Ch 5 Electrons in Atoms
Light and
Quantized
Energy
Light
• The study of light led to the development of the
quantum mechanical model
• Light is a kind of electromagnetic radiation
• Electromagnetic radiation includes many kinds
of waves
• All move at 3.00x108 m/s or 3.00x1010 cm/s
(abbreviated: c)
c = ln
Parts of a wave
Parts of a Wave
•
•
•
•
•
Origin - the base line of the energy
Crest - high point on a wave
Trough - low point on a wave
Amplitude - distance from origin to crest
Wavelength – shortest distance between
equivalent points on a continuous wave
l
• abbreviated
= Greek letter lambda
• Usually measured in meters, or in the case of
electromagnetic radiation, nanometers (1 nm =
1x10-9m)
Frequency
• The number of waves that pass a given
point per second.
• Units are cycles/sec, 1/s, s-1 or hertz (Hz)
• Abbreviated n
- the Greek letter “nu”
Frequency and
Wavelength
• Inversely related
• As one goes up the other goes down.
• Different frequencies of light are
different colors of light.
• There is a wide variety of frequencies
• The whole range is called a spectrum
Electromagnetic Spectrum
High
Low
energy
energy
Radio Micro Infrared
Ultra- XGamma
waves waves
violet Rays Rays
Low
High
Frequency
Frequency
Long
Short
Wavelength
Wavelength
Visible Light
Wave Equation
Example Problems
• A light has a wavelength of 550 nm. What
is its frequency?
5.45x1014Hz
• A light has a frequency of 4.25x1014 Hz.
What is its wavelength in nanometers?
What about meters?
706 nm
7.06x10-7m
Particle Nature of
Light
• Understanding light as a wave does not
explain all of light’s interactions with matter.
• People knew that when you heat up some
objects they change to specific colors
• Ex: Heating up an electric stove top burner.
• As the metal gets hotter it has more energy and
gives off different colors
• 1900, German physicist Max Planck started
researching a way to explain this
phenomenon
Light is Quantized
Energy
• Energy is quantized.
• It can be lost or gained only in specific amounts.
• Light is energy.
• Therefore light must be quantized.
• Matter can only gain or lose energy in these specific
amounts called quanta (plural for quantum)
• A quantum is the certain amount of energy that can
be gained or lost by an atom.
• You cannot have amount that are fractions of a quantum.
• Think about walking up stairs – you cannot walk up or down
a fraction of a stair
Energy and
Frequency
• Max Planck developed a way to describe this
property of light mathematically.
• Energy and frequency are directly related
• E = hn
• E is the energy of the quantum (Units of Joules)
• n is the frequency (Units of Hz)
• h is Planck’s constant; h = 6.626 x 10 -34 Js
Einstein used this theory to explain why
metals (and some semi-metals) will
eject e- from the surface when light of
specific a frequency hits it.
• This is called the photoelectric effect
• Used with solar panels
• The metal will not eject the e- if the
frequency is too low.
• The energy has to reach a threshold
frequency (minimum amount) for that
particular substance
Einstein’s Idea
• 1905, Einstein went on to further say
that light is made of particles
• These smallest pieces (particles) of
“electromagnetic radiation” (light) are
called photons and carry a quantum of
energy
• Light can act as both waves and
particles = wave-particle duality of light
Example 1
• What is the energy of a photon of radiation
with a frequency of 7.23 x 1014 Hz?
E = 4.79 x 10 -19 J
Example 2
• What is the energy of a photon of radiation
with a frequency of 6.32 x 1020 Hz?
E = 4.19 x 10 -13 J
Example 3
• What is the frequency of a photon of radiation with
an energy of 6.96 x 10 -18 J? If a metal needs an
energy of 5.45 x 10-17 J to emit electrons will it
happen with this photon?
n = 1.05 x 1016 Hz
Example 4
• What is the energy of a photon with a
wavelength of 4.00 x 10-7 m?
E = 4.97 x 10-19J
Atomic Spectra
How light & color tells us about atoms
Prism
• White light is made
up of all the colors
of the visible
spectrum.
• Passing it through
a prism separates
it.
If the light is not white
• By electrifying a gas
(like Neon) or exciting
other elements with
enough energy
scientists can get it to
give off colors.
• Passing this light
through a prism or
diffraction grating
does something
different.
Atomic Spectrum
• Each element gives
off its own
characteristic colors.
• Can be used to
identify the atom.
• Like “atomic
fingerprints”
• Used to I.D. elements
stars are made of
• Used to I.D. unknown
elements in
compounds
Atomic Spectrum
• Color is given off only
when electrons are
LOSING energy so
they can return to a
more stable state
• These are called
Line Spectra
• Made from
emission of light
(also called
emission spectra)
• Unique to each
http://jersey.uoregon.edu/elements/Elements.html
element.
5.2
Quantum Theory & The Atom
An explanation of Atomic Spectra
Bohr’s Model
• Niels Bohr – Danish physicist – proposed
model to explain the emission spectra of
elements – 1922 received Nobel Prize in
Physics
• Electrons move like planets around the
sun in circular orbits at different levels.
