The Evolution of
the Atomic
Model
Rutherford - Einstein
What We Learned Last Class…

Rutherford modified
Thomson’s model as
follows:

Assume the atom is
spherical but the
positive charge must
be located at the
center, with a diffuse
negative charge
surrounding it
Rutherford and the Nuclear
Atom

Rutherford’s model became known as the
“planetary model”


The “sun” was the positively-charged dense
nucleus and the negatively-charged
electrons were the “planets”
Further experiments with alpha radiation
led to the disintegration of the nuclei of
nitrogen atoms

One of the products was a “new” positivelycharged subatomic particle – the proton!
But Wait – There’s More!
 James
Chadwick was a
student of Rutherford
 He realized that the atomic
mass of most elements was
double the number of
protons

This lead to the discovery of a
neutral (uncharged) particle in
the nucleus


Called it the “neutron”
He opened a new era in nuclear
physics research – more on this
later!
4
A Summary of What We Know
So Far….
 The
atom consists of positive, negative,
and neutral entities (protons, electrons,
and neutrons)
 Protons and neutrons are located in the
nucleus of the atom, which is small
 There
can be a variable number of neutrons
for the same number of protons – isotopes!
 Isotopes
have the same number of protons
but different numbers of neutrons
 Electrons
nucleus
are located outside of the
Important Definitions to Know
 Atomic

Number of protons in the nucleus
 Mass

number (Z)
number (A)
Total number of nucleons in the nucleus (i.e., protons
and neutrons)
 Isotopes
have the same Z but different A!
The Evolution of the Atomic
Model and Its Tie to Energy
The Planetary Model is
Doomed!
 The
classical laws of motion and gravitation could
easily be applied to neutral bodies like planets, but
NOT to charged bodies such as protons and
electrons
 According to classical physics, an electron in orbit
around an atomic nucleus should emit energy in
the form of light continuously (like white light)
because it is continually accelerating in a curved
path

Like a satellite orbiting Earth
Why Doesn’t the Model Work?
 Resulting
loss of energy implies that the electron
would necessarily have to move close to the
nucleus due to loss of potential energy

Eventually, it would crash into the nucleus and the
atom would collapse!
WAIT…What?!
Electron crashes into the nucleus!?
Since this does not happen, the Rutherford
model could not be accepted!
Electron Behavior and Atomic
Structure



As you can see, scientists discovered that the
absolutely small (quantum) world of the electron
behaves differently than the large (macroscopic) world
that we are used to observing
Before we explore electrons and their behavior within
the atom, we must understand a few things about light
This is because much of what has been learned about
atomic structure has come from observing the
interaction of light with matter


In doing so, light was (surprisingly) found to have many
characteristics in common with electrons
Therefore, an understanding of light would be helpful at
this point!
So, What Exactly is Light?
 James
Maxwell developed the classical wave
theory of light in 1864

This is a mathematical theory that describes all forms
of radiation (light) in terms of electromagnetic
radiation
 EM
radiation is formally defined as a wave-like form
of energy that is composed of oscillating, mutually
perpendicular electric and magnetic fields
propagating through space

EM radiation does not require a medium to travel
through
Some Properties of EM
Radiation
 An
EM wave, like all waves, can be characterized
by the following properties:

Amplitude (A)


Wavelength (λ)



Half of the vertical distance from the top to the bottom of a
wave
Distance between two consecutive peaks or troughs in a
wave
Measured in meters (SI system)
Frequency (ν)


Number of waves that pass a given point per second
Measured in hertz (sec-1)
Waves
y axis
Wavelength (λ)
Amplitude (A)
-
Nodes
+
+
+
-
-
Frequency (ν) 3.5 waves/s
x axis
Relationships of EM Wave
Properties
 In
a vacuum, all of types of EM radiation move
at a constant speed of 3.00 x 108 m/s, which is
symbolized by the letter “c”
 Wavelength and frequency are related via the
speed of light in a vacuum (c)
 In order to keep speed constant, wavelength
and frequency of light must be inversely
proportional to each other
c = λ· ν


As wavelength increases, frequency decreases
As wavelength decreases, frequency increases
The Electromagnetic
Spectrum


There are many types of electromagnetic radiation
including visible light, radio waves, infrared radiation,
and x-rays
Why do different types of electromagnetic radiation
have different properties?

