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Atomic Physics -2
Atomic Spectra
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Fill a glass tube with pure atomic gas
Apply a high voltage between electrodes
Current flows through gas & tube glows
Color depends on type of gas
Light emitted is composed of only certain wavelengths
Atomic Spectra
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Emission Spectrum: diagram or graph that indicates the
wavelengths of radiant energy that a substance emits
(bright lines)
Absorption Spectrum: same thing, just for light absorbed
by a substance (dark lines)
What does this have to do with atomic models?
Energy Levels & Emission Spectra
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Lowest energy state: ground state
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Radius of this state: Bohr radius
Electrons usually here at ordinary temps
How do electrons “jump” between states?
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Absorb photon with energy (hf) exactly equal to energy
difference between ground state & excited state
Absorbed photons account for dark lines in absorption
spectrum
Energy Levels & Emission Spectra
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Spontaneous emission:
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Electron in excited state
jumps back to a lower energy
level by emitting a photon
Does NOT need to jump all
the way back to the ground
state
Emitted photon has energy
equal to energy difference
between levels
Accounts for bright lines on
emission spectrum
Jumps between different
energy levels correspond to
various spectral lines
Photon Energy

The equation for determining the energy of
the emitted photon in any series:

 1
1
E = 13.6 eV 2 − 2 
ni 
 nf
Balmer Wavelengths
The Balmer Series

In the Balmer Series
nf = 2
 There are four prominent wavelengths
 656.3 nm (red)
 486.1 nm (green)
 434.1 nm (purple)
 410.2 nm (deep violet)

The Balmer Series Wavelength
Equation

RH is the Rydberg constant
1
1
= R H 2 − 2 
λ
 2 ni 
1
RH = 1.0973732 x 107 m-1
Two Other Important Series
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Lyman series (UV)
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nf = 1
Paschen series (IR)
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nf = 3
Different Elements = Different
Emission Lines
Emission Line Spectra
So basically you could look at light
from any element of which the
electrons emit photons. If you
look at the light with a diffraction
grating the lines will appear as
sharp spectral lines occurring at
specific energies and specific
wavelengths. This phenomenon
allows us to analyze the
atmosphere of planets or galaxies
simply by looking at the light
being emitted from them.
The Absorption Spectrum
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An element can absorb the same wavelengths
that it emits.
The spectrum consists of a series of dark lines.
Energy levels Application:
Spectroscopy
Spectroscopy is an optical technique by which we can
IDENTIFY a material based on its emission spectrum. It is
heavily used in Astronomy and Remote Sensing. There are
too many subcategories to mention here but the one you
are probably the most familiar with are flame tests.
When an electron gets excited inside a
SPECIFIC ELEMENT, the electron
releases a photon. This photon’s
wavelength corresponds to the energy
level jump and can be used to indentify
the element.
Identifying Elements
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The absorption spectrum was used to
identify elements in the solar atmosphere.
 Helium
was discovered.
Thermal vs. Atomic Spectra
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How could you tell if the light from a
candle flame is thermal or atomic in origin?
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If the spectrum is continuous, the source
must be thermal.
Three Types of Spectra
Three Types of Spectra
(continued)
Three Types of Spectra
(continued)
Quantum Numbers
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Set of 4 numbers which identify an electron.
Principal quantum number
n 1-7
sublevel quantum number
l spdf
orientation quantum number m
spin quantum number
s +-
Four Quantum Numbers

The state of an electron is specified by four
quantum numbers.
These numbers describe all possible electron states.
 The total number of electrons in a particular energy
level is given by:

# = 2n
2
Principle Quantum
Number
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The principal quantum number (n) where n
= 1, 2, 3, …
Determines the energy of the allowed states of
hydrogen
 States with the same principal quantum number are
said to form a shell
 K, L, M, … (n = 1, 2, 3, …)
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Orbital Quantum Number
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The orbital quantum number (l) where l
ranges from 0 to (n – 1) in integral steps
Allows multiple orbits within the same energy level
 Determines the shape of the orbits
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States with given values of n and l are called
subshells
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s (l = 0), p (l = 1), d (l = 2), f (l = 3), etc…
Electron Subshells
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Generally, the electrons in the s subshell are at
the lowest energy level and those in the f
subshell in the highest shell occupy the highest
energy level.
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As the shell number (n) increases the energy
difference between the shells diminishes, as
shown by the decreasing distance between each
successive shell.
Electron Subshells
Magnetic Quantum
Number
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The magnetic quantum number (ml) where
ml ranges from - l to + l in integral steps
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Explains why strong magnetic fields can cause single
spectral lines to split into several closely spaced lines
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Called the Zeeman effect
Spin Magnetic Quantum
Number
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The spin magnetic quantum number (ms) where
ms can only be + 0.5 or – 0.5
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Accounts for the fine structure of “single” spectral
lines in the absence of a magnetic field
Quantum Mechanics And The
Hydrogen Atom

A review of the various quantum number ranges
which are used to determine allowable states
n can range from 1 to infinity in integral steps
 l can range from 0 to (n - 1) in integral steps
 ml can range from – l to + l in integral steps
 ms can only be + ½ or – ½

Orbitals
•Each orbital has its own set of quantum
numbers.
•Each orbital can contain 2 electrons, one with
spin +1/2 the other with spin -1/2
•The quantum number and energy levels can
be described with an orbital diagram.
•A summary of an orbital diagram is called an
electron configuration.
Energies of Orbitals in MultiElectron Atoms
•Several factors affect the energy of electrons in
multi electron atoms:
–Nuclear charge
–Electron repulsions
•Additional electrons in the same orbital (shielding)
•Additional electrons in inner orbitals
–Orbital shape (ml)
–spin (ms)
–Pauli Exclusion Principle: No two electrons in the same
atom can have the same set of four quantum numbers.
Hund’s Rule

Electrons enter orbitals one at a time before
becoming paired.
Aufbau Principle
Placement of electrons occur in the lowest energy levels of
orbitals first then into higher levels
They go into the orbitals one with spin +1/2, the other
with spin - 1/2.
An orbital diagram is useful in showing this arrangement.
Orbital Diagrams
Electronic
Configurations
By adding electrons to the
diagram, lowest energy to
highest, remembering Hund’s
rule and the quantum rule
that no orbital can hold more
than two electrons, an
elcetronic configuration can
be created
The Octet Rule
 The maximum number of electrons in the outer energy
level of an atom is 8.
 Atoms form compounds to reach eight electrons in their
outer energy level.
 Atoms with less than 4 electrons in their outer level tend to
lose electrons to form compounds.
 Atoms with more than 4 electrons in their outer level tend
to gain electrons to form compounds.
Electron Configurations can be
Determined From the Position in
the Periodic Table:
•Elements in group 1(1A) end in ns1.
•Elements in group 2 (2A): end in ns2
•Elements in group 13 (3A) end in ns2np1
•Elements in group 14 (4A): end in ns2np2
•Elements in group 15 (5A) end in ns2np3
•Elements in group 16 (6A) end in ns2np4
•Elements in group 17 (7A) end in ns2np5
•Elements in group 18 (8A) end in ns2np6
Periodic Table Family Filling
Diagram
The Pauli Exclusion Principle
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Two electrons in an atom can never have
the same set of 4 quantum numbers.
Because of this, the elements all have different
chemical properties.
 The n = 1 energy level is filled with electrons first.
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The Pauli Exclusion Principle
And The Periodic Table
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Mendeleev arranged the elements in a
periodic table according to their atomic
masses and chemical similarities.
He left gaps which were filled in within the next
20 years.
 Vertical columns have similar chemical
properties.
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The Periodic Table
Hydrogen Like Atoms
 Two
important equations for
hydrogen-like atoms:
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Orbital energy
Z (13.6) )
En = −
eV
2
n
2
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Orbital radius
n2
rn = (0.0529 nm)
Z
Wave Properties
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It became generally agreed upon that wave
properties were involved in the behavior of
atomic systems.
Bohr’s Model was improved upon
in the 1920’s with the Quantum
Mechanical Model.
•Since Bohr’s model only worked for the hydrogen atom, a
more sophisticated model was needed.
•The next breakthrough was made by Louis de Broglie,
who suggested that electrons, like photons have wave
properties
•De Broglie thought that Bohr’s energy levels were created
by the wave properties of the electron
Matter Waves
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Louis de Broglie (1924) suggested that if waves can behave like
particles, maybe particles can behave like waves.
He proposed that electrons are waves of matter. The reason for
the size and number of electrons in a Bohr electron shell is the
number of wave periods that exactly fit.
Schrödinger’s Wave
Equations
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In 1926, Erwin Schrödinger published a general theory of “matter
waves.”
Schrödinger’s equations describe 3-dimensional waves using probability
functions
Gives the probability of an electron being in a given place at a given
time, instead of being in an orbit
The probability space is the electron cloud.
Heisenberg’s Uncertainty
Principle
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Werner Heisenberg
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German physicist, 1901-1976
Schrödinger’s equations give the
probability of an electron being
in a certain place and having a
certain momentum.
Heisenberg wished to be able to
determine precisely what the
position and momentum were.
Heisenberg’s Uncertainty
Principle
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It is impossible to know a particles’ exact
position and velocity simultaneously.
The act of observing alters the reality being
observed.
There is a limit on measurement accuracy that is
significant but of practical importance when
dealing with particles of atomic and subatomic
size
Heisenberg’s Uncertainty
Principle, 2
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To “see” an electron and determine its position it has
to be hit with a photon having more energy than the
electron – which would knock it out of position.
To determine momentum, a photon of low energy
could be used, but this would give only a vague idea of
position.
Note: the act of observing alters the thing observed.
Heisenberg’s Uncertainty
Principle, 3
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Using any means we know to
determine position and
momentum, the uncertainty of
position, ∆q, and the
uncertainty of momentum, ∆p,
are trade-offs.
∆q∆p≥ h/2π, where h is
Planck’s constant
Particles or Waves?
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Question: Are the fundamental constituents of
the universe
Particles – which have a position and momentum,
but we just can’t know it,
or
 Waves (of probability) – which do not completely
determine the future, only make some outcome
more likely than others?
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Evidence for Matter Waves
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1927: Davisson & Germer, showed that electrons can be
diffracted by a single crystal of nickel
Electron diffraction is possible because the de Broglie
wavelength of an electron is approx. equal to distance
between atoms (the size of the diffraction grating)
Large-scale objects don’t demonstrate this well because
large momentum generates wavelengths much smaller
than any possible aperture through which the object
could pass (won’t be diffracted)
The Copenhagen
Interpretation
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Niels Bohr and Werner
Heisenberg:
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The underlying reality is more
complex than either waves or
particles.
We can think of nature in terms of
either waves or particles when it is
convenient to do so.
The two views complement each
other.
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Neither is complete in itself and a
complete description of nature is
unavailable to us.
Heisenberg & Bohr
The Copenhagen
Interpretation
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Niels Bohr and Werner
Heisenberg:
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The underlying reality is more
complex than either waves or
particles.
We can think of nature in terms of
either waves or particles when it is
convenient to do so.
The two views complement each
other.

