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Atomic & Nuclear Physics
Early Models of the Atom
• J.J Thomson
– 1856-1940
– 1st to discover the
existence of the negatively
charged electron.
– Since all atoms are
electrically neutral,
Thomson developed his
Plum-Pudding Model of the
atom which consists of
negatively charged
electrons moved around
inside a sphere of positive
charge.
Early Models of the Atom
• Rutherford’s Gold Foil Experiment
– Using the setup seen below Rutherford
accelerated alpha (a) particles at a thin sheet
of Gold foil. Rutherford observed that most of
the particles simply passed right through the
foil without having their travel path affected by
the charged particles.
– Observations showed that atom could not
look like the Plum-Pudding model as
Thomson predicted.
Early Model of the Atom
• Rutherford’s
experiment showed
that the atom must
consist of primarily
empty space with the
positively charged
particles in a
centralized nucleus
and the negatively
charged particles
orbiting around it.
Early Model of the Atom
• Rutherford’s Solar System Model
Early Model of the Atom
• Problems with the Rutherford Model:
– The new model of the atom suggested that due the
curved paths of the electrons (centripetal
acceleration) the atom would continuously be emitting
light. To release this energy the electron would have
to lose energy and as a result would spiral into the
nucleus…NOT GOOD!!!
– The model also suggested that the light being emitted
would cover the entire spectrum, due to the loss of
energy
– Why is this a problem?...Well, that’s not was
observations showed.
Early Model of the Atom
• Line Spectrum
– Experiments showed that when gas molecules were
excited by exposing it to an electric field the gas
would emit light. Contrary to the Rutherford model
the gas did not emit a continuous spectrum of light
but a series of very specific wavelengths.
Early Models of the Atom
• Bohr Model
– In 1913 Niels Bohr (1885-1962), proposed a
model for the hydrogen atom that would
combine classical mechanics and work done
in quantum mechanics by Max Planck and
Albert Einstein.
Quantum Theory
• Blackbody Radiation
– Have you ever wondered why the coil of an
electric stove glows red or orange as its
temperature increases?
– Have you ever noticed that almost all
materials show the same effect when heated?
– A blackbody is a system that absorbs all light
that is incident on it.
Quantum Theory
• Given the fact that a blackbody is effective
at absorbing radiation it is also very
effective at giving off radiation as well.
– Blackbody experiment:
• Heat a blackbody to a specific temperature and
measure the amount of EM radiation being emitted
at a specific frequency. Repeat for different
frequencies and plot the intensity versus frequency
– This experiment showed some interesting
results
Quantum Theory
• Blackbody Results
– The distribution of
energy in blackbody
radiation is
independent of the
material from which
the blackbody is
constructed. It
depends only on the
temperature
Quantum Theory
• Problems with Blackbody experiments
– Although observations were consistent and
the experiment was clearly understood,
attempts to explain the results using classical
physics failed miserably.
Quantum Theory
• Planck’s Quantum Hypotheses
– Max Planck (1858-1947) was able to
construct a mathematical formula that agreed
with experimental results. To actually derive
the equation he needed to make a bold
assumption.
• The radiation in a blackbody at the frequency f,
must be an integral multiple of a constant (h) times
the frequency. In other words, the energy is
quantized
Quantum Theory
• Quantization of Energy
E  nhf
•
•
•
•
n = 1, 2, 3, …
f = frequency
h = Planck’s constant
h = 6.63x10-34 Js
Quantum Theory
• Problems with Planck’s theory
– Although Planck’s theory of energy
quantization explained the results of
blackbody radiation, Planck did not think the
light in a blackbody had a quantized energy.
• Most physicists looked at light as being a wave,
which can have any energy.
– Hello Uncle Albert!!!!
Quantum Theory
• The photon:
– Albert Einstein took Planck’s idea of energy
quantization seriously and applied it to
blackbody radiation.
– Einstein proposed that light comes in bundles
of energy called, photons, that obey Planck’s
quantization hypotheses, and the energy of
that photon can be found by:
E  hf
Quantum Theory
• Einstein’s photon model looked at a beam
of light as a beam of particles each
carrying the energy hf.
– Therefore, if the intensity is increased keeping
the frequency the same, more photons pass a
given point in a given time.
• This now begins to pose the question:
– Is light a wave or a particle? Hmmmmm…
Quantum Theory
• The Photoelectric Effect
– When two separated plates
are connected to a battery
an electric field is
established.
– When light of a high
enough frequency is
incident on the negative
plate electrons are
