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28 Cards in this Set

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Einstein's mass - energy equation


Energy is conserved in radioactive decay, therefore...?

The mass of the daughter nucleus and α particle in α decay is less than that of the original nucleus, because energy is released. The same is true for β decay.

Minimum energy of two gamma Photons produced in an annihilation reaction

1. Δm=me+mp, as all mass is converted to energy, so Δm=2m.

2. E=(2m)c^2.

3. Therefore the minimum energy is 2mc^2.

Pair production

The production of a particle-antiparticle pair from a single photon.

Minimum energy of a photon in pair production

1. Minimum energy of a electron is mc^2.

2. Minimum energy of the photon is double that.

Mass in atomic units


Mass defect

Mass difference between particles joined in a nucleus and the mass of the particles added together when they are separate.

Binding energy

Minimum energy required to completely separate a nucleus into its constituent protons and neutrons.

Binding energy equation

Binding energy=mass defect of nucleus×c^2

Graph of binding energy per nucleon helps us understand 3 processes

1. Radioactive decay

2. Fission

3. Fusion

For nuclei with A<56, binding energy per nucleon?

Increases as A increases.

For nuclei with A>56, binding energy per nucleon?

Decreases as A increases.

Iron is the?

Most stable isotope in nature. It has the highest binding energy per nucleon.

Helium-4, carbon-12, and oxygen-16 have...?

Abnormally high binding energy per nucleon.

In the fusion process

Two nucleons join to produce a nucleus which has a much higher binding energy than the initial nuclei, therefore releasing energy.

In the fission process

An atom with a high A splits into two lower A nuclei. Energy is released because the two nuclei produced have a higher binding energy than the parent nucleus.

Fuel used for induced fission

1. Uranium is the most common fuel used in reactors.

2. U-235 is only 0.7% of the mined uranium, 99.3% is U-238.

3. U-235 is good at absorbing thermal neutrons, causing them to undergo fission.

4. U-238 usually just captures these neutrons instead of undergoing fission.

Thermal neutrons

Mean kinetic energy is similar to the thermal energy of particles in the reactor core.

When the U-235 absorbes a proton...

It becomes U-236, which is highly unstable, splitting to produce two daughter nuclei and three protons.

Daughter nuclei can be Barium-141 and Krypton-92.

Difference in binding energies after the fission reaction is...?

Equal to the energy released in the reaction.

Key components of a fission reactor

1. Fuel rods are placed within a steel-concrete vessel; the reactor core.

2. Coolant removes the thermal energy from the fission reactions.

3. Fuel rods are surrounded by the moderator.

4. Control rods can be moved in and out of the core.

Fuel rods

Consists of enriched uranium, mainly U-238, and 2-3% U-235.


1. Slows down the neutrons in the reaction.

2. Must be cheap and readily available.

3. Must not absorb the neutrons.

4. Thermal neutrons have a mean kinetic energy if about 3/2kT, and a root mean square speed of a few kms^-1.

5. Fast neutrons just bounce off U-235 nuclei with negligible energy loss, however when they collide elastically with protons or carbon nuclei, they transfer significant kinetic energy and slow down.

6. This makes water and carbon good candidates for the moderator.

7. Some reactors use water as the coolant and the moderator.

Control rods

1. Made of a material which readily absorbs neutrons.

2. Often made of cadmium or boron.

3. Control rod position is monitored to ensure an average of one neutron survives per fission reaction.

4. To slow down or stop the reaction, the rods can be pushed in further.

Environmental impact

1. U-238 nuclei absorb some of the faster protons and quickly decay into plutonium-239.

2. Has a half-life of 24 thousand years.

3. High-level waste, such as fuel rods, has to be buried deep underground for many centuries.

4. They must be safe from leaking into our water supplies. The burial ground must be geologically stable, and safe from attack.

How to make fusion occur

Must bring nuclei within 10^-15m of each other, because the strong nuclear force is attractive at that range, and overcomes electrostatic repulsion.

Proton - proton cycle




Fusion on earth is...?

Not possible, requires very high temperatures for a very long time, which we do not have the technology to achieve.