• Energy separates one level from another.
• The smaller the orbit, the lower the energy
Bohr’s Model
Nucleus
Electron
Orbit
Energy Levels
Bohr’s Model
Increasing energy
Fifth
Fourth
Third
Second
First
Nucleus
 Further away from
the nucleus the
electron is means
it has more energy.
 There is no “in
between” energy
 Chemists call
these the
electrons’
Energy Levels
Where the electron
starts
The energy level an electron starts from
is called its ground state.
• Let’s look at a hydrogen atom
Electron’s
ground
state
Changing the energy
• Heat, electricity or light can move the
electron up energy levels
• How much it moves depends on amount of
energy absorbed
• As the electron falls back to ground state it
gives the energy back as light.
• Electrons may fall down in steps
• Each step has a different energy
Hydrogen atom’s atomic
n=4
emission
n=3
n=2
n=1
36
Getting these wavelengths you can
calculate the Energy
• We can calculate the energy the electrons
had:
DE = E high-energy orbit – E lower-energy orbit
• Don’t forget that E=hn
• Further the e- fall, the more energy, so
higher frequency.
• The electrons can emit or absorb only
certain amounts of energy
There is one issue with this model:
• Unfortunately this model’s calculations
ONLY worked for Hydrogen b/c Bohr didn’t
understand how electrons actually moved in
an atom
The Quantum Mechanical
Model of the Atom is born!
• Bohr model was fixed by Louis de
Broglie (French physicist - 1924)
• The electron is treated mathematically
as a wave.
• The energy levels are described in
terms of the probability of locating the
electron in a region of space outside the
nucleus.
The de Broglie Equation
• de Broglie came up with l = h/mv
 l = wavelength, h = Planck’s constant, m =
mass, and v = velocity (m/s)
• He decided that since waves can act like
particles why couldn’t particles act like waves?
• The equation finds the wavelength of a
particle.
Matter can behave like a Wave
- that’s what Einstein said!
• But it does not apply to things bigger than an
atom
• A major league baseball (0.142 kg) has a
wavelength of about 10-32 m when moving 30 m/s
• Too small to measure
• An electron (9.109x10-31kg) at the same speed has
a wavelength of 10-3 cm
• Big enough to measure.
The physics of the very
small
• Quantum mechanics explains how the
very small behaves.
• Quantum mechanics is based on
probability because…
• It is impossible to know exactly the speed and
position of a particle at the same time.
• The better we know one, the less we know
the other.
• The act of measuring changes the properties
for tiny objects.
• This fact is called:
Heisenberg Uncertainty
Principle
• To measure where a electron is, we use
light.
• But the light moves the electron
• And hitting the electron changes the
frequency of the light.
• See the next slide
Before
Photon
Moving
Electron
After
Photon
changes
wavelength
Electron
changes velocity
The Quantum Mechanical
Model
• Austrian physicist Erwin
Schrödinger derived a mathematical
equation whose solutions describes
the probability of finding an electron a
certain distance from the nucleus.
• Again he treated electrons as waves
• Called the solutions quantum numbers
Schrodinger is given credit for:
The Quantum Mechanical
Model
• It does have energy levels for electrons.
• It does not have orbits.
• It has orbitals.
The Atomic Orbital:
• The electron is found
inside a blurry “electron
cloud”
• A 3-D area where there is
a 90 % chance of finding
an electron around the
nucleus.
• They have different
energies, sizes and
shapes
Principal Quantum Number
• Given n quantum number
• Tells principal energy levels
• Tells relative sizes and energies of orbitals
• As n increases, orbital size increases & energy
level increases
• Right now we are up to 7 energy levels
with values of 1 – 7
• Always whole numbers
• The maximum number of electrons in any
principal energy level is 2n2
Energy sublevels
• These are given the quantum number l
• The number of sublevels in any principal
energy level is equal to the value of the
principal quantum number
• So the 1st principal energy level has 1 sublevel =
s-sublevel
• The 2nd principal energy level has 2 sublevels = ssublevel and p-sublevel
• Sublevels are labeled s, p, d, or f depending
on the shape of the orbitals
Orbitals
• Quantum number, m
• These give the orientation of the
electron in space
• Each individual orbital can only hold a
maximum of 2 electrons
s-orbitals
• There is one s-orbital for every energy level
• Spherical
shaped
• Each s orbital can hold a maximum of 2
electrons
• Called the 1s, 2s, 3s, etc.. orbitals.
p-orbitals
•
•
•
•
Start at the second energy level
3 different directions
3 different shapes (dumbell or propeller)
Each orbital can hold a maximum of 2
electrons
p-orbitals
This is a
picture of all 3
p-orbitals
overlapped
d-orbitals
• Start at the third energy level
• 5 different shapes
• Each can hold up to 2 electrons
f-orbitals
• Start at the fourth energy level
• Have seven different shapes
• 2 electrons per shape
f-orbitals
Images
J mol
Summary
# of orbital Max. # of
shapes electrons
Starts at
energy level
s
1
2
1
p
3
6
2
d
5
10
3
f
7
14
4