released, travel across the
gap and are collected by
the positive plate (i.e.
current flows)
Quantum Theory
• Wave Theory vs. Particle Theory
– Classical wave theory gave very different predictions
from Einstein’s photon theory. To begin analyzing the
differences we measure the maximum kinetic energy
(Kmax) of the emitted electrons.
• To do this we reverse the connection of the battery. In this
configuration the electrons will be repelled by the negative
plate. If the electrons have sufficient enough energy they
can still bridge the gap. The voltage that prevents any
electrons from bridging the gap is called the stopping
potential (Vo)
K max  eVo
Quantum Theory
•
Wave Theory
–
Assume a monochromatic light source (one color)
•
–
Maintains a constant frequency and wavelength
Predictions:
1. If the intensity is increased, the number of electrons
ejected and their maximum kinetic energy should be
increased because the higher intensity means a greater
electric field amplitude (i.e. greater electron energy), and
the greater electric field should eject electrons with higher
speed.
2. The frequency of light should not effect the kinetic energy
of the ejected electrons. Only the intensity should affect
Kmax
Quantum Theory
• Experimental observations found that
there was a certain frequency that below
which no electrons were emitted. It also
showed that the intensity of the light
incident on the metal had no effect on the
kinetic energy of the emitted electrons.
This violated the wave theory since, the
intensity, based on the wave theory, is
directly proportional to the energy carried.
Quantum Theory
•
Photon model:
–
Einstein’s photon model made completely different
predictions to the wave model.
–
Predictions:
1. An increase in intensity of the light beam means more
photons are incident, so more electrons will be ejected; but
since the energy of each photon is not changed, the
maximum kinetic energy of electrons is not changed.
2. If the frequency of light is increased the maximum kinetic
energy of the emitted electrons increases linearly.
3. The minimum frequency needed to emit an electron is
dependent on the material that light is incident upon. This
implies the existence of a “cutoff” frequency.
Quantum Theory
• Work Function (f)
– Einstein’s 3rd prediction implies that the atoms
in the metal need to absorb a certain energy
to release one of its electrons. Since the
energy a photon carries is dependent on the
frequency, there is a certain minimum photon
frequency required to release an electron in
the metal. This minimum energy required is
called the work function of the metal.
Quantum Theory
• Kinetic Energy of emitted Photoelectrons
– Given the existence of the work function, the
maximum kinetic energy of an emitted
photoelectron is now dependent on both the
energy of the incident photons and the
material it is striking. It can be found using
the following expression:
K max  hf  f
Quantum Theory
• Support of Photon Theory:
– In 1914 Robert Millikan performed a series of
experiments that showed that Einstein’s
photon model accurately predicted the results
of the photoelectric effect, and the wave
theory fell short.
– These findings began the idea that light has
both wave characteristics and particle
characteristics.
Quantum Theory
• Support of Photon model
– Compton Scattering
• In 1923 Arthur H. Compton performed an experiment in
which he scattered short-wavelength light (x-rays) from
various materials.
• He observed that the scattered light had a slightly lower
frequency than the incident light. This indicated a loss of
energy.
Quantum Theory
• Compton Scattering
– Through his experimental observations and
using the idea that light carried particle
properties, Compton applied the laws of
conservation of energy and momentum and
found that the energy of the photon could also
be found by using its momentum and the
following relationship:
E  pc
Quantum Theory
• Wave-Particle Duality
– Through the observations of the Photoelectric
Effect and Compton’s experiments the particle
nature of light was supported.
– However, since light can be reflected,
diffracted, and refracted light also shows wave
characteristics.
– This dichotomy is known as wave-particle
duality, in which light can be considered both
a particle and a wave. CRAZY!!!!
Quantum Theory
• Wave Nature of Matter:
– In 1923, Louis DeBroglie extended the
particle theory of light.
– He felt through the symmetry of nature that if
light can be thought of as both a wave and
particle under certain conditions, then material
objects such as electrons and other material
objects (i.e. particles) might also have wave
properties.
Quantum Theory
• DeBroglie Wavelength
– Through his ideas, DeBroglie proposed that
the wavelength of a material particle would be
related to its momentum in the same way as a
photon. He therefore predicted that
wavelength of a particle can be found by:
h

p
Quantum Theory
• Davisson-Germer Experiment
– In 1927 Clinton Davisson and Lester Germer
performed an experiment in which they
scattered electrons from the surface of a
metal crystal. These scattered electrons
formed a diffraction pattern much like light
does shown in Young’s Double-Slit
experiment.
Quantum Theory
• Verification of the DeBroglie Wavelength
– The diffraction pattern formed in the
Davission-Germer experiment was used to
calculate the wavelength. Through their
calculations they found the experimental
results were in complete agreement with
DeBroglie’s predictions.
– This means that the wave-particle duality
does not just apply to light but also to ordinary
matter.
Back to the Atomic Model
• We left our analysis of the early model’s of
the atom with the model presented by
Niels Bohr in 1913. Bohr’s model
attempted to explain why atoms emit only
very specific wavelengths of light when
excited (atomic spectra).
Early Models of the Atom
• Bohr felt that Rutherford’s solar system model of
the atom has some validity but classical physics
predicted that the electrons would spiral into the
nucleus as they lost energy (light), and as a
result destroys the atom.
• In order for this model to work, Bohr realized that
the new quantum theory postulated by Planck
and Einstein would have to be incorporated.
Early Models of the Atom
• Bohr Postulates for the Hydrogen atom:
– Postulate 1 – The force that holds the electron to the
nucleus is the Coulomb force between electrically
charged bodies.
– Postulate 2 – Only certain stable, non-radiating orbits
for the electron’s motion are possible. Each stable
orbit represents a discrete energy state.
– Postulate 3 – Emission or absorption of light occurs
when the electron makes a transition form one stable
orbit to another, and the frequency of the light f is
such that the difference in orbital energies equals hf.
Early Models of the Atom
• Bohr Model
– Electrons are located
in specific orbital
states around the
nucleus that carry a
discrete amount of
energy
– Light is emitted when
an electron drops from
a higher energy level
to a lower
hf
Early Models of the Atom
• Energy Level Diagrams
– Each specific energy level
an electron can be found in
has an associated amount
of quantized energy (eV).
The energy of an emitted
photon carries can be
found by.
E photon  hf  Ehigh  Elow
Early Models of the Atom
• Results of Bohr Model
– An atom must absorb a very specific amount of
energy to have an electron jump from one energy
level to another. (n=1  n=2)
– An electron in the atom must lose a specific amount
of energy in order for the atom to release a photon.
(n=2  n=1)
– If an atom absorbs enough energy an electron can be
completely removed from the atom (i.e. ionization).
This specific amount of energy is referred to as the
binding energy or ionization energy.
Nuclear Physics
• Our understanding of the structure of the
atom and specifically the nucleus, and our
ability to harness its energy have brought
significant changes to our lives…both
good and bad.
– Nuclear Weapons
– Nuclear Power
– Medicinal (radiation treatment, MRI)
– Safety (smoke-detectors)
Nuclear Physics
• Structure of the Nucleus:
– The nucleus as we know is built by a combination of
protons and neutrons, also known as nucleons.
• Z = Atomic Number (Number of protons in the nucleus)
– This is also equal to the number of electrons surrounding the
nucleus. Must keep the atom electrically neutral.
• N = Number of neutrons in the nucleus
– Each element in nature is determined by how many
nucleons exist in the nucleus, mass number (A).
A Z N
Nuclear Physics
• General Notation
A
Z
X
– X = Element
– Z = Atomic number
– A = Mass number
• Example
14
6
C
• Element = Carbon
• Protons = 6
• Neutrons = 14 – 6 =8
Nuclear Physics
• Isotopes:
– All nuclei of a given element have the same
number of protons, but they can have different
numbers of neutrons.
– Nuclei with the same number of protons but
different number of neutrons are referred to as
isotopes.
12
6
C
13
6
C
Nuclear Physics
• Atomic mass:
Particle
Mass (kg)
Mass
(MeV/c2)
Mass (u)
Charge (C)
Proton
1.672623x10-27
938.28
1.007276
+1.6x10-19
Neutron
1.674929x10-27
939.57
1.008664
0
Electron
9.109390x10-31
0.511
0.0005485799
-1.6x10-19
– Atomic Mass Unit (u)
• 1u = 1.660540x10-27kg
Nuclear Physics
• Energy-Mass Equivalence
– In 1905 Albert Einstein published his special
theory of relativity. Among the many other
implications this theory had on the laws of
physics was the fact that mass and energy we
one in the same. We could create mass from
energy and create energy from mass.
E  mc
2
Nuclear Physics
• What holds the nucleus together:
– If like charges repel each other and neutrons
carry no charge…how does the nucleus hold
itself together?
• The Strong Force
– The strong force is short range, acting at distances
of ~10-15m (femtometers)
– The strong force is an attractive force and acts
nearly equally between all nucleons.
– At short distances the strong force dominates over
both electromagnetic and gravitational forces
Nuclear Physics
• Comparing the forces of Nature
Type
Range
Strong Nuclear
Relative Strength
(2 protons)
1
Electromagnetic
10-2
Infinite
Weak Nuclear
10-6
~10-3 fm
Gravitational
10-38
infinite
~1fm
Nuclear Physics
• The stability of a nucleus
is based on the
competition between the
repulsive electrostatic
forces and the attractive
strong force.
• If the number of protons
increases eventually the
strong force is overtaken
by the electrostatic force
and the nucleus begins to
disintegrate.
Nuclear Physics
• Radioactivity
– When an unstable nucleus changes its composition
by emitting a particle of one form or another.
– Process known as radioactive decay.
– Three particles could be released during decay.
• Alpha Particles (a) – nuclei of 24 He
• Beta Particles (b) - electrons
• Positron emission – positively charged electron (antiparticle)
• Also could decay by emission of a photon
– Gamma ray (g)
Nuclear Physics
• Alpha Decay
– When a nucleus decays by giving off an a
particle it loses 2 protons and 2 neutrons
A
Z
X
A 4
Z 2
Y  He
– X = Parent Nucleus
– Y = Daughter Nucleus
4
2
Nuclear Physics
• Energy released during alpha decay:
238
92
U
Nuclear Physics
Nuclear Physics
• Beta Decay
– The basic process of b-decay is the
conversion of a neutron to a proton and
electron
1
0
n p  e
1
1