Neither is complete in itself and a
complete description of nature is
unavailable to us.
Heisenberg & Bohr
Evolving
Theories of the
Atom
Electromagnetic Radiation
•Before we can explore our model of the atom
further, we need to look more closely at energy
•Chemistry is the study of matter and energy.
One type of energy is electromagnetic radiation.
Let us look more closely at the properties of
electromagnetic waves. Electromagnetic waves
consist of oscillating, perpendicular electric and
magnetic fields.
•The wavelength of radiation is the distance
between peaks in a wave. (λ)
•The frequency is the number of peaks that pass a
point in a second. (ν )
Wavelength of Light
A Simple Frequency and
Wavelength Formula
• λν = c
• λ = c/ν
• ν = c/λ
• λ is wavelength measured in length units (m,
cm, nm, etc.)
• ν is frequency measured in Hz (s-1).
• c is the velocity of light in vacuum
= 3.0 x108 ms-1
Electromagnetic Spectrum
•
•
•
•
Recognize common units for λ, ν.
λ wavelength
meters (m) radio
micrometers υm
(10-6 m) microwaves
• nanometers nm
• (10-9 m) light
• A angstrom (10-10 m)
ν frequency
Hertz Hz s-1
(cycles per
second)
megahertz
MHz (106 Hz)
Electromagnetic Waves
• Describe electromagnetic radiation and give
examples of it in relation to the
electromagnetic spectrum.
Type
•
•
•
•
•
•
λ (nm)
ν (H z)
1012
radio (Rf)
108 104-109
microwave
106-108
109-1012
infrared (IR)
750-106
1012-1014
visible (vis)
400-750
1014-1015
ultraviolet (UV)
10-400
1015-1016
X-rays, γ rays
10-4-1
1016-1022
The Electromagnetic Spectrum
Light Quanta and Photons
•Quantum- A packet of energy equal to hν. The
smallest quantity of energy that can be emitted or
absorbed.
•Photon- A quantum of electromagnetic radiation.
•Thus light can be described as a particle (photon) or as
a wave with wavelength and frequency. This is called
wave-particle duality (one of the most profound
mysteries of science)
Emission Lines
Modern Atomic Theory
 All matter is composed of atoms.
 Atoms of the same element are chemically alike with a characteristic average
mass which is unique to that element.
 Atoms cannot be subdivided, created, or destroyed in ordinary chemical
reactions. However, these changes CAN occur in nuclear reactions!
 Atoms of any one element differ in properties from atoms of
another element
 The exact path of electrons are unknown and e-’s are found in the
electron cloud.
The Atomic
Scale
 Most of the mass of the atom is in the
nucleus (protons and neutrons)
 Electrons are found outside of the nucleus
(the electron cloud)
 Most of the volume of the atom is empty
space
“q” is a particle called a “quark”
Albert Einstein 1879-1955
He published 5 papers
in 1905.
Photoelectric effect using
Planck’s ideas of quanta
of energy
won Nobel prize
E=mc2 became the
basis of the atomic
bomb.
Albert Einstein
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Used Planck’s hypothesis to describe light in
terms of particles rather than waves
photoelectric effect-electrons are emitted
when certain metallic materials are exposed to
light
Photons-packets of energy
E=hf
f= c/wavelength
the shorter the wavelength =more energy
Dual nature of light
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Light acts sometimes like a wave and sometimes
like a particle
Wavelength of light must have enough energy to
free electrons
Photon=particle of energy
atoms absorb quanta of energy and emit
electrons
Max Planck
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German 1900’s
1. Quantum Physics
2. Planck’s hypothesisenergy was quantized or
oscillators could have only
discrete or certain amount
of energy and depends on
its frequency
E=hf h=6.63 x 10 -34
Max Planck is famous for proposing a
quantum hypothesis for light
