wavelength are inversely proportional (ν = 1/ λ )
λ↑
λ↓
ν ↓ E↓
ν↑ E↑
E=hν
Atomic emission spectrum: the pattern formed
when light passes through a prism or diffraction grating
to separate it into the different frequencies of light it
contains
 Each element has a unique line-emission spectrum
Emission spectrum of Hydrogen and Iron:
1st level = 1 orbital, shape is spherical (s)
1”s” orbital- (shape- spherical) (1s)
1 “s” orbital- (shape- spherical) (2s)
2nd level = 4 orbitals
3 “p” orbitals- (shape- dumbbell) (2p)
1 “s” orbital- (shape- spherical) (3s)
3rd level= 9 orbitals
3 “p” orbitals- (shape- dumbbell) (3p)
5 “d” orbitals- shape- most are four leaf clover (3d)
1”s” orbital- (shape- spherical) (4s)
4th level=16 orbital
3 “p” orbitals- (shape- dumbbell) (4p)
5 “d”orbitals- shape- most are four leaf clover (4d)
7 “f” orbitals- shapes are complicated (4f)
Atomic Orbitals
The numbers and types of atomic orbitals
depend on the principal energy level.
Summary of Principal Energy Levels and Sublevels
Maximum
number of
electrons
Principal
energy level
Number of
sublevels
n=1
1
1s (1 orbital)
2
n=2
2
2s (1 orbital), 2p (3 orbitals)
8
n=3
3
3s (1 orbital), 3p (3 orbitals),
3d (5 orbitals)
18
4
4s (1 orbital), 4p (3 orbitals),
4d (5 orbitals), 4f (7 orbitals)
32
n=4
Type of sublevel
Do Now
Ho does E, λ, ν change as the wave goes from A to B?
→
A.
B.
Do Now #1
Draw a picture of a wave with high frequency and low
frequency.
Label wavelength
Circle the wave with high energy
λ
low frequency.
λ
high frequency
The visible red light has a wavelength of
about 650 nm. At sunrise and sunset, red or
orange colors are present because the
wavelengths associated with these colors are
less efficiently scattered by the atmosphere
than the shorter wavelength colors (e.g.,
blue and purple). A large amount of blue
and violet light has been removed as a result
of scattering and the longwave colors, such
as red and orange, are more readily seen.
```