– The decay of an atomic nucleus undergoing
b-decay is as follows
A
Z
X Y e
A
Z 1

A
Z
X Y e
A
Z 1

Nuclear Physics
• Gamma (g) Decay
– Occurs when an excited nucleus decays to a
lower energy state….Since nuclear energies
are so much larger than atomic energies the
photon released is of very high energy.
C N  e
14
6
14
7
14
7
*

N  N g
*
14
7
Nuclear Physics
• Binding Energy
– The minimum amount of energy required to
break a stable nucleus into its constituent
nucleus.
Nuclear Physics
• Nuclear Fission
– The process of large nuclei splitting into two
smaller nuclei
– Discovered in 1939 by Otto Hahn and Fritz
Strassman, with the observation of a uranium
nucleus splitting into two smaller nuclei.
– Energy released is many orders of magnitude
larger that the energy released in chemical
reactions.
Nuclear Physics
• Nuclear Fission
– Amount of energy
released in a fission
reaction is equal to the
difference in the
binding energies of the
parent nuclei and the
daughter nuclei
multiplied by the
number of nucleons in
the parent nucleus.
• Example:
235
92
U
Nuclear Physics
• Chain Reactions
– Occurs due to the fact that more than one
neutron is released from a fission reaction.
– Starting with one fissionable 235
92 U nucleus…
after only 100 generations, the number of
nuclei undergoing fission is 1.3x1030. If each
reaction gives off 200MeV of energy the total
energy released is 4.1x1019J.
• Enough energy to supply the needs of the entire
U.S. for 6 months
Nuclear Physics
• Elementary Particles
– The basic building blocks of all matter.
– In the early part of the 20th century there were
only 3 elementary particles.
• Proton, Neutron, and Electron
– Of these 3 only the electron has since
remained an elementary particle. In the last
half of the 20th century ~300 new particles
have been discovered.
Nuclear Physics
Nuclear Physics
• Elementary Particles
– Leptons
• Leptons are particles that are only affected by the
weak nuclear force which is responsible for most
radioactive decay.
• No internal structure to any of these particles
• There are 6 leptons and all are classified as
elementary
Nuclear Physics
• Leptons
Particle
Symbol
Antiparticle Rest
symbol
Energy
(MeV)
Lifetime (s)
e  or b 
e  or b 
0.511
Stable
Muon



105.7
2.2x10-6
Tau


1784
10-13
Electron
Neutrino
e
e
~0
Stable
Muon
Neutrino


~0
Stable
Tau Neutrino


~0
Stable
Electron

Nuclear Physics
• Hadrons
– Particles that experience the weak, strong, and
gravitational forces
– All Hadrons have finite mass and internal structure
– Most common:
• Proton
• Neutron
• Hundreds of Hadrons exist in Nature
– Two subcategories of Hadrons
• Mesons
• Baryons
Nuclear Physics
• Mesons
– Hadron formed form the combination of two
quarks
• Bayrons
– Hadron formed from the combination of three
quarks
Nuclear Physics
• Quarks
– To account for the internal structure observed in all
hadrons, Murray Gell-Mann and George Zweig
independently proposed in 1963 the existence of truly
elementary particles in which Gell-Mann called quarks
– Originally there were three quarks
• Up (u)
• Down (d)
• Strange (s)
– In 1974 due to the discovery of large hadrons 3 more
quarks have been added
• Charmed (c)
• Top (c) (a.k.a. Truth)
• Bottom (b) (a.k.a. Beauty)
Nuclear Physics
Nuclear Physics
• Standard Model of Atom