Do Now (5/2/12):
• What is an istope?
• What makes an isotope different than its
element?
Nuclear Reactions
5/2/12 
Lesson Objectives
–Describe nuclear reactions and
perform balancing of nuclear
reactions by solving problems.
–Apply radioactivity equations
by solving problems.
Sub-atomic particles
The numbers:
• Protons and neutrons are approximately equal
in size
– mp = 1.67 x 10-27 kg
– mn = 1.67 x 10-27 kg
– me = 9.11 x 10-31 kg
Isotope
• Atomic nuclei having the same number of
protons but different number of neutrons
Vocab Review:
• Nuclear reaction: the number of
protons or neutrons in the nucleus
of an atom changes.
• Atomic number: Number of protons
in the nucleus of the atom
• Mass number: Sum of protons and
neutrons in the nucleus of the
atom
Nuclear Structure
Z = Atomic number
N = Number of neutrons
A = Atomic mass
A=Z+N
Relative Size of Nuclei
One fermi (f) = 10-15 m
Radius versus Atomic Mass
r = 1.2 A1/3 (in f)
------------------------Helium: A = 4
r = 1.2 (4)1/3
= 1.9 f
------------------------Uranium: A = 238
r = 1.2 (238)1/3
= 7.4 f
Atomic Mass Units
• From carbon-12 as the basis.
• Neutron = 1.008u
• Proton = 1.007u
• An amu = 1.66 x 10-27 kg = 931MeV/c2
• Also expressed in MeV from E=mc2
Einstein's Equation
• Mass is just a type of energy where one is
measured in Joules, J, and one in kilograms,
kg.
• The conversion factor between mass and
energy is just the square of the speed of light.
• E = mc2
Einstein's Equation cont.
• E = mc2
• Mass of a proton, m, is 1 atomic mass unit =
1.7 x 10-27kg
• Speed of light, c, is 3 x 108m/s
• What is E?
• E = 15.3 x 10-11Joules
• 1eV = 1.6 x 10-19J so what is E in eV.
• E = 9.56 x 108eV = 956MeV
Albert Einstein’s E = mc2 Is Called Mass-Energy
Equivalence
Mass is energy: E = mc2
Energy is mass: m = E /c2
Binding energy
• Mass of a single nucleon is higher than its
mass when incorporated into a nucleus.
• Mass defect is reflective of the binding energy
(how tightly are the nucleons bound.)
Nuclear Force
• No precise mathematical formula known…yet.
• Short-range force (10-15 m)
• Related to ratio of protons and neutrons in the
nucleus.
Nuclear Decay
• Natural process occurring in some
atoms/isotopes because the nucleus is
unstable (too big).
• Increases stability of the nucleus.
• New (daughter) elements form.
• Half life varies from fractions of a second to
thousands of years.
Radioactivity vs Radiation
• Radioactivity – The property of an atom that
describes spontaneous changes in its nucleus
that create a different nuclide (isotope).
• Radiation - The energy that is released as
particles or rays, during radioactive decay.
The Nucleus
Radioactivity
• 3 types of radioactive
emission:


x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Pb

x
x
x
x
x
x
Types of radiation
• Alpha – a helium nucleus (two neutrons, two
protons)
• Beta – a high energy electron
• Gamma – high energy photons
Penetrating Power
He (nucleus)
e-
Alpha (α) Decay
• The parent nucleus loses a cluster of 2 protons and
2 neutrons.
226
88
Z = # of protons + neutrons
A = # of protons
+
+
Ra  Rn He
222
86
+
+
+
+
+
+
+
+
+
+
+
+
4
2
Beta (β) Decay
• The parent nucleus has a neutron turn into a proton and
an extra electron is created to conserve charge.
