Ch 5 - Electrons in Atoms
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Transcript Ch 5 - Electrons in Atoms
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 Js
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