Because they have different wavelengths!

As a result, the energy associated with each type of
radiation is different


As wavelength decreases, the energy of radiation increases
The various types of EM radiation can be arranged in
order of decreasing wavelengths via the
electromagnetic spectrum
Let’s Take a Closer Look at the
EM Spectrum!
Electromagnetic Spectrum
The Electromagnetic
Spectrum
 As
you learned, the electromagnetic spectrum is
the range of all possible frequencies (or
wavelengths) of electromagnetic radiation
 The highest energy form of electromagnetic
waves is gamma rays and the lowest energy form
is radio waves
 In a vacuum, every electromagnetic wave has a
velocity (speed) of 3.00 x 108 m/s
 Speed
of light in a vacuum is a constant which means
that ALL ELECTROMAGNETIC RADIATION TRAVELS AT THIS
SPEED!
Relationship of EM Wave
Properties
Watch This Khan
Academy Video!
What’s the Matter with
Light?
The Nature of Matter
 By
the end of the 19th century, physicists
were feeling rather smug

They thought that all of physics had been
explained and that matter and energy
were two distinct entities:
 Matter
was a collection of particles
 Energy was a collection of waves
The Problem with Light as a
Wave
 Although
the wave model of light explains many
aspects of the behavior of light, several
observations could not be resolved by this
model:

Blackbody radiation
 Referred
to as blackbody radiation because objects
appeared black before they were heated


The photoelectric effect
Elements in gaseous form emit light when electricity
passes through them
What is Blackbody Radiation?
 Any
object with a temperature above absolute
zero emits light at all wavelengths
 If the object is perfectly black (so it doesn’t reflect
any light), then the light that comes from it is called
blackbody radiation
 During the late 1800s, many physicists studied
blackbody radiation, trying to understand the
relationship between temperature and the
intensity and wavelength of the emitted radiation
What’s Wrong with Blackbody
Radiation and Classical Physics?
 According
to classical physics, there should be no
limit to the energy of light produced by the
electrons vibrating at high frequencies
 However, the emission of light from hot elements in
the solid form did not emit all forms of radiation as
predicted

A red-hot object is cooler than a yellowish or a whitehot one
 Around
the year 1900, a physicist named Max
Planck solved the “Ultraviolet Catastrophe” with
an incredible assumption…
Let’s Read Planck’s
Obituary!
Planck and Quanta

Max Planck assumption about blackbody radiation
was:


Energy is not shared equally by electrons that vibrate with
different frequencies
Instead, energy comes in discrete “chunks” called
quantum (meaning “fixed amount”)


The size of quantum depends on the frequency of vibration of
electron
To understand quantization, consider walking up a
ramp versus walking up the stairs

For the ramp, there is a continuous change in height
whereas up stairs, there is a quantized change in height
Planck’s Idea of Quantized
Energy

Mathematically, a quantum (packet) of energy is
given by:

h = Planck’s constant = 6.626 x 10-34 J· s
 ν is the lowest frequency that can be absorbed or
emitted by the atom
Planck determined that all amounts of energy are a
multiple of a specific value, h
 Planck’s constant, h, can be thought of just like a penny
 This is the same as saying that all currency in the US is a
multiple of the penny

Relating Blackbody Radiation
to Quanta


According to Planck’s theory, matter can emit and
absorb energy only in whole-number multiples of hν,
such as hν, 2hν, 3 hν, and so forth
In other words, there is no such thing as a transfer of
energy in fractions of quanta

Only whole numbers of quanta
 So,
the electron has to have at least one quantum
of energy if it is going to vibrate


