Post on 09-Jun-2022
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 Power Is it Green & Safe?
Nuclear Waste 250,000 tons of Spent Fuel
10,000 tons made per year
Health Effects of Ionizing Radiation
Radiocarbon Dating
Atomic Notation
A
Z X
Atomic Mass Number
A = # protons + neutrons
Atomic #
1 3 238
1 1 92H, H, U
Atomic Number
Z = # protons
Neutron Number N
N = # neutrons
N = A - Z
E = mc2
Energy Released: The Mass Defect Parent atoms have more mass than product atoms.
The difference is released in the form of Kinetic energy.
parents productsm m m
Atomic Mass Units 1u = 1/12 mass of Carbon-12
27 21 1.6605 10 931.5 /u x kg MeV c
238.0508u 234.0436u 4.0026u
238.0508 234.0436 4.0026 0.0046m u u
2 2 2.0.0046 (931.5 / ) 4.3E mc u MeV c c MeV
Some Masses in Various Units
191 1.6 10eV x J
27 21 1.6605 10 931.5 /u x kg MeV c
131 1.6 10MeV x J
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.
If Helium loses a proton,
it becomes a different element
Isotopes and Elements
If Helium loses one of its
neutrons, it becomes an
isotope
p
n n
e
3He
p
p n
e
e
3H =T
The Hydrogen Atom
• One electron orbiting a nucleus
• 1 proton = Z = atomic number
• 0 neutrons = N
• Total mass = A = Z+N =1
• Singly ionized Hydrogen is missing one electron = 1H+
• Add a neutron and you have Deuterium = 2H = D
• Add 2 neutrons and you have Tritium = 3H = T
p
e
1H
The Helium Atom
• Two electrons orbiting a nucleus with:
2 protons = Z = atomic number
2 neutrons = N
• Total mass = A = Z+N
• Singly ionized Helium is missing one
electron = 4He+
• Doubly ionized Helium is missing both
electrons = a particle = 4He++
p
p n
n
e
e
4He
The Size of the Nucleus
• First investigated by Rutherford in scattering experiments
• He found an expression for d: how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force
• d is called the distance of closest approach
– d gives an upper limit for the size of the nucleus
– For gold, he found d = 3.2 x 10-14 m
– For silver, he found d = 2 x 10-14 m
2
2
4 ek Zed
mv
Nuclei • 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
• ro = 1.2 x 10-15 m
• A is the mass number
1 3
or r A
HW 44.7
Protons repel each other!
How is an Atomic Nucleus Stable?
Strong Force is STRONGER than
the Coulomb Force over short
distances: Short Range Force
~100Strong CoulombF F
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.
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).
Fission
Light elements FUSE into larger elements, releasing energy
in the process by E = mc2.
Fusion
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.
Quantum
Tunneling
Binding Energy It takes energy to break up an atom.
Energy must be put into a system to break it apart.
That energy is converted to mass.
That energy is called the Binding Energy.
Eb = (Zmp + Nmn – MA) x 931.494 MeV/u
The masses are expressed in atomic mass units.
Add the atomic mass of the electron to the proton.
Mass per Nucleon The smaller the mass per nucleon, the greater the binding energy.
Elements fission down or fuse up to Iron, the most stable element,
releasing energy by E = mc2.
Fission
Fusion
Binding Energy per Nucleon The most stable atoms have the most Binding Energy per nucleon.
Radioactive Atoms mutate by fission or fusion until they have
maximum Binding Energy per nucleon which occurs at Ni-62.
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.
HW 44.9
Calculate the binding energy per nucleon for
(a) 2H, (b) 4He, (c) 56Fe, and (d) 238U.
HW 44.10
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
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.
There is NO Spontaneous Fusion
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 232Th
• 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
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.
Alpha Decay
• Decay of 226 Ra
• 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
HeRnRa 4
2
222
86
226
88
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
– X is called the parent nucleus
– Y is called the daughter nucleus
4 4
2 2X Y HeA A
Z Z
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
– 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
1
1
X Y e
X Y e
A A
Z Z
A A
Z Z
• The fundamental process of e- decay is a neutron changing into a proton, an electron and an antineutrino
• In e+, 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
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
– The X* indicates a nucleus in an excited state
X X*A A
Z Z γ
12 12
5 6
12 12
6 6
B C e
C C
*
*
ν
γ
Summary of Decays
Hw 44.28
Q Values for Alpha Decay
• The disintegration energy Q of a system is defined as
Q = (Mx – My – Mα)c2
• The disintegration energy appears in the form of kinetic energy in the daughter nucleus and the alpha particle
• A negative Q value indicates that such a proposed decay does not occur spontaneously
Q Values for Beta Decay
• For e- decay and electron capture, the Q value is Q = (Mx – MY)c2
• For e+ decay, the Q value is
Q = (Mx – MY - 2me)c2
– The extra term, -2mec2, is due to the fact that the atomic
number of the parent decreases by one when the daughter is formed
– To form a neutral atom, the daughter sheds one electron
• If Q is negative, the decay will not occur
HW 44.34
Activity: Rate of Disintegration
( )( )
dN tA N t
dt
N(t) is the # of radioactive atoms in the sample at time t.
The activity, A, is the rate at which they decay.
is the “decay constant”.
( ) 1 disintegration/secondA Becquerel Bq
A CURIE is the activity of 1 gram of Radium.
101 3.7 10 ~ Ci x Bq billion Bq
Example: Activity of 1Kg of Carbon is ~250 Bq ~ 7nCi
Inhaling a sample with 1Ci of activity will kill you.