14
6
C  N e
14
7

+
+
+
+
+
+
e
+
Watch this neutron
14
6
Energy Release in C Decay
• Mass of Parent Atom = 14.003242 u
• Combined mass of products = 14.003074 u
m  0.000168 u
E  mc
2

2
1.66x1027 kg 
 3x108 m / s  2.51x1014 J or 156,870eV
E   0.000168u 
1u




Alpha decay
•the nucleus of an atom
emits an alpha particle
Alpha Particle
• Nucleus of a
helium atom
Beta decay
• occurs when a neutron is
changed to a proton within the
nucleus of an atom, and a beta
particle and an antineutrino are
emitted
Gamma decay
• Radioactive process of decay
that takes place when the
nucleus of an atom emits a
gamma ray.
• http://library.thinkquest.org/17940/texts/
radioactivity/radioactivity.html
Mass Defect:
• The difference between the sum of the mass of the
individual nucleon (proton or neutron) and the actual mass.
m  matom


Z m  m 
p
e

 


(A

Z)m

n 
Example #1:
Fermium-253 has a half-life of
0.334 seconds. A radioactive
sample is considered to be
completely decayed after 10 halflives. How much time will elapse
for this sample to be considered
gone?
Binding Energy
E binding 
(m assdefect(inu))(931.49MeV /u)
• The energy equivalent of the mass defect; it is
always negative
 It
is the minimum amount of energy needed to break
the nucleus into its component nucleons.
Example #2:
• The half life of Zn-71 is 2.4
minute. If one had 100 g at
the beginning, what is the
decay rate of Zn-71?
Mass remaining
m  m0e
• m=mass remaining
• Original mass
 t
Example #3:
• The half life of Zn-71 is 2.4
minute. If one had 100 g at the
beginning, how many grams
would be left after 7.2 minutes
elapsed?
Practice:
•Use the rest of class to
work on the paper:
Radioactivity; problems:
#2,5,6, and 7
Do Now (4/24/12):
• Pd-100 has a half-life of 3.6 days. If one had
6.02x1023 atoms at the start, how many
atoms would be present
Decay Sequence
Alpha decay sequence:
235
4
U
92
231
He +
2
209
4
Po
84
Th
90
205
He +
2
Pb
82
Decay Sequence
Beta decay sequence:
14
14
C
6
e
N +
7
228
Ra
88
0
-1
228
0
e
Ac +
89
-1
Natural Transmutation
The changing
of one element
to another is
called
transmutation.
Half-life
• Time for half of a radioactive sample to
undergo decay.
• First order decay process.
• T1/2 = 0.693/ where =decay constant
• N = N0e-t
Protons and neutrons in the nucleus
are collectively referred to as
nucleons.
The Strong Force
Protons which would otherwise
strongly repel at close distances
are held in place by an extremely
strong, but extremely short range
force called the strong force.
Other names for the strong force
are strong nuclear force, or
nuclear force.
The strong force between two
protons is about the same as
the strong force between two
neutrons, or a proton and a
neutron.
Beyond about one fermi
the strong force declines
extremely rapidly.
As more protons are
added to the nucleus,
more neutrons are
needed to bind the
protons together, but
the larger the nucleus
becomes, the farther
apart are the protons
and the less effective
is the strong force
Neutron Number versus Proton Number
Electric force is longer range than the strong
force.
Eventually separation becomes too great for
the strong force to compensate for the
repulsive forces. Nuclei spontaneously
disintegrate for proton numbers larger than
83.
The release of light and or particles which
accompanies the disintegration is called
radiation, first discovered by Henri
Becquerel in 1896.
The Binding Energy of a Nucleus
The larger the binding
energy of a nucleus,
the more stable it is.
The binding energy is
the difference between
the rest energies.
Atomic Mass Unit
One atomic mass unit (amu) = 1.6605 x 10-27 kg
-------------------------------------------------------------------E = (1.6605 x 10-27 kg) (3 x 108 m/s)2
= 1.49 x 10-10 J
1.49 x 10-10 J / 1.6 x 10-19 J /eV = 9.31 x 108 eV
931 x 106 eV
= 931 MeV
one amu = 931 MeV
An amu is often abbreviated u
The Binding Energy of Helium
m = 4.0330 - 4.0026
= 0.0304 u
E = (931 MeV /u) 0.0304 u
= 28.3 MeV
There are four nucleons, so
the binding energy per nucleon
is about 28/4, or about 7 MeV
per nucleon.
Binding Energy per Nucleon
Nuclei with the largest binding energy
per nucleon are the most stable.
----------------------------------------------------The largest binding energy per nucleon
is 8.7 MeV, for mass number A = 60.
Beyond bismuth, A = 209, nuclei
are unstable.
Atoms in the Middle of the Periodic Table are
the Most Stable
• The most tightly bound of
the nuclei is 62Ni
• The most tightly bound
nuclides are all even-even
nuclei
Binding Energy of Alpha Particle
For the alpha particle Δm= 0.0304 u which
gives a binding energy of 28.3 MeV
It Takes a Lot More Energy to Split a Nucleus
Than to Ionize an Atom
Uranium Decays via Alpha-Particle
Emission
The first particle that was recognized as having been
ejected from an unstable nucleus was called an alpha
particle because alpha is the first letter of the Greek
alphabet. It's now known to consist of two protons and
two neutrons, which is the same as a helium nucleus.
Carbon-14 Decays by Beta Emission
The beta particle
is now known to
be just an electron.
Is the nucleon
count conserved?
Is the total charge
conserved?
Reaching Stability Through Gamma
Ray Emission
Nuclei with excess
energy emit
gamma-rays, which
are extremely shortwavelength electromagnetic waves, i.e.,
very high energy
photons.
Nuclear Notation
Alpha Particle Emission
The alpha
particle
is a helium
nucleus.
Balancing Nuclear Decay Equations
92U
238
--------> 90Th234 + 2He4
Subscripts are "proton
numbers"
Superscripts are "nucleon
numbers"
Proton and nucleon counts
must be the same:
92 = 90 + 2
238 = 234 + 4
Distribution of Energy in Alpha Emission
m = 0.0046 u
E = 0.0046 x 931
= 4.3 MeV
----------------------Which particle
has the greater
kinetic energy?
Energy Distribution in Radioactive Decay
Conservation of momentum:
Mv = mV
(2)
Rearranging, we get
V/v = M/m
Ratio of kinetic energies: KEm / KEM:
(1/2 mV2) / (1/2 Mv2) = (m/M)(V2/v2)
= (m/M)(V/v)2 (1)
(3)
Substitute (3) into (1):
Ratio = (m/M)(M/m)2
= M/m
(4)
Smaller mass gets more energy
Marie Curie
Marie and Pierre Curie
isolated 1/30 ounce of
radium from one ton of
uranium ore.
Marie died from
radiation-induced
leukemia.
Marie Sklodowska Curie
(1867-1934)
Lithograph entitled "Radium"
appeared in the December 22,
1904 issue of Vanity Fair.
The pages of her lab
notebook were later
found to be
contaminated with
radioactive
fingerprints.
Radioactivity in Radium
In "balancing" a nuclear disintegration equation, note that the
subscripts and superscripts add up.
Plutonium Powered Spacecraft
238
94Pu
-----> 92U234 + 
Smoke Detectors Use Radiation
Sources
Alpha particles emitted from
source ionize the air and
provide the charge necessary
to conduct current through
the air.
Charges stick to the heavy
smoke particles and the
current decreases, causing
the alarm to buzz.
Beta Particle (Electron) Emission
The neutron number of an
electron is zero, and the
proton number is negative
one.
90Th
234
------>
234
91Pa
+ -1e0
Negative beta particles
are emitted when a neutron
is transformed into a
proton and an electron.
Beta Particle (Electron) Emission by Carbon-14
14
6C
-----> 7N14 + -1e0
The subscripts represent
the "proton" number
(electrons have a negative)
proton number.
Superscripts represent the
nucleon number; electrons
are not nucleons, so their
nucleon number is zero.
Beta Particle (Positron) Emission by Oxygen-15
8O
15
A positron has the same
mass as the electron, but
opposite charge.
15
-----> 7N15 + 1e0
The subscripts represent
the "proton" number
(a positron has a positive
proton number)
Superscripts represent the
nucleon number; positrons
are not nucleons, so their
nucleon number is zero.
PET Imaging of Brain Is Based On
Positron Annihilation
Healthy brain
Brain with Alzheimer's
disease
Wavelength of a Gamma Ray
What is the wavelength of a 1 MeV gamma ray?
Using the 1240 rule:
 = 1240 eV-nm / E
= 1240 eV-nm / 1 x 106 eV
= 1.24 x 10-6 nm
= 1.24 x 10-15 m
= 1.24 fermi
This gamma radiation is extraordinarily harmful
to humans and other living things since its
wavelength is comparable to the diameter of
a nucleon; transmutations are likely when
such radiation reaches nuclei.
Brain Surgery with the Gamma Knife
The Geiger Counter
Hans Geiger invented
the "Geiger counter".
---------------------------------It was Hans Geiger who,
while working in Ernest
Rutherford's lab, was the
first to see the alpha
particles reverse direction
in the alpha particle
experiment, but it was
Rutherford's calculation
which proved the
existence of the nucleus
The Scintillation Counter
Scintillator is material which will
emit photons when struck by
high energy charged particles
or high energy photons.
Photon strikes metal plate,
ejecting electrons which are
pulled toward 100 V anode.
The anode is coated with a
material which is easily
ionizable and releases two or
more electrons for each one
that strikes it.
Transmuting Uranium to Neptunium
Neutron enters nucleus and is transformed into a proton
and an electron (which leaves the nucleus).
Nuclear Energy Map
Nuclear Fission Produces Far More
Energy Than Combustion
Average number of neutrons
released is 2.5.
Combined kinetic energy of
particles is about 200 MeV.
100,000,000 times more
energy than is released when
coal is burned:
C + O2 => CO2
(about 2 eV)
Estimating Energy Released During Fission
About 7.5 MeV
to about 8.5 MeV
per nucleon.
Mass difference
is about one MeV
per nucleon.
If A = 235, then
energy released
is about 235 MeV
Calculating Binding Energies—What is
the binding energy of C12?
One atom of C12 consists of 6 protons, 6 electrons, and 6 neutrons. The mass of
the uncombined protons and electrons is the same as that of six H1 atoms (if
we ignore the small binding energy of the electron proton pair).
Mass of six H1 atoms = 6 x 1.0078 u = 6.0468 u
Mass of six neutrons= 6 x 1.0087 u = 6.0522 u
Total mass of particles=
12.0990 u
Mass of C12=
12.0000 u
Loss in mass on forming C12=
0.0990 u
Binding energy= 931 MeV x 0.0990= 92 MeV
Slow Neutrons Cause Chain Reactions
Slow neutrons are required.
A chain reaction occurs if
more than one neutron
goes on to cause another
fission.
Neutrons can be slowed by
bouncing them off of small
objects, such as carbon
nuclei.
One pound of U-235, if
completely fissioned, yields
the same energy as
100,000,000 pounds of coal.
Cadmium Control Rods Absorb
Neutrons
Enrico Fermi
supervised
construction of the
world's first nuclear
reactor.
Cadmium is a good absorber of neutrons.
World's First Controlled Nuclear Chain
Reaction
Handball court under the bleachers at the University of
Chicago, 1942. Uranium-235 is at the center of the stack
of graphite blocks; the carbon acts as a moderator,
slowing neutrons.
The Manhattan Project
Oak Ridge, Tennessee. 60,000 workers worked for three
years to separate 2 kilograms of uranium-235 from
uranium-238.
World's First Fission Explosion
Trinity Site--5:30 am, July 16, 1945,
Alamogordo, New Mexico.
Dr. Robert J.
Oppenheimer and
Maj. Gen. Leslie L.
Groves,
The First Atomic Bomb
"Little Boy", two feet in diameter, ten feet long, 9000
pounds, dropped on Hiroshima, Japan, was a uranium
bomb, equivalent to 20,000 tons of explosive.
“Gun” Bomb
Concept
Two sub-critical masses
are smashed together to
create a super-critical
mass.
