NUCLEAR PHYSICS

E = mc²

• E = energy

• m = mass

• c = speed of light in a vacuum, 3 x 10⁸ ms^-1

Mass is a form of energy

Annihilation: electron and positron completey destroy each other

Entire mass of particles transformed into two gamma photons

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Energy has mass

Moving object has E_k

∴ mass > rest mass

Parent nucleus decays into a daughter nucleus when it emits an alpha particle

Total mass and energy in a system is conserved

Energy is released

Must be a decrease in mass

Mass of parent nucleus > mass of alpha particle + daughter nucleus

Δm = ΔE

Electron and positron completey destroy each other

Entire mass transformed into energy in the form of two gamma photons

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Δm = 2m_e

ΔE = 2m_ec²

Minimum energy of two gamma photons = 2m_ec²

Minimum energy of one gamma photon = m_ec²

= (9.11 x 10^-31) x (3 x 10⁸)²

= 0.51 MeV (greater if the particles also have E_k)

X-ray photon disappears to produce an electron-positron pair

Minimum energy of the electron-positron pair = 2m_ec²

Minimum energy of the x-ray photon = 2m_ec²

= 2 x (9.11 x 10^-31) x (3 x 10⁸)²

= 1.02 MeV

1 proton + 1 neutron

Bound together by the strong nuclear force

Work must be done to overcome the force

Mass is a form of energy

Mass of proton + neutron > mass of deuterium nucleus

Difference between the mass of a nucleus and the mass of its separated constituent nucleons

Minimum energy required to separate a nucleus into its constituent nucleons

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Binding energy of nucleus = mass defect x c²

↑ nucleons = ↑ binding energy

↑ binding energy per nucleon = nucleons more tightly bound = nucleus more stable

• A < 56: ↑ A = ↑ BE per nucleon

• A > 56: ↑ A = ↓ BE per nucleon

• Greatest BE per nucleon = most stable isotope = Fe-56

• He-4, C-12 and O-16 have an abnormally higher BE per nucleon than their immediate neighbours

U from mined ore = 99.3% U-235 + 0.7% U-238

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Thermal neutron: slow neutron, mean E_k similar to thermal energy of particles in reactor core

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U-235 + thermal neutron → unstable U-236 → daughter nuclei + fast neutrons

²³⁵₉₂U + ¹₀n → ²³⁶₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n

Total mass of particles before fission > total mass of particles after fission

Δm = ΔE

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Total binding energy before fission < total binding energy after fission

Δ binding energy = ΔE

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ΔE

• E_k of daughter nuclei
• E_k of neutrons
• Energy of neutrinos
• Gamma photons

3 fast neutrons produced in a fission reaction slowed down

Start 3 more fission reactions

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Number of neutrons = 3ⁿ where n = number of fission reactions

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Number of neutrons and rate of energy release increase exponentially with time

Not ideal in a nuclear rector

One thermal neutron survives between successive fission reactions

Coolant

• Removes thermal energy

Moderator

• Slows down (but does not absorb) fast neutrons

• Collide elastically with protons, transferring E_k and slowing down

• Water/ carbon- cheap and readily available

Control rods

• Boron/ cadmium- their nuclei readily absorb neutrons

• Ensure that one slow neutron survives between successive fission reactions

• Pushed into reactor core to slow down/ stop fission

Fuel rods

• Contain enriched uranium (U-235 + U-238)

²³⁸₉₂ + ¹₀n → ²³⁹₉₂U → ²³⁹₉₃Np + ⁰_-1e + v_e → ²³⁹₉₄Pu + ⁰_-1e + v_e

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Pu-239

• Toxic and radioactive

• Daughter nuclei produced from its fission reactions are radioactive

• Half-life of 24 thousand years

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• Must not enter water and food supplies

• Buried deep underground for many centuries

• Burial locations must be geologically stable/ secure from attack

• Repulsive electrostatic force between the positive nuclei

• High temperature = nuclei move faster and are closer together

• Short-range strong nuclear force attracts them into a larger nucleus

• High density = high number of fusion reactions per second 

• ¹₁p + ¹₁p → ²₁H + ⁰₁e + v_e

• ²₁H + ¹₁p → ³₂He

• ³₂He + ³₂He → ⁴₂He + 2¹₁p

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Difference in BE (nucleon number x BE per nucleon) = energy released

• Cannot maintain high temperatures for long enough to sustain fusion

• Cannot confine extremely hot fuel within a reactor