Download Chapter 12 - Bruder Chemistry

Chapter 6
Wavelength
Light
• The study of light led to the development
of the quantum mechanical model.
• Light is a kind of electromagnetic
radiation.
• In Wave Model, Light is considered to
consist of electromagnetic waves that
travel in a vacuum @ speed of
3.00 x 108 m/s
• Electromagnetic radiation includes many
kinds of waves
• All move at 3.00 x 108 m/s ( c)
ER
•
•
1.
2.
3.
4.
5.
6.
7.
•
Electromagnetic Radiation – forms of energy that exhibits
wavelight behavior as it travels thru space
Examples of Electromagnetic Radiation:
Radio Wvaes
Microwaves
Infrared
Visible Light
Ultraviolet
X-Rays
Gamma Rays
ER has measurable wave properties of wavelength and
frequency
Parts of a wave
Crest
Wavelength
Amplitude
Orgin
Trough
Parts of Wave
• Orgin - 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 - distance from crest to crest
• Wavelength - is abbreviated l Greek letter
lambda.
Frequency
• The number of waves that pass a given
point per second.
• Units are cycles/sec or hertz (hz)
• Abbreviated n the Greek letter nu
c = ln
Frequency and wavelength
• Are inversely related
• As one goes up the other goes down.
• Different frequencies of light is different
colors of light.
• There is a wide variety of frequencies
• The whole range is called a spectrum
• Frequency and Wavelength are
mathematically related, they are inversely
related
• The relationship is shown by the following
equation:
• c = ln
• c= speed of light
l= Wavelength
• Long Wavelength
=
Low Energy
Low Frequency
• Short Wavelength
=
High Energy
High Frequency
High
Low
energy
energy
Radio Micro Infrared
Ultra- XGamma
waves waves .
violet Rays Rays
Low
High
Frequency
Frequency
Long
Short
Wavelength
Wavelength
Visible Light
Calculating Light
• What is the wavelength if light with a
frequency of 5.89 x 105 Hz?
• What is the frequency of blue light with a
wavelength of 484 nm?
H.W. Questions
1. List 5 examples of E.R.
2. What is the speed of all forms of E.R. in a
3.
4.
5.
vacuum
Relate Frequency and Wavelength
The speed of light is 3.00 x 108 m/s and the
frequency is 7.500 x 1012 Hz. Calculate the
Wavelength of E.R.
Determine the frequency of light w/ a
wavelength of 4.257 x 10-7 cm.
Atomic Spectrum
How color tells us about atoms
Spectrum
• Spectrum- Range of wavelengths of E.R.,
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•
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•
wavelengths of visible light are separated when
a beam of white light passes thru a prism
Example of Spectrum
Rainbow (also a phenomenon)
Each droplet of water acts as a prism to produce
a spectrum
Each color blends into the next color.
Colors of the Spectrum
•
1.
2.
3.
4.
5.
6.
7.
•
Colors of the Spectrum:
Red (Longest Wavelength & Lowest Frequency)
Orange
Yellow
Green
Blue
Indigo
Violet (Shortest Wavelength & Highest Frequency)
These colors are known as the visible part of the
spectrum
Prism
• White light is made
•
up of all the colors
of the visible
spectrum.
Passing it through a
prism separates it.
Diffraction
• When light passes through, or reflects off,
a series of thinly spaced line, it creates a
rainbow effect
• because the waves interfere with each
other.
A wave
moves toward
a slit.
Comes out as a curve
with two holes
with two holes
Two Curves
with two holes
Two Curves
Interfere with
each other
with two holes
Two Curves
Interfere with
each other
crests add up
Several waves
Several waves
Several Curves
Several
Severalwaves
waves
Several Curves
Interference
Pattern
Spectroscopic analysis of the visible spectrum…
…produces all of the colors in a continuous spectrum
If the light is not white
• By heating a gas
•
•
with electricity we
can get it to give off
colors.
Passing this light
through a prism
does something
different.
More on that Later
Quantum Concept
• Laws of Physics state no limits on how
much or how little energy can be gained
or lost.
• Classic physics assumed atoms and
molecules could emit any arbitrary amount
of radiant energy.
• Does not explain the Emission Spectrum
of Atoms
Max Plank
• Tried to explain why the body changed colors as
•
•
it heated.
He could only explain the change if assumed
energy of the body changes in small discrete
units (brick by brick).
Plank showed mathematically that the amount of
radiant energy, absorbed or emitted by a body is
proportional to the frequency of radiation
Plank’s Quantum Concept
• Plank went against classic physics
• Stated: atoms and molecules could emit
energy only is discrete quantities, like
small packages or bundles
• Quantum- smallest quantity of energy that
can be emitted in the form of E.R.
• The energy of a single quantum is given
by E = hν
Planck’s Quantum Theory Cont.
• According to theory, energy is always
emitted in multiples of hν.
• Example: 2hv, 3hv, ect…..
• Never in 1.67hv and so on
• Could not explain why energies are fixed
but explained the emission of solids over
the entire range or wavelengths.
Energy and frequency
•
•
•
•
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•
E=hxn
E is the energy of the photon
n is the frequency
h is Planck’s constant
h = 6.6262 x 10 -34 Joules sec.
joule is the metric unit of Energy
Examples
• What is the wavelength of blue light
15
10
with a frequency of 8.3 x
hz?
• What is the frequency of red light with
a wavelength of 4.2 x 10-5 m?
• What is the energy of a photon of each
of the above?
Solving for photons
• Calculate the energy of:
• A) photon with a wavelength 5.00 x 104
nm (infrared region)
• B) photon with a wavelength of 5.00 x 102
nm (X ray region)
Einstein and Photoelectric Effect
• 5 years later Einstein used Planck’s theory
to derive the Photoelectric Effect
• Photoelectric Effect- a phenomenon in
which electrons are ejected from the
surface of certain metals exposed to light
of at least a certain minimum frequency
• Threshold Frequency
Photoelectric Effect
• Number of electrons ejected was proportional to
•
•
the intensity (brightness) of the light, but the
energies of the electrons were not.
Below the threshold frequency no electrons were
ejected no matter how intense the light.
Could not be explained by the wave theory of
light.
Photoelectric cont.
• Einstein proposed:
• That a beam of light is really a stream of
•
•
•
particles.
Particles of light are now called Photons.
Used Planck’s equation to determine:
Electrons are held in a metal surface by
attractive forces, and removing them from the
metal requires light of a sufficiently high
frequency ( which corresponds to sufficiently
high energy) to break them free.
• Shining a beam of light onto a metal
surface can be though as shooting a beam
of particles/photons at the metal atoms.
• Frequency of photons = binding energy,
then light will have just enough energy to
knock them free
• What if the frequency is higher?
Photoelectric cont.
• If frequency is stronger they will acquire
some K.E. and be knocked loose.
• KE = hv – BE
• Shows more energetic the photon, greater
the K.E. of the ejected electron.
Wave-Particle Duality
JJ Thomson won the Nobel prize for describing the
electron as a particle.
His son, George Thomson won the Nobel prize for
describing the wave-like nature of the electron.
The
electron is
a particle!
The
electron is
an energy
wave!
Light is a Particle
• Energy is quantized.
• Light is energy
• Light must be quantized
• These smallest pieces of light are called
photons.
• Energy and frequency are directly related.
Energy Change
• The size of an emitted or absorbed
Quantum depends on the size of the
energy change.
• Ex.
A.Small energy change involves emission or
absorption of low frequency radiation.
B.Large energy change involves emission or
absorption of high frequency radiation.
The Math in Chapter 12
• Only 2 equations
• c = ln
• E = hn
• Plug and chug.
An explanation of Atomic
Spectra
Atomic Spectrum
• Each element gives
•
•
off its own
characteristic colors.
Can be used to
identify the atom.
How we know what
stars are made of.
Atomic Emission Spectrum
• Atomic Emission Spectrum- it passes light emitted by an element
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thru a prism
Atoms first absorb energy and then lose energy as they emit light
Each line in the emission spectrum corresponds to one exact
frequency of light being given off or emitted by an atom.
The light emitted by an electron moving from a higher to lower
energy level has a frequency directly proportional to the energy
change of the electron
Therefore each line corresponds to one exact amount of energy
being emitted.
Emission Spectrum of each element is unique to that element.
The emission spectrum is obtained by an instrument called Emission
Spectrograph
• These are called
discontinuous
spectra
• Or line spectra
• unique to each
element.
