E = mc2 and Energy from Nuclear Fission
Integrated Science 3
6/06
Name
Per.
Background
Matter and energy are directly related. All matter contains energy and energy is needed to change
matter (move it, rearrange it, etc.) Matter can change in three ways. The types of change are: physical,
chemical and nuclear. The changes differ based on what happens to the particles that make up the matter.
If the atoms and/or molecules of a substance are not changed into something new (their chemical formulas
are preserved), then the change is just physical. If the atoms are rearranged to form new molecules with
new chemical formulas then the change is chemical. If the nuclei of atoms are changed so that the original
atom ‘turns into’ a new atom, then the change is a nuclear change.
All changes in matter involve energy. During physical and chemical changes of matter, stored energy is
released and/or outside energy is absorbed. Furthermore, the mass of the substances before and after the
change is the same (conserved).
In a nuclear change mass is not conserved. The ‘missing matter’ is turned into pure energy. This
phenomena was not understood until the early 1900’s. As a result, the Law of Conservation of Matter was
changed to the Law of Conservation of Matter and Energy. Scientists now know that a tremendous amount
of energy is stored inside the nuclei of atoms. When these nuclei are split apart (fission) or joined together
(fusion), a tiny bit of mass is ‘lost’ and a huge amount of energy is released.
This worksheet will focus on a fission reaction. The specific masses of the reactants and products will
be compared and then turned into their energy equivalent.
Nuclear Fission
When a U-235 atom is bombarded with a neutron, the atom splits up and its nuclear components
reorganize into smaller atoms. When this happens, it gives off energy in the form of heat and other types of
radiation. The split Uranium atom also gives off ‘spare’ neutrons. These spare neutrons fly out with
enough force to split other Uranium atoms in the sample. In theory, it is necessary to split only one U-235
atom, and the neutrons from this will split more and more atoms until all that were available in the original
sample of Uranium are broken down. This is called a chain reaction. In an atomic bomb, this progression
takes place at an exponential rate within a millionth of a second. In a nuclear reactor, however, this rate of
decay is controlled. Devices called control rods are used to absorb excess neutrons so that fewer Uranium
atoms are split and therefore, less energy is released.
Consider a different U-235 fission reaction below. This shows a nucleus of U-235 and a neutron
combining to make a nucleus of U-236. The products displayed represent only one of many possible
reactions that might occur, but this is the most common. Lanthanum and Molybdenum are the end
products of a rapid radioactive decay chain resulting from the original reaction. Notice the 7 electrons that
accompany the decay. These particles are the same as Beta radiation.
U-235 Fission Reaction:
235
92
U + 01n 236
92
U 95
42 Mo +
139
57
La + (7)10 e + (2) 01 n
So far, we've been balancing nuclear equations by accounting for all the protons and neutrons on
both sides of the equation. This method, however, does not take into account the true masses of all the
particles. When using a value of 1 atomic mass unit (amu) for both protons and neutrons, we come pretty
close to their actual mass, but it’s not exact. One amu is actually 1.6604 X 10-24 grams. Knowing this value
will allow us to study the mass of substances before and after a nuclear reaction in more depth.
Procedures
• The following tables list the masses of the individual particles found in the U-235 fission reaction
described above. Use them to complete the following set of procedures.
1. Add up the mass of the reactants and products.
Mass of Reactants
Mass of Products
Reactants
Mass (amu)
Products
Mass (amu)
U-235 nucleus
235.0439
molybdenum nucleus
94.9058
one neutron
1.0087
lanthanum nucleus
138.9061
Total
7 electrons
0.0039
2 neutrons
2.0174
Total
• For all calculations, box answers, include units and round to 4 decimal places. Show your work.
2. Calculate the difference between the mass of the reactants and the products.
3. Convert the amu value difference to grams knowing that 1 amu = 1.6604 X 10-24 grams.
4. Explain why this difference in mass occurs.
• Consider Einstein's Equation E = mc2. Ultimately, the world's most famous equation demonstrates that at
an extremely high speed, matter and energy are interchangeable. In other words, the amount of potential
energy (joules) in a given amount of mass (kilograms) can be determined. In the equation, (c) is the speed
of light or 2.998 X 108 meters per second.
5. Convert the mass determined in step 3 to energy in joules (J). First, convert grams (g) to kilograms
(kg). Then use the following equation: (energy in J) = (mass in kg) X (speed of light in meters per second)2
6. Remember that the value you just calculated represents the energy (in joules) evolved due to the
conversion of mass to energy from a single atomic fission episode. But in a gram of U-235, there are
2.6 X 1021 atoms. Calculate the amount of energy evolved if an entire gram of U-235 underwent fission.
7. The fission process is very inefficient. Only 10% (0.10) of the atoms of U-235 are actually split by the
nuclear chain reaction. Given this inefficiency, what is the actual energy yield of a gram of U-235?
8. Convert energy in joules to ft-lbs (1 J = 0.73756 ft-lbs) and then to work days (1 wrk. dy. = 150,000 ft-lbs).
Where does the energy go? Energy is released from fission reactions as: 84 % is kinetic energy of fission products,
2.5 % is kinetic energy of neutrons, 2.5 % is instantaneous release of gamma rays, and 11.0 % is gradual radioactive
decay of fission products. Since anything in motion has heat energy, all forms of radiation actually release heat (which
is what is used to generate electricity). Note that, per particle, about 7 times as much energy is released in nuclear
fusion (when hydrogen atoms fuse) than in fission.