Lecture 6: Relativity in Action

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Lecture 6 Relativity in Action
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Imagine you convert five grammes of matter into
pure energy ...

• How much energy would be released?
• By Einsteins formula

E mc2 4.494 x 1014 Joules 1.249 x
108 kW hr
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What does this translate into?

• Enough energy to supply electricity for an
  average Singapore household for more than 25,000
  years!
• At current electricity tariffs, this would be
  worth more than 20 million!
• This shows that there is an enormous amount of
  energy locked inside matter

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An atom is composed of

• Electrons light, -ve charged particles
• A heavy nucleus made up of nucleons, namely
• Protons ve charged
• Neutrons neutral
• Protons and neutrons have roughly the same mass,
  and are 1800 times more massive than electrons

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Nuclei are identified by

• Atomic number Z no. of protons
• Mass number A no. of protons plus neutrons

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Symbols for different nuclei
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The Periodic Table of Elements is classified by
atomic number
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Example
Z 1 Hydrogen Z 2 Helium Z 3
Lithium etc.
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Isotopes

• Nuclei with the same no. of protons (Z) but a
  different no. of neutrons (so A is different)
• E.g., isotopes of hydrogen

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Table of Isotopes
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Atomic Mass Unit
1 amu 1/12 x mass of one 126C atom
1.6604 x 10-27 kg 937.48 MeV
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Table of Isotope Masses
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Consider the following fusion reaction
i.e., neutron proton ? deuterium
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Masses of initial and final products
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Mass is lost in this reaction
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What happens to the extra mass?

• Extra mass is known as the binding energy of
  deuterium
• It is released in this reaction, in the form of
  KE of deuterium and radiation

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Another example of nuclear fusion
i.e., deuterium tritium ? helium
neutron
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Nuclear Fusion Simulation
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Nuclear fusion is what makes stars shine
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Nuclear Binding Energy

• This is the energy released when the constituent
  protons and neutrons combine to form a nucleus
• Recall
• Equivalently, this is the energy needed to
  separate a nucleus into its constituent protons
  and neutrons

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Binding Energy Graph
The higher the binding energy per nucleon, the
more tightly bound the nucleus is
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Binding Energy Graph (contd)

• The iron nucleus has the highest binding energy
  per nucleon (i.e., it is the most tightly bound
  or stable nucleus)
• Note that the graph starts decreasing after iron
• This suggests that there is an opposite process
  to fusion that also releases energy

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Another reaction which releases energy is
fission
i.e., a large uranium nucleus splits into two
smaller ones while releasing energy
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Nuclear Fission Simulation
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In this reaction ...

• For every neutron causing a fission reaction, an
  average of 2.44 neutrons are produced
• The resulting neutrons then cause even more
  fission reactions to occur
• Could cause a runaway chain reaction to occur

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Chain Reaction Simulation
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Critical Mass

• A chain reaction will occur when the amount of
  fissionable material reaches a certain critical
  mass
• For uranium-235, the critical mass is only in the
  tens of kilogrammes
• This makes small atomic bombs carried by planes
  possible (e.g., Hiroshima)

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Little Boy (Hiroshima)
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Fission in a Nuclear Reactor
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Control Rods

• Rate of fission is controlled by means of
  control rods, which are made from materials
  that are good absorbers of neutrons (e.g., boron)

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Controlled Fusion?

• Main problem in getting hydrogen to fuse
  together is their electrostatic repulsion
• When it is hot enough (about a million Kelvin),
  the KE of the hydrogen would overcome this
  repulsion, and fusion can occur

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Tokamak Fusion Reactor