Nuclear Physics
The unleashed power of
the atom has changed
everything save our
modes of thinking and we
thus drift toward
unparalleled catastrophe.
-Albert Einstein
Bronze Buddha at Hiroshima
Nuclear Power
Nuclear Weapons
Nuclear Waste
250,000 tons of Spent Fuel
10,000 tons made per year
Health Effects of Ionizing Radiation
Radiocarbon Dating
Fission
Heavy elements FISSION into lighter elements, releasing energy
in the process by E = mc2, where m is the difference in mass
between the parent and products.
~ 4.3 MeV is released in this reaction
Most of the Energy is released in the form of Kinetic Energy (heat).
Fusion
Light elements FUSE into larger elements, releasing energy
in the process by E = mc2.
Atomic Notation
Atomic Mass Number
A = # protons + neutrons
A
Z
X
Atomic #
Neutron Number N
N = # neutrons
N=A- Z
1
1
H,
3
1
H,
238
92
Atomic Number
Z = # protons
U
Energy Released: The Mass Defect
Parent atoms have more mass than product atoms.
The difference is released in the form of Kinetic energy.
E=
2
mc
m   mparents  mproducts 
Some Masses in Various Units
1eV  1.6 x10 J
19
1MeV  1.6 x10 J
13
1u  1.6605x10
27
kg  931.5MeV / c
2
Atomic Mass Units
1u = 1/12 mass of Carbon-12
1u  1.6605x10
238.0508u
27
kg  931.5MeV / c
234.0436u
2
4.0026u
m   238.0508  234.0436  4.0026  u  0.0046u
E  mc2  0.0046u(931.5MeV / c2 )c2.  4.3MeV
All Elements Have Isotopes
Same # of protons - different # of neutrons
Atomic Mass of an Element is an average of all Isotopes
Isotopes have the same chemistry as the atom.
This is why radioactive isotopes can be so dangerous.
The body doesn’t see the difference between water made
with hydrogen and water made with tritium.
Isotopes and Elements
e
If Helium loses a proton,
it becomes a different element
p
n
n
3H
If Helium loses one of its
neutrons, it becomes an
isotope
3
He
=T
e
p
n p
e
The Hydrogen Atom
• One electron orbiting a nucleus
• 1 proton = Z = atomic number
• 0 neutrons = N
• Total mass = A = Z+N =1
p
• Singly ionized Hydrogen is
missing one electron = 1H+
e
1H
• Add a neutron and you have
Deuterium = 2H = D
• Add 2 neutrons and you have
Tritium = 3H = T
The Helium Atom
e
p
n
n
p
• Two electrons orbiting a nucleus with:
2 protons = Z = atomic number
2 neutrons = N
• Total mass = A = Z+N
e
4He
• Singly ionized Helium is missing one
electron = 4He+
• Doubly ionized Helium is missing both
electrons = a particle = 4He++
Nuclear Theory
• The volume of the nucleus
(assumed to be spherical) is
directly proportional to the total
number of nucleons
• This suggests that all nuclei
have nearly the same density
– Since r3 would be proportional to
A
• Nucleons combine to form a
nucleus as though they were
tightly packed spheres
• Average radius is
r  ro A
13
• ro = 1.2 x 10-15 m
• A is the mass number
Nuclei
Nuclear Size and Density
Experimentally, the
radius of a nucleus
with mass number A
is found to be:
where
r0 = 1.2 fm = 1.2  1015 m.
© 2013 Pearson Education, Inc.
Slide 42-36
Nuclear Size and Density
 The volume of the nucleus (proportional to R3) is directly
proportional to A, the number of nucleons.
 A nucleus with twice as many nucleons will occupy
twice as much volume.
 This finding implies:
 Nucleons are incompressible. Adding more nucleons
doesn’t squeeze the inner nucleons into a smaller
volume.
 The nucleons are tightly packed.
 Nuclear matter has a constant density:
nuc = 2.3  1017 kg/m3
© 2013 Pearson Education, Inc.
Slide 42-37
Nuclear Size and Density
 The graph shows the
density profiles of three
nuclei.
 The constant density
right to the edge is
analogous to that of a
drop of incompressible
liquid.
 One successful model
of many nuclear
properties is called the
liquid-drop model.
© 2013 Pearson Education, Inc.
Worksheet 42.1
Slide 42-38
Protons repel each other!
How is an Atomic Nucleus Stable?
