IB Physics 12

Nuclear Physics 6

Mr. Jean

The plan:

• Video clip of the day– Example of fission energies– Example of fusion energies– Recap of nuclear physics

Conservation LawsFor any nuclear reaction, there are three conservation laws which must be obeyed:For any nuclear reaction, there are three conservation laws which must be obeyed:

Conservation of Charge:Conservation of Charge: The total charge The total charge of a system can neither be increased nor of a system can neither be increased nor decreaseddecreased..

Conservation of Nucleons:Conservation of Nucleons: The total The total number of nucleons in a reaction must be number of nucleons in a reaction must be unchanged.unchanged.

Conservation of Mass Energy:Conservation of Mass Energy: The total The total mass-energy of a system must not change mass-energy of a system must not change in a nuclear reaction.in a nuclear reaction.

Example 7: Use conservation criteria to determine the unknown element in the

following nuclear reaction:1 7 41 3 2

AZH Li He X energy

Charge before = +1 + 3 = +4Charge before = +1 + 3 = +4

Charge after = +2 + Z = +4Charge after = +2 + Z = +4

Z = 4 – 2 = 2Z = 4 – 2 = 2

Nucleons before = 1 + 7 = Nucleons before = 1 + 7 = 88Nucleons after = 4 + A = 8Nucleons after = 4 + A = 8

(Helium has(Helium has Z = Z = 22))

(Thus, (Thus, A =A = 44))

1 7 4 41 3 2 2H Li He He energy

1 7 4 41 3 2 2H Li He He energy

Conservation of Mass-EnergyThere is always mass-energy associated There is always mass-energy associated with any nuclear reaction. The energy with any nuclear reaction. The energy released or absorbed is called the Q-value released or absorbed is called the Q-value and can be found if the atomic masses are and can be found if the atomic masses are known before and after.known before and after.

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2Q H Li He He

Q is the energy released in the reaction. Q is the energy released in the reaction. If Q is positive, it is exothermic. If Q is If Q is positive, it is exothermic. If Q is negative, it is endothermic.negative, it is endothermic.

Example 8: Calculate the energy released in the bombardment of lithium-7 with hydrogen-

1.1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2Q H Li He He

73 7.016003 uLi

42 4.002603 uHe1

1 1.007825 uH

Substitution of these masses gives:Substitution of these masses gives:

QQ = 0.018622 u(931.5 = 0.018622 u(931.5 MeV/u)MeV/u)

Q =17.3 MeV

Q =17.3 MeV

42 4.002603 uHe

The positive Q means the reaction is The positive Q means the reaction is exothermic.exothermic.

Nuclear Fission:

• Critical Mass: if mass of uranium is too small, too many neutrons escape without causing further fission in uranium so the reaction cannot be sustained

• Thermal Neutron: low-energy neutron (≈1eV) that favors fission reactions – energy comparable to gas particles at normal temperatures

Nuclear Reactions:

Fission & Fusion Problems:

Natural Isotopes:

• Naturally Occurring Isotopes of Uranium:

• Uranium-238: most abundant, 99.3%, very small probability of fissioning when it captures a neutron, not used for fuel, more likely to capture high energy neutron than low energy one

• Uranium-235: 0.3%, 500 times greater probability of fissioning when captures a neutron but must be a low-energy (thermal) neutron, used for fuel

Fuel Enrichment:

• This process of increasing proportion of uranium-235 in a sample of uranium – 1) formation of gaseous uranium (uranium

hexafluoride) from uranium ores– 2) Separated in gas centrifuges by spinning –

heavier U-238 moves to outside– 3) increases proportion of U-235 to about 3%

to be used as fuel in nuclear reactors

Fuel Enrichment:

• Advantage: more uranium is available for fission and reaction can be sustained

• Disadvantage: enriched fuel can be used in the manufacture of nuclear weapons – threat to world peace – 85% = weapons grade

Inside the reactor:

• Moderator: material (water, graphite) used to slow down high-energy neutrons emitted from fission reactions to thermal levels for use in further fission reactions to sustain the chain reaction - slow neutrons by collisions

• Control Rods: inserted between fuel rods – made of neutron-absorbing cadmium or boron -used to control reactor temperature to prevent overheating – lowered if too many neutrons/reactions and excess thermal neutrons are absorbed

Nuclear Waste:

• Low-level waste: radioactive material from mining, enrichment and operation of plant – must be disposed of – left untouched or encased in concrete

• High-level waste: disposal of spent fuel rods- some isotopes have ½ lives of thousands of years – plutonium 240,000 years

• stored under water at reactor site for several years to cool of then sealed in steel cylinders, buried underground

• reprocessed to remove any plutonium and useful uranium, remaining isotopes have shorter ½ lives and long-term storage need is reduced

• Nuclear Weapons Manufacture: – Enrichment technology could be used to make

weapons grade uranium (85%) rather than fuel grade (3%)

– Plutonium is most used isotope in nuclear weapons and can be gotten from reprocessing spent fuel rods

Example Question: Suppose the average power consumption for a household is 500 W per day. Estimate the amount of uranium-235 that would have to undergo fission to supply the household with electrical energy for a year. Assume that for each fission, 200 MeV is released.

Nuclear Fission:

• http://www.youtube.com/watch?v=szpnRx7U41M (Yelling guy)

• http://www.youtube.com/watch?v=0kLXGTob9s8 (Non-yelling)

Example Question #2:

• A fission reaction taking place in a nuclear power station might be– Estimate the initial amount of uranium-235 needed

to operate a 600 MW reactor for one year assuming 40% efficiency and 200 MeV released for each fission reaction.

235 1 141 92 192 0 56 36 03U n Ba Kr n

Nuclear Fusion:

Nuclear Fusion: • Nuclear Fusion: Two light nuclei combine to form

a more massive nucleus with the release of energy.

• Write the reaction equation for the fusion reaction shown below.

2 3 4 11 1 2 0H H He n

• To calculate how much energy is released in this fusion reaction we would need to again use the change in mass vs. energy relationship.

• Plasma: fuel for reactor – high energy ionized gas (electrons and nuclei are separate) – if energy is high enough (hot enough), nuclei can collide fast enough to overcome Coulomb repulsion and fuse together

• Magnetic confinement: charged particles are contained via magnetic fields – travel in a circle in a doughnut shaped ring (tokamak)

• Heating Plasma: accelerate nuclei by means of magnetic fields and forces = high temperatures (high kinetic energies)

• Problems with current fusion technology: – Maintaining and confining very high-density and

high-temperature plasmas – very difficult to do – uses more energy input than output – not commercially efficient

Fusion Reactions: