Einstein’s Formula
E = mc2 or ∆E = (∆m)c2
When nuclear reactions occur a significant (measurable) mass change of the nucleus occurs, ∆m.
Einstein’s famous formula, ∆E = (∆m)c2, is used to convert the nuclear mass change (∆m) into energy (∆E).
(c = 2.99792 x 108 m/s)
∆E is generally expressed using the SI unit of J with mass in kg.
The electron volt (eV) and the megaelectron volt (MeV) are also used. An electron volt is the energy an electron
acquires when it is accelerated through a potential difference of 1 V.
Remember from electrochemistry, V*C = J.
(1 V)(1.602x10-19 C/1 e-) = 1.602x10-19 J = 1 eV
1 MeV = 106 eV
Simplified conversion factors between mass and energy:
on a particle basis:
1 electron = 0.5110 MeV = 8.185x10-14 J
1 proton = 938.3 MeV = 1.503x10-10 J
on a mass basis:
1 neutron = 939.6 MeV = 1.505x10-10 J
1 g = 5.610x1026 MeV = 8.988x1013 J
1 amu = 931.5 MeV = 1.492x10-10 J
Nuclear Chemistry
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ENERGY = Einstein’s Formula: E = mc2 or ∆E = (∆m)c2
The thermite reaction is:
Fe2O3(s) + 2Al(l) → 2Fe(s) + Al2O3(s)
∆H = –851.5 kJ/mol
This is one of the most exothermic chemical reactions known. Since the heat released is
sufficient to melt the iron product, the reaction is used to weld metal under the ocean. How
much heat is released when 1.0 mole of Fe(s) is produced? What mass change is equivalent
to this amount of energy.
Nuclear Chemistry
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ENERGY = Einstein’s Formula: E = mc2 or ∆E = (∆m)c2
Compare the mass and energy change for the thermite reaction to the energy released when
2 mole of protons and 2 mole of neutrons combine to form 1 mole of alpha particles.
particle
β− = β+
1
0
n
Mass per Mole?
NA = 6.02214 x 1023
g
0.000548580 9.10939x10-28
1.00866
1.67492x10-24
p
1.00728
1.67263x10-24
α
4.00151
6.64466x10-24
1
1
4
2
amu
3
Nuclear Chemistry
Nuclear Binding Energy, Eb
The Nuclear Binding Energy, Eb, is the “glue” that holds the
nucleons together in the nucleus. This Binding Energy is the
energy required to separate a nucleus into individual protons
and neutrons. (This is analogous to the lattice energy for ionic
compounds.)
Nucleons
Eb = (∆m)c2
Eb
(Eb) + Nucleus → Separate Nucleons
Where does all this energy come from?
From measurements, we know that the mass of atomic nuclei
are ALWAYS less than the sum of the masses of individual
protons and neutrons. This “missing mass” is called the mass
defect, ∆m. This missing mass has been converted to energy
(released) upon formation of the nucleus and this is the
Nuclear Binding Energy, Eb.
energy to break apart
the nucleus (mass ↑)
Nucleus
Nucleons
-Eb = (∆m)c2
–Eb
energy released when
nucleus forms (mass ↓)
∆m = (mass separated nucleons) - (mass nucleus)
What is the nuclear binding energy in kJ/mol for deuterium?
Nuclear Chemistry
Nucleus
4
Mass Defect, ∆m, and Nuclear Binding Energy
To compare the stability of different nuclei, the nuclear binding energy is often reported as
energy per nucleon. The greater the binding energy per nucleon, the more stable the nucleus.
1.
Ne-21 has a atomic mass of 20.993846 amu and the atomic mass of a 1H atom is 1.007825 amu. What is the
nuclear binding energy of Ne-21 in MeV/per nucleon?
2.
Which is more “stable”, 12C or 21Ne? The nuclear binding energy of 12C is 7.680 MeV/nucleon.
5
Nuclear Chemistry
Stability of Nuclei - Nuclear Binding Energy
Copyright
The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
The variation in
binding energy per
nucleon.
• The most stable nucleus is Fe-56.
• He-4 is also very stable. There are tremendous amounts of He-4 in stars as the hydrogen
isotopes combine in fusion reactions.
• The lighter elements tend to undergo fusion to make heavier - more stable nuclei.
• The heavier elements tend to undergo fission to produce lighter - more stable nuclei.
U-235 is used in nuclear reactors.
Nuclear Chemistry
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Nuclear Fission Reactions
The fission process produces more neutrons that can initiate fission in other nearby U-235 nuclei. If there is a critical
mass of U-235, this can lead to an uncontrollable chain reaction.
A fission chain reaction has three steps:
1. Initiation: A neutron source is introduced to
begin the first fission process of U-235.
(Example: polonium)
2. Propagation: The release of neutrons in the
first fission process initiates fission in nearby
nuclei. This creates an exponentially increasing
fission rate. Lots of energy is released in a very
short time.
3. Termination: When most of the U-235 is used
up or the neutrons escape without being
captured.
• This shows one set of daughter
nuclei from the induced fission
of 235U. There are other
possibilities. On average, 2.4
neutrons are emitted per
fission of a 235U nucleus.
• One mole of 235U releases
about 2.1x1013 J during this
step.
Nuclear Chemistry
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Mass Change and Energy
Determine the energy change when 1 mole of Uranium-235 decays to Ba-141 and krypton-92 in a nuclear reactor:
92
1
U + 01n → 141
56 Ba + 36 Kr + 3 0 n
235
92
The NUCLEAR masses are:
U = 234.9935 amu
235
92
141
56
92
36
Ba = 140.8833 amu
Kr = 91.9021 amu
Nuclear Chemistry
8
Trinity Test - The First Nuclear Explosion
Trinity Test July, 16 1945 - A 239Pu
device to test the theory of an implosion
trigger. Developed by Edward Teller, this
was the precursor to the Fat Man bomb
dropped on Nagasaki.
Play Movie
Fat Man
Nuclear Chemistry
9
Little Boy - The First Atomic Bomb
To achieve a sustained chain reaction a critical mass of 235U must be present. For the Little Boy bomb of WWII small
amounts of TNT were used to push subcritical masses of 235U together to produce a single critical mass of 235U.
Little Boy
Little Boy - a 235U bomb. Untested before use.
At 8:12 AM on August 6, 1945, a B-29 bomber called the 'Enola Gay' piloted by Col. Paul
Tibbets dropped an atomic bomb codenamed 'Little Boy' over the city of Hiroshima, Japan
and made a sharp high speed banking turn away from the city.
The bomb detonated 1900 feet (545 meters) over the city at 8:15 AM local time killing
140,000 people instantly or later due to the radiation sickness. Three days later a second
bomb code named 'Fat Man' was dropped over the city of Nagasaki killing another 70,000
people. Japan surrendered August 15, ending World War II.
Nuclear Chemistry
10
The First Nuclear Power Reactor
Play Movie
Nuclear Chemistry
11
Nuclear Power Reactor
Play Movie
Nuclear Chemistry
12
Nuclear Power Reactor - Enriched U-235 (3%)
1. The control rods absorb neutrons and limit the nuclear reaction. They are made from cadmium, boron or graphite.
“Heavy water” can also be used to control the neutron flux.
2. The heat generated is captured and used to generate electricity.
3. The products of fission degrade the system. The reactor must be shut down to replace and reprocess the fuel rods.
4. In a “Breeder” nuclear reactor the abundant U-238 that is present is converted into Pu-239 through neutron
absorption and beta emission. Hence, fissionable material Pu-239 is made from non-fissionable material U-238.
Breeder reactors are the source of plutonium for nuclear weapons. (Hanford, Washington)
238U + 1n → 239U
Neutron capture to make U - 239
92
0
92
239U → 239 Pu +2 0β
Production of Pu - 239
92
94
−1
Nuclear Chemistry
13
Nuclear Reactor “Melt Down”
Nuclear reactors never have uranium or plutonium in high enough mass to create a
critical mass. Nuclear reactors cannot explode like a nuclear bomb. There is no chance a
nuclear power plant’s fuel rods can go critical and explode like a nuclear bomb.
Malfunctions in the nuclear core result in a “meltdown” of the core creating tremendous amounts of
heat. The heat causes enormous amounts of
radioactive (contaminated) steam and dust to be
expelled into the air. This steam and dust will
eventually “fallout” of the air onto nearby land. The
land closest to the nuclear core is contaminated most
heavily, the further from the nuclear core the less
contamination. Fallout can occur several hundreds of
miles away from the nuclear core. The accident at
Chernobyl in the 1980’s was a partial meltdown of
the core. The nuclear process control was lost and
too much heat was generated. This basically melted
the nuclear core, allowing radioactive material to
escape into the air and the nearby surroundings. The
nearby lands are still heavily contaminated with U
and Pu wastes. Strontium-90 is a particular problem
in the area.
Nuclear Chemistry
14
Nuclear Fusion and H-Bombs
In a hydrogen bomb, nuclear fusion of tritium and deuterium provides most of the energy.
3
2
4
1
∆E = - 1.7x109 kJ/mol
1H + 1 H → 2 H e+ 0 n
A H-bomb contains three stages.
1. A conventional explosive that provides the “trigger” for
the nuclear reactions to occur.
2. A “standard” fission reaction to produce the necessary
energy to initiate the fusion reaction.
3. The hydrogen fusion reaction at the core of the bomb.
The complete nuclear process, stages 1, 2 and 3 occur in less
than a second!
Ivy Mike was the first H-Bomb test, it was exploded at 7.15 am local time on November 1st 1952. The mushroom cloud was 8 miles
across and 27 miles high. The canopy was 100 miles wide. Radioactive mud fell out of the sky followed by heavy rain. 80 million
tons of earth was vaporized. Ivy Mike was the first ever megaton yield explosion.
Ivy Mike Nuclear Test
Enewetak Atoll, before Mike shot.
Note island of Elugelab on left.
Nuclear Chemistry
Enewetak Atoll, after Mike shot.
Note crater on left.
15
Sustained Nuclear Fusion - the Holy Grail?
In nuclear fusion, smaller nuclei react to form a larger nucleus. This process also releases a tremendous amount of
energy. The classic example is the fusion of tritium and deuterium.
3
2
4
1
1H + 1 H → 2 H e+ 0 n
∆E =
- 1.7x109 kJ/mol
Products are generally not radioactive. No long-term waste problems.
To make fusion possible three critical requirements are needed:
1. Extremely high T, on the order of 106 to 107 K, are required. This is like the interior of the sun. At
this T, all matter is in the plasma state, individual nuclei and electrons. (Fusion reactions are also
called thermonuclear reactions.) Much research has been directed at using powerful lasers to
produce the needed temperatures.
2. The plasma must be confined long enough for the fusion reaction to occur. (Use of powerful
magnets to contain the reaction have been researched.)
3. The output of energy must be captured in a useable form.
To date, sustainable fusion is still a goal not a reality.
The tokamak design for magnetic
containment of a fusion plasma.
Nuclear Chemistry
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