Strong Force is STRONGER than
the Coulomb Force over short
distances: Short Range Force
FStrong ~ 100FCoulomb
Over a range of 10-15 m.
Why are Atoms Not Stable?
Why do Atoms Decay?
As nuclear size
increases, the distance
between nucleons
increases and the strong
force becomes too weak
to overcome the
Coulomb electrical
repulsion.
The nucleus is unstable
and can decay.
Stable Nuclei
Neutrons:
Nuclear Glue
With few exceptions,
naturally occurring stable
nuclei have N  Z.
For Z  20, N = Z is stable.
Elements with Z 83 are
unstable and spontaneously
decay until they turn into
stable lead with Z = 82.
Nuclear Stability
© 2013 Pearson Education, Inc.
Slide 42-39
Nuclear Stability
 The stable nuclei cluster very close to the curve is
called the line of stability.
 There are no stable nuclei with Z  83 (bismuth).
 Unstable nuclei are in bands along both sides of the
line of stability.
 The lightest elements, with Z  16, are stable when
N  Z.
 As Z increases, the number of neutrons needed for
stability grows increasingly larger than the number
of protons.
© 2013 Pearson Education, Inc.
Slide 42-40
The Nuclear Binding Energy
© 2013 Pearson Education, Inc.
Slide 42-41
Binding Energy
 The binding energies of nuclei are tens or hundreds of
MeV, energies large enough that their mass equivalent is
not negligible.
 Consider a nucleus with mass mnuc: it is found
experimentally that mnuc is less than the total mass of the
Z protons and N neutrons that form the nucleus.
 The atomic mass matom is mnuc plus the mass Zme of Z
orbiting electrons.
 The binding energy is then:
where all three masses are in atomic mass units.
© 2013 Pearson Education, Inc.
Worksheet 42.2
Slide 42-42
Binding Energy per Nucleon
For energy release in fusion or fission, the products need to have a
higher binding energy per nucleon (proton or neutron) than the
reactants. As the graph above shows, fusion only releases energy for
light elements and fission only releases energy for heavy elements.
The Shell Model
 The shell model of the
nucleus, using multielectron
atoms as an analogy, was
proposed in 1949 by Maria
Goeppert-Mayer.
 The shell model considers
each nucleon to move
independently with an
average potential energy
due to the strong force of
all the other nucleons.
© 2013 Pearson Education, Inc.
Maria Goeppert-Mayer received the 1963 Nobel Prize in
Physics for her work in nuclear physics.
Slide 42-52
Low-Z Nuclei
 The figure shows the
three lowest energy
levels of a low-Z
nucleus (Z < 8).
 The neutron energy
levels are on the left,
the proton energy
levels on the right.
© 2013 Pearson Education, Inc.
Slide 42-55
Low-Z Nuclei
 The figure shows the energy diagram for 12C.
 Exactly six protons are allowed in the n  1 and n  2
energy levels.
 Likewise for the six
neutrons.
 Thus 12C has a
closed n  2
proton shell and
a closed n  2
neutron shell.
© 2013 Pearson Education, Inc.
Slide 42-56
Low-Z Nuclei
 The figure shows the energy diagram for 12N.
 The sixth proton fills the n  2 proton shell, so the
seventh proton has to go into the n  3 energy level.
 The n  2 neutron shell has one vacancy because
there are only five neutrons.

12N
has significantly
more nuclear energy
than 12C.
© 2013 Pearson Education, Inc.
Slide 42-57
Low-Z Nuclei
 The figure shows the energy diagram for 12B.
 The sixth neutron fills the n  2 neutron shell, so the
seventh neutron has to go into the n  3 energy level.
 The n  2 proton shell
has one vacancy
because there are
only five protons.
 12B has significantly
more nuclear energy
than 12C.
© 2013 Pearson Education, Inc.
Worksheet 42.4
Slide 42-58
Nuclear Radiation
Atomic decay by Alpha and Beta radiation causes atomic transmutation.
Gamma radiation does not transmutate the atom, it changes its energy.
Alpha Decay
Atomic Mass Number, A, and charge is conserved for all reactions!
Beta Decay
Atomic Mass Number, A, and charge is conserved for all reactions!
Neutrino: Weak Force
Spontaneous Nuclear Decay: Fission
Beta Decay
Neutron Decay into a Proton
(Neutron Half life ~ 12 minutes)
Alpha Decay
Induced Nuclear Fission
Next Time
Heavy elements FISSION into lighter elements, releasing energy
in the process by E = mc2, where m is the difference in mass
between the parent and products. About 250 MeV is released in this
reaction in the form of kinetic energy of the products.
