4. Nuclear Fission Flashcards
Fissions means to ____ __ into 2 fragments.
Split up
Why are the fission fragments more stable than the parent nucleus?
Because the fragments have a higher binding energy per nucleon than a large parent nucleus (A > 200).
________ _______ is released by a fission reaction.
Excess energy
Why doesn’t fission usually occur spontaneously even though it is energetically favourable?
The barrier region (Coulomb potential barrier) prevents it
How can fission be triggered?
By bombarding a nucleus with neutrons.
Why is fission a chain reaction?
Because the process of nuclear fission produces ~3 more neutrons when only one is required to trigger it initially.
Briefly describe the process of Uranium fission
- The neutron is fired, causing the U nucleus to be distorted when it is absorbed.
- If the deformation is large enough, the electrostatic repulsion between protons can overcome the strong force.
- The nucleus splits in two (not always evenly as there are many possible combinations for the two products).
What is the energy production from fission of 1 uranium nucleus?
~ 200 MeV of energy
Why is the tunnelling probability lower for fission than for alpha decay?
Because the Coulomb potential barrier is wider, meaning that it is MUCH less likely to occur and an energy input is required instead.
What is the activation energy?
The amount of energy required to overcome the Coulomb potential energy barrier, equal to the height of the height of the barrier. The activation energy must be reached for fission to occur.
An incident nucleon _______ the nucleus.
Deforms
What is the liquid drop model?
A model of how the nucleus deforms due to an incident nucleon.
Which two terms determine whether the nucleus returns to its original shape or splits into two drops when an incident nucleon hits it?
- Surface term
- Coulomb term
(not volume, asymmetry, or pairing term because they depend purely on nucleus composition)
Does volume change when a sphere turns into an ellipsoid?
No
What are the major and minor axes of a prolate ellipsoid?
Major axis: R(1 + ε)
Minor axis: R(1 + ε) ⁻¹/²
R = radius
ε = small deformation parameter
State the surface area of an ellipsoid for small deformations
R = radius
Give the equation for the (modified) surface term of the liquid drop model
Give the equation for the (modified) coulomb term of the liquid drop model
As k increases in the liquid drop model, the surface term __________ so binding energy __________.
Increases
Decreases
As k increases in the liquid drop model, the Coulomb term __________ so binding energy __________.
Decreases
Increases
State the condition for an overall increase in binding energy when a nucleus deforms from a sphere into an ellipsoid
Why can fission occur spontaneously for Z²/A > 47?
Because the deformed nucleus is more stable than the spherical nucleus so a feedback loop develops and fission can occur. This does not happen in reality because the nucleus would have to be much heavier than any known elements.
What is the fission cross-section?
The probability of fission occurring for incident neutrons with a given energy. It has units of area and is usually measured in barns.
A larger fission cross-section equals a ______ probability for fission.
Higher
Convert barns to metres-squared
Describe the plot of the cross-section for neutron induced fission for various isotopes of Uranium
Resonance peaks are due to the internal energy level structure.
Low energy neutrons can cause fission for U-233 and U-235.
U-233 and U-235 have odd protons and neutrons.
U-236 and U-238 have even protons and neutrons.
Why is there an extreme difference in the fissionability by low-energy neutrons depending on the chosen isotope of Uranium?
The pairing term of the semi-empirical binding energy formula determines whether isotopes can undergo fission from a low-energy neutron.
What is the nuclear excitation energy?
The addition of a discrete amount of energy that results in the nucleus being excited from it’s ground state.
What is an excited state denoted by?
*
When a nucleus captures a neutron, it will be in an _______ state.
Excited
How can the excitation energy be calculated?
By calculating the difference in nuclear mass between the excited state and the ground state, assuming that the neutron’s kinetic energy is 0.
Why can fission be induced in U-236 even when an incident neutron has 0 kinetic energy?
Because the excitation energy is 6.5 MeV when the neutron has 0 kinetic energy but its activation energy is only 6.2 MeV. The means that the excited state is enough to induce fission even though the incident neutron has 0 kinetic energy.
Why can’t fission be induced in U-238 when an incident neutron has 0 kinetic energy?
Because the energy of the excited state (U-239*) is not enough to induce fission in comparison to the activation energy (6.6 MeV) unless the incident neutron carries significant kinetic energy (of order MeV).
Even-odd pairing has _ pairing so, when a neutron is captured the pairing becomes ____-____ and the effect of the pairing term is to ________ the excitation energy.
0
Even-even
Increase
Even-even pairing has ___ pairing so, when a neutron is captured the pairing becomes _____-____ and the effect of the pairing term is to ________ the excitation energy.
+ ve
Even-odd
Decrease
Odd-even pairing has _ pairing so, when a neutron is captured the pairing becomes ____-____ and the effect of the pairing term is to ________ the excitation energy.
0
Odd-odd
Decrease
Odd-odd pairing has ___ pairing so, when a neutron is captured the pairing becomes _____-____ and the effect of the pairing term is to ________ the excitation energy.
-ve
Odd-even
Increase
What 4 things typically comprise a fission reactor?
- Fuel rods
- Moderator
- Control rods
- Coolant
What is the purpose of fuel rods in a fission reactor?
To provide the fissionable material. They are usually made of Uranium (99.8% U-238 and 0.72% U-235) or enriched uranium (3% U-235).
How many fast neutrons are produced by each fission on average?
2.44
What is the purpose of a moderator in a fission reactor?
To slow neutrons down by collisions to sustain the chain reaction. They are usually light nuclei like carbon.
What is the purpose of control rods in a fission reactor?
They have a high neutron absorption cross-section to control the rate of fission and prevent the reaction from getting out of control. They are usually made of boron or silver.
What is the purpose of coolant in a fission reactor?
To absorb heat and then to generate power. The coolant is typically water.
In fission, some neutrons will ______ or be ________ without producing another fission.
Escape
Absorbed
When is a chain reaction self-sustaining?
If on average one neutron from a fission goes on to produce a further fission.
When is a chain reaction building?
If each fission leads to > 1 further fissions.
What happens when a fission reaction is building rather than purely being self-sustaining?
If not checked it can result in a catastrophe like in Chernobyl or atomic bombs.
Define the reproduction factor, k
The ratio of the number of neutrons in a given fission generation to the preceding one (should be greater or equal to 1 for a self-sustaining chain reaction).
What is the critical reproduction factor for a fission reactor?
k = 1
When is the reproduction factor for a fission reactor supercritical?
When k > 1
When is the reproduction factor for a fission reactor subcritical?
When k < 1
Give the formula for the reproduction factor
k = reproduction factor
η = effective number of (fast) neutrons per fission per original thermal neutron
ε = fast fission factor from fissions with U-238
p = neutron capture from U-238
f = other absorptions
What is the typical value of η in the reproduction factor formula?
Typically ~ 1.3 for natural uranium
What is the typical value of ε in the reproduction factor formula?
Typically ~ 1.03
What is the typical value of p in the reproduction factor formula?
Typically ~ 0.9
What is the typical value of f in the reproduction factor formula?
Typically ~ 0.9