The energy of a light quantum has
been found to be directly proportional
to the frequency of the light.
Quantum
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A discrete amount of energy
emitted or absorbed
electromagnetic waves 3x 108
m/s
quanta-bundles of energy
Blackbody Radiation
One of the earliest indications that classical physics
was incomplete came from attempts to describe
blackbody radiation.
A blackbody is an ideal surface that absorbs all
incident radiation.
Blackbody radiation is the emission of electromagnetic
waves from the surface of an object. The distribution
of blackbody radiation depends only the temperature
of the object.
The Blackbody Distribution
The intensity spectrum emitted
from a blackbody has a
characteristic shape.
The maximum of the intensity is
found to occur at a wavelength
given by Wien’s Displacement Law:
fpeak = (5.88 × 1010 s-1·K-1)T
T = temperature of blackbody (K)
The Ultraviolet Catastrophe
Classical physics can describe the shape of the
blackbody spectrum only at long wavelengths. At
short wavelengths there is complete disagreement.
This disagreement between
observations and the
classical theory is known as
the ultraviolet catastrophe.
Planck’s Solution
In 1900, Max Planck was able to explain the observed
blackbody spectrum by assuming that it originated
from oscillators on the surface of the object and that
the energies associated with the oscillators were
discrete or quantized:
n = 0, 1, 2, 3…
En = nhf
n is an integer called the quantum number
h is Planck’s constant: 6.62 × 10-34 J·s
f is the frequency
Quantization of Light
Einstein proposed that light itself comes in chunks of
energy, called photons. Light is a wave, but also a particle.
The energy of one photon is
E = hf
where f is the frequency of the light and h is Planck’s
constant.
Useful energy unit: 1 eV = 1.6 × 10-19 J
Quantum Mechanics
The essence of quantum mechanics is that
certain physical properties of a system (like the
energy) are not allowed to be just any value, but
instead must be only certain discrete values.
The PhotoElectric Effect
When light is incident on a
surface (usually a metal),
electrons can be ejected.
This is known as the
photoelectric effect.
Around the turn of the century, observations of the
photoelectric effect were in disagreement with the
predictions of classical wave theory.
Observations of the Photoelectric Effect
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No electrons are emitted if the frequency of the
incident photons is below some cutoff value,
independent of intensity.
The maximum kinetic energy of the emitted electrons
does not depend on the light intensity.
The maximum kinetic energy of the emitted electrons
does depend on the photon frequency.
Electrons are emitted almost instantaneously from the
surface.
The Photoelectric Effect Explained
(Einstein 1905, Nobel Prize 1921)
The photoelectric effect can be understood as follows:
 Electrons are emitted by absorbing a single photon.
 A certain amount of energy, called the work function, W0, is
required to remove the electron from the material.
 The maximum observed kinetic energy is the difference
between the photon energy and the work function.
Kmax = E – W0
E = photon energy
The Mass and Momentum of a Photon
Photons have momentum, but no mass. We cannot use the
formula p = mv to find the momentum of the photon.
Instead:
hf
h
p=
=
c
λ
The Wave Nature of Particles
We have seen that light is described sometimes as a wave
and sometimes as a particle.
In 1924, Louis deBroglie proposed that particles also
display this dual nature and can be described by waves
too!
The deBroglie wavelength of a particle is related to its
momentum:
λ=
h/p
Wave Model
The Wave Model