The Two Bombs Used In WWII Were of
Different Types
Little Boy and Fat Man
Implosion Weapon Concept
Pu “pit” 4.5 cm
with 2.5 cm
center
hole
Energy From Fission
~kinetic energy of fission products
~ gamma rays
~ kinetic energy of the neutrons
~ energy from fission products
~ gamma rays from fission products
~ anti-neutrinos from fission products
165 MeV
7 MeV
6 MeV
7 MeV
6 MeV
9 MeV
200 MeV
Atomic Bomb Targets
The only nuclear weapons ever used in anger were the two atomic
bombs dropped in 1945.
The Scorched Remains
Nagasaki, Japan
Nagasaki survivor.
(Click here for panoramic view of Hiroshima.)
Modern Nuclear Reactors
The water in the reactor vessel has three
purposes.
The water, being composed of relatively light
molecules, acts as a moderator. In Fermi's
reactor, carbon in the form of graphite was the
moderator.
Water also acts to remove heat from fuel rods
which otherwise would melt.
The heated water, converted to steam, is then
converted into electrical energy.
A Nuclear Reactor
Heat generated by fission
in uranium rods creates
steam which turns turbine
blades connected to a
coil of wire in magnetic
field.
Uranium Fission
• If a massive nucleus like uranium-235 breaks apart
(fissions), then there will be a net yield of energy
because the sum of the masses of the fragments
will be less than the mass of the uranium nucleus.
• If the mass of the fragments is equal to or greater
than that of iron at the peak of the binding energy
curve, then the nuclear particles will be more tightly
bound than they were in the uranium nucleus, and
that decrease in mass comes off in the form of
energy according to the Einstein equation.
Fission Energy Release
Fission Particle and Energy Yields
Fission Fragments
•
•
•
When uranium-235 undergoes
fission, the average of the fragment
mass is about 118, but very few
fragments near that average are
found.
It is much more probable to break up
into unequal fragments, and the
most probable fragment masses are
around mass 95 and 137.
Most of these fission fragments are
highly unstable (radioactive), and
some of them such as cesium-137
and strontium-90 are extremely
dangerous when released to the
environment.
Fission Fragment Example
•
A common pair of fragments from
uranium-235 fission is xenon and
strontium:
•
Highly radioactive, the xenon decays
with a half-life of 14 seconds and
finally produces the stable isotope
cerium-140.
Strontium-94 decays with a half-life of
75 seconds, finally producing the
stable isotope zirconium-94.
These fragments are not as dangerous
as intermediate half-life fragments
such as cesium-137.
•
•
Fission Fragment Decay
This particular set of fragments
from uranium-235 fission
undergoes a series of beta decays
to form stable end products
Chain Reactions
• If at least one neutron from each fission strikes another U-235 nucleus and initiates
fission, then the chain reaction is sustained.
• If the reaction will sustain itself, it is said to be "critical", and the mass of U-235 required
to produced the critical condition is said to be a "critical mass". A critical chain reaction
can be achieved at low concentrations of U-235 if the neutrons from fission are
moderated to lower their speed, since the probability for fission with slow neutrons is
greater.
• The smaller the sphere, the greater the ratio of surface area to
volume, and the greater the percentage of neutrons which escape the
sphere before causing fission.
• Critical mass--or, critical size--is that mass value at which an average
of more than one neutron per fission is used to cause another fission.
Uranium 235 Fission for Energy
Uranium As Fuel
• Natural uranium is composed of 0.72% U-235 (the fissionable
isotope), 99.27% U-238, and a trace quantity 0.0055% U-234 .
The 0.72%
– U-235 is not sufficient present in suficient cocentration to produce a
self-sustaining critical chain reaction in U.S. style light-water reactors.
For light-water reactors, the fuel must be enriched to 2.5-3.5% U-235.
– It can be used in Canadian CANDU reactors.
Fusion in Stars
10 million degrees at the core
causes fusion of hydrogen into
helium.