There is NO Spontaneous Fusion
Only in very extreme conditions like the interior of a star or
in a fusion bomb or reactor can you overcome the Coulomb
repulsion and force nucleons to fuse.
Quantum
Tunneling
In Fission, the alpha
particle escapes the
nucleus by Quantum
Tunneling.
In Fusion, protons fuse
to form helium by
Quantum Tunneling
through the repulsive
coulomb barrier.
Radioactive Series
Natural radioactivity: Unstable nuclei found in nature
Artificial radioactivity: Nuclei produced in the
laboratory by bombarding atoms with energetic
particles in nuclear reactions.
Natural Transmutation
Spontaneous Fission
Elements with Z 83 are
unstable and spontaneously
decay by alpha and beta
radiation until they turn into
stable lead with Z = 82.
Note: some elements can
decay by both modes.
Decay Series for U-238
Decay Series of
• Series starts with 232Th
• Processes through a
series of alpha and beta
decays
• The series branches at
212Bi
• Ends with a stable
isotope of lead, 208Pb
232Th
Alpha Decay
• Decay of 226 Ra
226
88
R a  2 82 62 R n  42 He
• If the parent is at rest before
the decay, the total kinetic
energy of the products is
4.87 MeV
• In general, less massive
particles carry off more of
the kinetic energy
Alpha Decay
• When a nucleus emits an alpha particle it
loses two protons and two neutrons
– N decreases by 2
– Z decreases by 2
– A decreases by 4
• Symbolically
A
Z
X
A4
Z 2
Y  He
4
2
– X is called the parent nucleus
– Y is called the daughter nucleus
Beta Decay
• During beta decay, the daughter nucleus has the
same number of nucleons as the parent, but the
atomic number is changed by one
• Symbolically
A
A

Z
X
Z 1
Ye
A
Z
X
A
Z 1
Ye

– The process occurs when a neutron is transformed into
a proton or a proton changes into a neutron
• The electron or positron is created in the process of the decay
– Energy must be conserved
Gamma Decay
• Gamma rays are given off when an excited
nucleus decays to a lower energy state
• The decay occurs by emitting a high-energy
photon
A
Z
X*  X  γ
A
Z
– The X* indicates a nucleus in an excited state
12
5
B
12
6
C* 
12
6
C*  e  ν
12
6
Cγ
• The fundamental process of e- decay is a neutron changing
into a proton, an electron and an antineutrino
• In e+ decay the proton changes into a neutron, positron and
neutrino
– This can only occur within a nucleus
– It cannot occur for an isolated proton since its mass is
less than the mass of the neutron
Neutrino
• Properties of the neutrino
–
–
–
–
Zero electrical charge
Mass much smaller than the electron, probably not zero
Spin of ½ - it is a lepton.
Very weak interaction with matter and so is difficult to detect
– in beta decay, the following pairs of particles are emitted
–An electron and an antineutrino
–A positron and a neutrino
A
Z
X
A
Z 1
A
Z
X
A
Z 1

Y e ν
Y  e  ν
Beta Decay & The Neutrino
•The emission of the electron or positron is from the nucleus
•The process occurs when a neutron is transformed into a
proton or a proton changes into a neutron
•The electron or positron is created in the process of the
decay
•Energy must be conserved BUT it wasn’t! Experiments
showed a range in the amount of kinetic energy of the
emitted particles
•To account for this “missing” energy, in 1930 Pauli
proposed the existence of another particle
•Enrico Fermi later named this particle the neutrino,
meaning, “little neutron”
Neutrinos are Leptons
They come in 3 Flavors.
They have antiparticles too.
Summary of Decays
Detecting Neutrinos
50 trillion solar neutrinos pass through your body
every second. Can you detect them?
Because of the reluctance of neutrinos to react with
atomic nuclei and thus allow themselves to be captured,
very large number of neutrinos and very large detector
volumes are required.
Frederick Reines and his colleage Clyde L. Cowan, Jr.
proposed in 1953 a reactor experiment to capture
neutrinos through the reaction:
antineutrino + proton –› neutron + positron.
The Nobel Prize in Physics 1995
The target in the Reines-Cowan experiment consisted of approximately 400 litres of
water containing cadmium chloride placed between large liquid scintillation
detectors. The neutrino collides with a proton in the water and creates a positron and
a neutron. The positron is slowed down by the water and destroyed together with an
electron, whereupon two photons are created. These are recorded simultaneously in
the two detectors. The neutron also loses velocity in the water and is eventually
captured by a cadmium nucleus, whereupon photons are emitted. These photons
reach the detectors a microsecond or so later than those from the destruction of the
positron and give proof of neutrino capture.
Solar Neutrino Measurement
Detecting solar neutrinos
would be PROOF that the sun
shines from nuclear fusion.
The Nobel Prize in Physics 2002
Raymond Davis Jr’s detector, which for the first time in history
proved the existence of solar neutrinos. Over a period of 30 years
he succeeded in capturing a total of 2,000 neutrinos from the Sun
and was thus able to prove that fusion provided the energy from
the Sun. The tank, which was placed in a gold mine, contained
more than 100,000 gallons of tetrachloroethylene. A neutrino
interacts with a chlorine nucleus to produce an argon atom.
Solar Neutrino Problem
From the Davis experiment, it became clear that the
number of solar neutrinos detected was lower than that
predicted by models of the solar interior. In various
experiments, the number of detected neutrinos was
between one third and one half of the predicted number.
This came to be known as the solar neutrino problem.
The solution to the
problem is called
Neutrino Oscillations:
The neutrinos change
into each other!
According to quantum mechanics, particles sometimes behave
like waves (and vice versa). When neutrinos "mix" as described
above, they combine in the same way that waves combine. When
sound waves combine, they "beat", as depicted in the picture to
the right. Neutrinos do a similar sort of thing, except we say that
they "oscillate".
It is the flavor of the neutrino that oscillates. If a neutrino
starts out as 100% νe, as it moves along its "νe-ness" will begin
to fade, while its νμ-ness or ντ-ness grows. The νe-ness soon
reaches a minimum, and begins to increase again. Then the
neutrino once again becomes a pure νe before fading away
again. The amplitude and frequency of the oscillation depends
on the particular values of the three masses and the mixing
parameters, which are still being studied.
http://www.youtube.com/watch?v=dhkCMO1lG7g
The Main Injector Neutrino Oscillation Search (MINOS)
experiment studies a neutrino beam using two detectors. The
MINOS near detector, located at Fermilab, records the
composition of the neutrino beam as it leaves the Fermilab site.
The MINOS far detector, located in Minnesota, half a mile
underground, again analyzes the neutrino beam. This allows
scientists to directly study the oscillation of muon neutrinos into
electron neutrinos or tau neutrinos under laboratory conditions.
Super-K is located 1,000 m underground in Mozumi Mine in
Japan. It consists of 50,000 tons of pure water surrounded
by about 11,200 detectors. A neutrino interaction with the
electrons or nuclei of water producing a flash of light which
can be detected. In 1998 discovered neutrino oscillations and
The Nobel Prize in Physics 20
mass.
Koshiba confrimed Davis’s results
and in 1987 detected the first cosmic
neutrinos from a supernova
explosion, capturing twelve of the
total of 1016 neutrinos that passed
through the detector.
Super Kamiokande
Masatoshi Koshib
AMANDA: Neutrino Telescope
at the South Pole
The Cherenkov Effect
Muons breaking the 'light barrier'
Neutrino Experiments at CERN
The Oscillation Project with EmulsionRacking Apparatus (OPERA)
OPERA is an instrument used
in a scientific experiment for
detecting tau neutrinos from
muon neutrino oscillations.
The experiment is a
collaboration between CERN in
Geneva, Switzerland, and the
Laboratori Nazionali del Gran
Sasso (LNGS) in Gran Sasso,
Italy and uses the CERN
Neutrinos to Gran Sasso
(CNGS) neutrino beam.
Neutrino Experiments at CERN
Cosmic Gall
John Updike
Neutrinos they are very small.
They have no charge and have no mass
And do not interact at all.
The earth is just a silly ball
To them, through which they simply pass,
Like dustmaids down a drafty hall
Or photons through a sheet of glass.
They snub the most exquisite gas,
Ignore the most substantial wall,
Cold-shoulder steel and sounding brass,
Insult the stallion in his stall,
And, scorning barriers of class,
Infiltrate you and me! Like tall
And painless guillotines, they fall
Down through our heads into the grass.
At night, they enter at Nepal
And pierce the lover and his lass
From underneath the bed – you call
It wonderful; I call it crass.