Today’s atomic model
is based on the
principles of wave
mechanics.
According to the
theory of wave
mechanics, electrons
do not move about an
atom in a definite
path, like the planets
around the sun.
The Wave Model


In fact, it is impossible to determine the exact location
of an electron. The probable location of an electron is
based on how much energy the electron has.
According to the modern atomic model, an atom has a
small positively charged nucleus surrounded by a large
region (a cloud) in which there are enough electrons to
make an atom neutral.
Electron Cloud:
Depending on their energy they are locked into a certain area in
the cloud.
 Electrons with the lowest energy are found in the energy
level closest to the nucleus
 Electrons with the highest energy are found in the
outermost energy levels, farther from the nucleus
 This model explains spectral lines of an atom.
Quantum model of the atom

e
+
e
e
+
+
e
+e
+e
e
+ e + e
e
+
-
Thomson’s plum-pudding
model (1897)
1803 John Dalton
pictures atoms as
tiny, indestructible
particles, with no
internal structure.
1897 J.J. Thomson, a British
scientist, discovers the electron,
leading to his "plum-pudding"
model. He pictures electrons
embedded in a sphere of
positive electric charge.
-
- +
Rutherford’s model
(1909)
1911 New Zealander
Ernest Rutherford states
that an atom has a dense,
positively charged nucleus.
Electrons move randomly in
the space around the nucleus.
1904 Hantaro Nagaoka, a
Japanese physicist, suggests
that an atom has a central
nucleus. Electrons move in
orbits like the rings around Saturn.
Bohr’s model
(1913)
1913 In Niels Bohr's
model, the electrons move
in spherical orbits at fixed
distances from the nucleus.
1924 Frenchman Louis
de Broglie proposes that
moving particles like electrons
have some properties of waves.
Within a few years evidence is
collected to support his idea.
Charge-cloud model
(present)
1926 Erwin Schrodinger
develops mathematical
equations to describe the
motion of electrons in
atoms. His work leads to
the electron cloud model.
1932 James
Chadwick, a British
physicist, confirms the
existence of neutrons,
which have no charge.
Atomic nuclei contain
neutrons and positively
charged protons.
Indivisible Electron
Greek
X
Dalton
X
Nucleus
Thomson
X
Rutherford
X
X
Bohr
X
X
Wave
X
X
Orbit
Electron
Cloud
X
X
shorthand
Atomic number Z = number of protons
Mass number A = mass of nucleons
a
z
x
35
17
12
6
Cl
C
Radioactive Isotopes and
radioactivity
Radioisotopes - isotopes that have unstable nuclei
and will spontaneously disintegrate and emit
radiation.
Becquerel 1896 mineral pitchblende
Curie 1898 radium and polonium
Three types or radiation:
1. Alpha particles
2. Beta particles
3. Gamma radiation
Isotopes

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
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Isotopes are atoms of the same element with
different numbers of neutrons
C12 C13 C14
Atoms which give out radioactivity are called
radioactive isotopes.
The nucleus of a radioactive isotope is unstable.
Einstein – Energy/Mass Equivalence
In 1905, Albert Einstein publishes a 2nd major theory
called the Energy-Mass Equivalence in a paper
called, “Does the inertia of a body depend on its
energy content?”
Energy Unit Check
2
m
EB = ∆mc → Joule = kg × 2
s
W = Fx → Joule = Nm
m
Fnet = ma → N = kg × 2
s
2
m
m
E = W = kg × 2 × m = kg × 2
s
s
2
Mass Defect
The nucleus of the atom is held together by a STRONG NUCLEAR
FORCE.
The more stable the nucleus, the more energy needed to break it apart.
Energy need to break the nucleus into protons and neutrons is called the
Binding Energy
Einstein discovered that the mass of the separated particles is greater than
the mass of the intact stable nucleus to begin with.
This difference in mass (∆m) is called the mass defect.
Mass Defect - Explained
The extra mass turns into energy
holding the atom together.
Mass Defect – Example