# NUCLEAR PHYSICS

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• Created by: CPev3
• Created on: 09-04-21 15:20

## Energy equation

E = mc2

• E = energy
• m = mass
• c = speed of light in a vacuum, 3 x 108 ms-1
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## Energy equation interpretations

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 Ek

∴ mass > rest mass

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## Alpha decay

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

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## Annihilation

Electron and positron completey destroy each other

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

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Δm = 2me

ΔE = 2mec2

Minimum energy of two gamma photons = 2mec2

Minimum energy of one gamma photon = mec2

= (9.11 x 10-31) x (3 x 108)2

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

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## Pair production

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

Minimum energy of the electron-positron pair = 2mec2

Minimum energy of the x-ray photon = 2mec2

= 2 x (9.11 x 10-31) x (3 x 108)2

= 1.02 MeV

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## Deuterium nucleus

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

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## Mass defect

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

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## Binding energy

Minimum energy required to separate a nucleus into its constituent nucleons

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Binding energy of nucleus = mass defect x c2

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## Binding energy per nucleon

↑ nucleons = ↑ binding energy

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

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## BE per nucleon-nucleon number graph

• 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
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## Induced fission

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

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Thermal neutron: slow neutron, mean Ek 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

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## Fission energy

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

• Ek of daughter nuclei
• Ek of neutrons
• Energy of neutrinos
• Gamma photons
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## Chain reaction

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

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## Fission reactor components

Coolant

• Removes thermal energy

Moderator

• Slows down (but does not absorb) fast neutrons
• Collide elastically with protons, transferring Ek and slowing down
• Water/ carbon- cheap and readily available

Control rods

• 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)
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## Environmental impact of nuclear waste

2389210n → 23992U → 23993Np + 0-1e + ve → 23994Pu + 0-1e + ve

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Pu-239

• 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
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## Fusion

• 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
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## Proton-proton cycle

• 11p + 11p → 21H + 01e + ve
• 21H + 11p → 32He
• 32He + 32He → 42He + 211p

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

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## Why fusion hasn't been achieved on Earth

• Cannot maintain high temperatures for long enough to sustain fusion
• Cannot confine extremely hot fuel within a reactor
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