Chernobyl released 50 million curies into the atmosphere.
The decay rate R of a sample is defined as the number of decays per second:
Ro = Noλ is the decay rate at t = 0.
( ) λt
oR t R e
( ) λt
oN t N e
The amount of undecayed radioactive particles present in the
sample at any time t is:
•λ is called the decay constant and determines the rate at which the material will decay •No is the number of undecayed nuclei at time t = 0
( )( )
dN tA N t
dt
From the activity we derive the following useful items:
The half life of a
radioactive
element is the time it
takes for a quantity
to decay to 1/2 its
original amount, N0.
Half Life ( ) λt
oN t N e
Activity & Half Life dNA N
dt
0( ) tN t N e The # of radioactive nuclei present at any
time t since t = 0 when the # was N0:
0( ) / 2N t N
Decay Constant:
1/ 2 1/ 2t
e
1/ 2ln ln1/ 2t
e
1/ 2 ln 2t
1/ 2
ln 2
t (ln2=0.693)
HW 44.37
Indoor Air Pollution Uranium is naturally present in rock and soil. At one step
in its series of radioactive decays, 238U produces the chemically inert gas radon-222, with a half-life of 3.82 days. The radon seeps out of the ground to mix into the atmosphere, typically making open air radioactive with activity 0.3 pCi/L. In homes 222Rn can be a serious pollutant, accumulating to reach much higher activities in enclosed spaces. If the radon radioactivity exceeds 4 pCi/L, the Environmental Protection Agency suggests taking action to reduce it, such as by reducing infiltration of air from the ground. (a) Convert the activity 4 pCi/L to units of becquerel per cubic meter. (b) How many 222Rn atoms are in one cubic meter of air displaying this activity? (c) What fraction of the mass of the air does the radon constitute?
Carbon Half-Life
Carbon-14 decays with a halflife of about 5730 years by the
emission of an electron of energy 0.016 MeV. At equilibrium with
the atmosphere, a gram of carbon shows an activity of about 15
decays per minute.
There is 1 atom of C-14 for every 8.3x1011 atoms of C-12.
14 14
6 7C N
Activity: Rate of Disintegration Determine the activity of C-14 in a gram of a living organism.
There is 1 atom of C-14 for every 8.3x1011 atoms of C-12.
# C-14 atoms in 1 gram of C:
2310
11
6.02 10 12 1 141 6.0 10 14
12 8 10 12
mol x C Cg x C atoms
g mol x C
A N
10
7
0.693 16 10
5730 3.15 10
yrx atoms
yr x s
.23Bq
1/ 2
0.693
t
0.693
5730yr
Carbon Dating While alive, an organic material absorbs
radioactive C-14 from the atmosphere
and has a fixed percent of C-14 in it with
a fixed rate of radioactivity. Once the
plant dies, it stops absorbing C-14 and so
the radioactivity is reduced. Measuring
the Activity gives a measure of the
amount of C-14 remaining and thus the
date when the object died.
Neolithic Iceman discovered in
1991 in Italy
Neolithic Iceman Material found with the body had a C-14
activity of about 0.121 Bq per gram of carbon.
Determine the age of the Iceman’s remains.
0 0.23 @ 0A Bq t Given:
0.121 @ A Bq t now 1/ 2 5730t yr
5730ln.23/ .121 5310
0.693
yryr
0
tA A e
0ln / ln tA A e t
0
1ln /t A A
1/ 2
0.693
t
Nuclear Reactions
• Structure of nuclei can be changed by bombarding them with energetic particles – The changes are called nuclear reactions
• As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation
• A target nucleus, X, is bombarded by a particle a, resulting in a daughter nucleus Y and an outgoing particle b a + X Y + b
Nuclear Reactions
• If a and b are identical, so that X and Y are
also necessarily identical, the reaction is
called a scattering event
– If the kinetic energy before the event is the
same as after, it is classified as elastic
scattering
– If the kinetic energies before and after are not
the same, it is an inelastic scattering
a + X Y + b
Q Values for Reactions
• The reaction energy Q is defined as the total change in mass-energy resulting from the reaction Q = (Ma + MX – MY – Mb)c
2
• The Q value determines the type of reaction – An exothermic reaction
• There is a mass “loss” in the reaction
• There is a release of energy
• Q is positive
– An endothermic reaction • There is a “gain” of mass in the reaction
• Energy is needed, in the form of kinetic energy of the incoming particles
• Q is negative
• The minimum energy necessary for the reaction to occur is called the threshold energy
Conservation Rules for Nuclear
Reactions
• The following must be conserved in any
nuclear reaction
– Energy
– Momentum
– Total charge
– Total number of nucleons
HW 44.42
HW 44.42
HW 44.44
HW 44.44
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”
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
1
1
X Y e
X Y e
A A
Z Z
A A
Z Z
ν
ν
–An electron and an antineutrino
–A positron and a neutrino
Neutrinos are Leptons
They come in 3 Flavors.
They have antiparticles too.
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 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.
The Nobel Prize in Physics 1995
Solar Neutrino Measurement
Detecting solar neutrinos
would be PROOF that the sun
shines from nuclear fusion.
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.
The Nobel Prize in Physics 2002
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.
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 Kamiokande
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
mass. The Nobel Prize in Physics 2002
Masatoshi Koshiba
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.
AMANDA: Neutrino Telescope
at the South Pole
The Cherenkov Effect Muons breaking the 'light barrier'
Neutrino Experiments at CERN
The Oscillation Project with Emulsion-
Racking 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
http://www.youtube.com/watch?v=dhkCMO1lG7g
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.