If it doesn’t it will not vibrate at all and can’t produce any
light
On the other hand at high frequencies, the amount of
energy in a quantum, hf, is so large that the vibrations
can never get going
Einstein and Quanta
A
few years after Planck presented his
quantum theory, scientists began to see
its applicability to many experimental
observations
 For example, Einstein used Planck’s idea
of energy quanta to understand the
photoelectric effect
What is the Photoelectric
Effect?
•
Remember, electrons are attracted to the (positively
charged) nucleus by the electrical force
•
In metals, the outermost electrons (valence electrons) are
not tightly bound, and can be easily “liberated” from the
shackles of its atom
•
•
It just takes sufficient energy
If light was really a wave, it was thought that if one shined
light of a fixed wavelength on a metal surface and varied the
intensity (made it brighter and hence classically, a more
energetic wave), eventually, electrons should be emitted
from the surface
Photoelectric Effect
“Classical” Method
Increase energy by
increasing amplitude
What if we try this ?
Vary wavelength, fixed amplitude
electrons
emitted ?
No
No
No
No
electrons
emitted ?
No
Yes, with
low KE
Yes, with
high KE
• No electrons were emitted until the frequency of the light exceeded
a critical frequency, at which point electrons were emitted from the
surface!
(Recall: small l  large n)
Photoelectric Effect Animation
Einstein’s Theory of Quantized
Light

If Planck’s idea that energy comes in quanta is correct,
then Einstein proposed that light must consist of a
steam of clumps of energy


Each clump of light energy is called a photon
Each photon carries an amount of energy that is given
by Planck’s equation
Ephoton = hν =

hc
λ
So, if the energy of the “light particle” is related to their
frequency, this would explain why higher frequency
light can knock the electrons out of their atoms, but
low frequency light cannot
In Summary…
•
•
Therefore, the energy of light is not evenly
distributed along the wave, but is concentrated in
the photons
The classical method of increasing the amplitude
of light was simply increasing the number of light
particles NOT increasing the energy of each one!
Practice!

Determine the energy, in kJ/mol of photons of
blue-green light with a wavelength of 486nm
Ephoton = hν =
=
hc
λ
(6.626 x 10-34 J.s)(2.998 x 108 m.s-1)
(4.86 x 10-7 m)
= 4.09 x 10-19 J / photon
Practice!

We now need to determine the energy for a mole
of photons (6.02 x 1023)
= (4.09 x 10-19 J / photon)*(6.02 x 1023 photons/mol)
= 246, 000 J/mol

Finally, convert to kJ
= ( 244 000 J/mol )
= 244 kJ / mol
1 kJ
103 J
Revisiting the Photoelectric
Effect Again…

How can a photon (which has no mass) knock an
electron (that does have mass) about?


You know Einstein for the famous E = mc2
Einstein used this theory of relativity to show that even
massless photons have momentum
Newton defined momentum = mv for a particle with mass,
but Einstein was able to show the momentum of a massless
photon depends on its wavelength
Rearranging Einstein’s equation and substituting in Planck’s
equation:


E hc/λ h
m= 2= 2 =
c
c
cλ
h
p=
×v
cλ

Hence, the smaller the wavelength, the greater the
momentum of the photon, the easier it is to knock an
electron
Confirming Einstein’s Particle
Theory of Light

So, does a photon has mass?


Yep!
In 1922, Arthur Compton performed experiments involving
collisions of X-rays and electrons that showed photons do exhibit
the apparent mass calculated above!
A Summary of Light as a “Waveicle”

Light travels through space as a wave


We can also treat a large number of photons
as a wave on the macroscopic scale
Light transmits energy as a particle

Each photon carries an amount of energy
that is given by Planck’s equation
Ephoton

hc
= hν =
λ
When dealing with subatomic phenomenon, we
are often dealing with a single photon, or a few
so the particle nature applies as well!
So is Light a
Wave or a
Particle ?
The Dualism of Light
 Dualism
is not such a strange concept
 Consider the following picture

Are the swirls moving, or not, or both?
Watch This Khan
Academy Video!
Then Watch This One!
Time for Practice!