Proton-Proton Fusion
This is the nuclear fusion
process which fuels the Sun
and other stars which have
core temperatures less
than 15 million Kelvin. A
reaction cycle yields about
25 MeV of energy.
P-P Fusion
• The fusing of two protons which is the first
step of the proton-proton cycle created great
problems for early theorists because they
recognized that the interior temperature of
the sun (some 14 million Kelvins) would not
provide nearly enough energy to overcome
the coulomb barrier of electric repulsion
between two protons.
With the development of quantum mechanics, it was realized that
on this scale the protons must be considered to have wave
properties and that there was the possibility of tunneling through
the coulomb barrier.
Fusion Options on Earth
Deuterium Fusion Cycle
These equations can be
combined as:
Which can be written as:
D-D Fusion
Deuterium must be moving extremely fast to fuse.
D-T Fusion
•
•
•
The most promising of the
hydrogen fusion reactions which
make up the deuterium cycle is
the fusion of deuterium and
tritium.
The reaction yields 17.6 MeV of
energy but requires a temperature
of approximately 40 million Kelvins
to overcome the coulomb barrier
and ignite it.
The deuterium fuel is abundant,
but tritium must be either bred
from lithium or gotten in the
operation of the deuterium cycle.
Deuterium-Tritium Fusion Using Lasers
Laser evaporates D-T, creating
a "plasma" of charged particles
which push away from one
another. The reaction force
compresses and heats core
Thermonuclear Weapons
Bikini Atoll, in the Marshall Islands (1954)
The hydrogen bomb uses an atomic bomb as the heat source to
fuse hydrogen into helium. The so-called H-bomb is vastly
more destructive than fission bombs. The Hiroshima bomb had
had explosive power of about 20,000 tons of TNT; H-bombs
commonly have 50-500 times the power (1-10 megatons).
Fusion Compared with Fission
If the final products have less mass than the reactants, energy is released.
Fission versus Fusion
A Binding Energy Comparison of
Fission and Fusion
The buildup of heavier
elements in the
nuclear fusion
processes in stars is
limited to elements
below iron, since the
fusion of iron would
subtract energy rather
than provide it.
Comparison of Fission and Fusion Yields
Fuel
• U-238 – 99 % of uranium on Earth,
• U-235 - 0.7 %
• Both decay naturally by alpha radiation, but U-235
can undergo induced fission.
• Plutonium-239 is created by bombarding U-238
with neutrons
• Uranium must be enriched so it contains more U235.
– 3% for nuclear power plants
– 90% for weapons-grade uranium
Fuel
• Splitting an atom releases large amounts of
heat and gamma radiation.
• The difference in mass between products and
the original U-235 atom is converted to energy
according to Einstein’s famous E = mc².
Fission vs. Fusion
• Fission – the splitting of a nucleus; used for
reactors and weapons
• Fusion – the fusing of two nuclei; used in
weapons and occurs in outer space (stars)
Drill
If an atom of nitrogen-13 releases a positron,
what particles would be present in the
nucleus?
What type of decay is this?
Objectives
Compare nuclear force with other forces.
Describe fission and fusion.
Apply mass-energy equivalence.
Nuclear Fission
Nuclear Fission
Average number of neutrons
released is 2.5.
Average combined kinetic energy of
particles is about 200 MeV.
100,000,000 times more
energy than is released when
coal is burned:
C + O2 => CO2
(about 2 eV)
Critical Mass
The smaller the sphere, the greater the ratio of surface area to volume, and the
greater the percentage of neutrons which escape the sphere before causing
fission.
Critical mass--or, critical size--is that mass value at which each fission event produces an
average of one more fission event.
Fusion
Fusion is the opposite of fission. Deuterium must be
moving extremely fast to fuse.
Deuterium-Tritium Fusion
Neutrons carry away 80 %
of the energy released
Fusion versus Fission
If the final products have less mass than the reactants, energy is released.
Nuclear fission
• http://library.thinkquest.org/17940/texts/fissi
on/fission.html
Nuclear reactors
What is Happening in Japan
• http://www.nytimes.com/interactive/2011/03
/12/world/asia/the-explosion-at-thejapanese-reactor.html?ref=asia