• These are
emission spectra
• The light is
emitted given off.
Where the electron starts
• When we write electron configurations we are writing
•
•
the lowest energy.
The energy level and electron starts from is called its
ground state.
If the energy levels are quantized, it takes Quantum
Energy (E = hn) to raise an electron from ground state to
excited state.
• Same amount of energy is emitted as a photon when the electron
drops from the excited state to the ground state.
• Only electrons in transition from higher to lower energy
levels lose energy and emit light.
• Electron transitions
•
involve jumps of
definite amounts of
energy.
This produces bands
of light with definite
wavelenghts
Emission Spectrum of Hydrogen
• Transition
• n = ¥ to n = 2
n
n
n
•n
n
=
=
=
=
=
7
6
5
4
3
to
to
to
to
to
n
n
n
n
n
=
=
=
=
=
2
2
2
2
2
Wavelength l (nm)
361
396
409
433
485
655
Changing the energy
• Let’s look at a hydrogen atom
Changing the energy
• Heat or electricity or light can move the
electron up energy levels
Changing the energy
• As the electron falls back to ground state it
gives the energy back as light
Changing the energy
• May fall down in steps
• Each with a different energy
Ultraviolet
Visible
Infrared
• Further they fall, more energy, higher
•
•
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frequency.
This is simplified
the orbitals also have different energies
inside energy levels
All the electrons can move around.
We are worried about the
change
• When the electron moves from one energy level
to another.
 DE = Efinal - Einitial
 DE = -2.178 x 10-18 J Z2 (1/ nf2 - 1/ ni2)
• Rydberg’s constant and it allowed the calculation
of the wavelengths of all the spectral lines of
hydrogen.
Calculating Energy Problems
• What is the energy of the photon emitted
when the electron in a hydrogen atom
drops from the energy level n=5 to
following:
• A) n=2
• B) n=3
More Energy Problems
• How much energy must a hydrogen atom
absorb to raise its electron from the
energy level n=1 to the following:
• A) n=2
• B) n=4
Positive or Negative
• When raising an electron the amount of
energy is always positive. Why?
• When an electron drops the amount of
energy is always negative. Why?
Calculating Wavelength of Photon
• First determine ∆E
• Then plug into:
• λ= c h / ∆E
• What is the wavelength (in nm) of a
photon emitted during a transition from ni
= 6 to nf = 4
What is light
• Light is a particle - it comes in chunks.
• Light is a wave- we can measure its wave
•
•
•
length and it behaves as a wave
If we combine E=mc2 , c=ln, E = 1/2
mv2 and E = hn
We can get l = h/mv
The wavelength of a particle.
Matter is a Wave
• Does not apply to large objects
• Things bigger that an atom
• A baseball has a wavelength of about 1032 m when moving 30 m/s
• An electron at the same speed has a
wavelength of 10-3 cm
• Big enough to measure.
Calculating Wavelength of a
Particle
• 1) Calculate the wavelength of a particle
in:
• A) The fastest serve in tennis is about
140 miles per hour, or 63 m/s. Calculate
the wavelength associated with a
6.0 x 10-2 kg tennis ball traveling at this
speed. What color would be produced?
• B) Calculate the wavelength associated
with an electron (9.1094 x 10-31 kg)
moving at 63 m/s
• Which color would be produced?
The Wave-like Electron
The electron propagates
through space as an energy
wave. To understand the
atom, one must understand
the behavior of
electromagnetic waves.
Louis deBroglie
The physics of the very small
• Quantum mechanics explains how the
very small behaves.
• Classic physics is what you get when you
add up the effects of millions of packages.
• Quantum mechanics is based on
probability because
More obvious with the very
small
• 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.
Before
Photon
Moving
Electron
After
Photon
changes
wavelength
Electron
Changes
velocity
• “One cannot
•
simultaneously
determine both the
position and
momentum of an
electron.”
“One cannot
simultaneously
determine both the
position and
momentum of an
electron.”
Heisenberg Uncertainty
Principle
• It is impossible to know exactly the position and
•
•
•
velocity (momentum) of a particle.
The better we know one, the less we know the
other.
The act of measuring changes the properties.
More precisely the velocity is measured, less
precise is the position (vice versa).