Download 7.3 – Nuclear Reactions, Fission and Fusion 7.3.1 – Describe and

7.3 – Nuclear Reactions, Fission and Fusion
7.3.1 – Describe and give an example of an artificial transmutation
7.3.3 – Define the term unified atomic mass unit
Students must be familiar with the units MeV c -2 and GeV c -2 for mass
7.3.4 - Apply the Einstein mass – energy equivalence relationship
7.3.5 – Define the concepts of mass defect, binding energy and binding energy per nucleon
7.3.6 – Draw and annotate a graph showing the variation with nucleon number of the
binding energy per nucleon
Students should be familiar with binding energies plotted as positive quantities
7.3.7 - Solve problems involving mass defect and binding energy
Transmutation
● Nuclei can change by emitting radioactive particles but they can also change by GAINING
nucleons through TRANSMUTATION
● This can happen naturally in places like the atmosphere or be artificial initiated by
bombarding a target with high energy particles
●
Furthermore the higher the charges of the things you are trying to smash together the more
energy they must possess in order to overcome the electrostatic repulsion.
Examples:
Complete the following transmutation equations
1.
2.
3.
Unified atomic mass unit:
● In nuclear physics it is more convenient to use a smaller unit than kilogram to measure
mass.
● This is the unified atomic mass unit (u) – defined to be 1/12 the mass of a carbon – 12
atom.
We know one mole of carbon has a mass of 12 g. Therefore we can find the mass of one u in terms
of kg.
1u=
Example:
Determine the mass in unified atomic mass units for each of the subatomic particles
Unified Atomic Mass
Electron
Proton
Neutron
1.6605402 X 10-27 kg
9.1093897 X 10-31 kg
1.6726231 X 10-27 kg
1.6749286 X 10-27 kg
Einstein’s Relationship:
We are all familiar with the equation E = mc 2. In this equation the rest energy of an object is given
by E, the rest mass of an object is given by m and c is the speed of light which is quite large c =
3.0 X 108 m/s. The reason we say rest mass is due to relativity the mass of an object actually
increases as it moves faster, but this phenomenon is really only seen when the object’s speed is
close to that of light.
As a result of this relationship we can state mass as
is given as MeV c -2 or GeV c -2.
, which means another unit of mass
Find the energy of one atomic mass unit in MeV.
Using this determine the energy for each of the subatomic particles in MeV.
Mass Defect and Binding Energies:
Binding Energy - This the amount of energy required to pull the nucleus completely apart. That is to
overcome both the electromagnetic and strong nuclear force!
Consider the helium nucleus:
The mass of the nucleus would simply equal the mass of the atom minus the mass of all the
electrons. Note we need a lot of decimal places here. The mass of helium is 4.002602 u.
Now the nucleus is made up of two protons and two neutrons so we can also determine the mass of
the nucleus by adding these up.
What do you notice about the two ways of determining the mass of the nucleus?
This is referred to as the mass defect!!!
Mass Defect: Is the amount of mass difference between a nucleus and the sum of its components.
It is a result of the nucleus bonding together, once a bond is formed energy is released according to
Einstein’s equation.
In the case of helium this means that the nucleons of helium are more stable together than apart
(because they have less energy together).
So going the opposite way to rip a helium nucleus apart you would have to put in this amount of
binding energy.
Now when dealing with these energies it is convenient to express the values in MeV instead of
joules. Let us express 1 u in terms of MeV.
The Math:
Determine the binding energy for helium:
Determine the binding energy for carbon given that the atomic mass of carbon is 12.00000 u
Now consider the alpha decay of Ra - 226 - Write the balanced nuclear equation:
Since Ra - 226 undergoes alpha decay this must mean that it is more stable after the decay than
before, so the alpha decay process releases energy. This energy is then transformed into kinetic
energy of the resulting particles.
Determine the mass defect given mass of radium is 226.0254 u and mass of radon is 222.0000 u
Use Einstein’s relationship to convert this to energy.
So this is the amount of energy released when each Ra - 226 decays. So determine how much
energy would be released by the decay of 50.0 g of Ra - 226.
Practice:
The binding energy for Fe - 56 is 492.4 MeV. Determine the atomic mass of Fe - 56.
Nuclear Reactions:
Nuclei can decay naturally or if energy is supplied to into in order to account for the binding energy.
For example N - 14 can collide with an alpha particle to produce O - 17 and a proton. This process
is called TRANSMUTATION, as we have an atom transforming into another atom.
Write the balanced nuclear reaction:
Determine which side has a greater mass:
What must be required for this transmutation to occur?
So looking back at the binding energy curve you can see that there is a section for fusion and a
section for fission. These are the two types of nuclear reactions.
FUSION:
FISSION:
Nuclear Fusion:
Consider the fusion reaction between two H -2 nuclei which produces H - 3 and a neutron. Write
the balanced nuclear reaction:
Determine the mass defect for this reaction and whether energy is required or released. Given that
the mass of deuterium is 2.014102 u and the mass of tritium is 3.016049 u.
Why do you think this reaction can only occur on the sun?
This process of nuclear fusion actually prevents stars from collapsing. In a star there is actually a
delicate balance between the force of gravity which is huge since it is so massive and the outward
force as a result of the fusion reaction. Once the fuel dries up and fusion is no longer possible a
star may undergo a supernova if it is heavy enough.
https://www.youtube.com/watch?v=Z4l6jqKL5Qo
Stars older than our Sun obtain part of their energy from the fusion of three He - 4 atoms to produce
C - 12. How much energy is liberated in this type of reaction, if the mass of He - 4 = 4.002602 u
and the mass of C - 12 = 12.00000 u.
Nuclear Fission:
This is a result of a heavy nucleus splitting into a lighter nucleus, but it often requires a little push.
In the case of U - 235 this push is given by neutron bombardment. U - 235 absorbs a neutron and
creates U - 236. The U - 236 then decays into Ba - 144, Kr - 89 and 3 neutrons. Write the
balanced nuclear reactions.
This is an example of a chain reaction since one neutron actually release three which can then go
an initial the decay of 3 more U - 235 etc.
Determine the amount of energy released by the reaction of 1 kg of Uranium.
IB Practice Problems - Topic 7
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
Problem 6:
Problem 7: