Nuclear Fission (Part 1) Flashcards
What do we assume in the liquid drop model?
- Assume all nuclei is a continuous medium
- Hold together by strong force (surface tension)
- Pushed apart by electrostatic force
What is neutron absorption?
When neutrons collide with nuclei and are absorbed, making the atom gain a neutron.
What happens to Uranium-238 after it absorbs a neutron?
It can undergo beta decay twice to form Pu-239.
What is the new U-239 like and what happens?
It is highly deformed and therefore there may be fission fragments which repel due to electrostatics.
What is the average number of neutrons which are released?
~2.5
What is an example of fission fragments?
Kr-92 and Ba-141, with 3 neutrons released.
What is the approximate energy release of nuclear fission?
~200 MeV
What is the chain reaction which happens in nuclear fission?
Since the number of neutrons which are released is > 1, a chain reaction occurs when these neutrons are absorbed by other atoms.
What is the equation for the probability of hitting a nuclei?
P = #of nuclei*σ/A, where σ is the effective cross section area of nucleus
What kind of ‘target’ does a neutron ‘see’ and why? What is the equation for the area of the target?
A spherical target as it is not effected by nuclear charge.
σ = π*R^2
What happens in an elastic scattering event?
- Total KE is conserved
- If nuclear mass»_space; n mass, n is scattered without loss in KE (heave atoms diffuse n’s)
- If nuclear mass ~ n mass then n loses KE (light atoms diffuse and slow down n’s)
What are the 3 possibilities after neutron absorption?
- n emitted with lower KE and some gamma rays
- n capture
- Fission with the reaction cross section σ(f)
What happens in neutron capture?
- Nucleus relaxes by emitting gamma rays
- U is now unstable so beta decays to Np and then to Pu
What happens in the fission reaction? What is the tot cross section of this reaction?
Atom divides into two new atoms and more neutrons.
σ(total) = σ(elastic)+σ(inelastic)+σ(gamma)+σ(fission)
What are thermal neutrons?
Neutrons in thermal equilibrium with their surroundings.
What does a graph of neutron energy against spectral shape look like?
Negative skew going off to zero on right
What is the equation for the de Broglie wavelength?
λ = h/mv
On a graph of σ(f) against neutron energy, what does the dotted line represent?
Resonance region dominated by spikes at resonant energies.
What is σ(f) approximately equal to for neutrons with E<1 MeV?
~0
What is σ(f) approximately equal to for neutrons with E>1 MeV?
~1/4* σ(g)
About how many neutrons from the first fission initiate secondary fission?
0.46
Why can’t you have reactors with only U-238 in it?
Because each reaction reduces the number of neutrons.
Why is it better to slow neutrons down?
Because the cross section for fission increases with lower energy neutrons.
What are 2 things which can power thermal nuclear reactors?
Fuel, moderator (used to slow neutrons down, thus increasing reaction rate), control rods, or coolant.
What are 3 common moderators?
- Hydrogen (but can absorb neutrons)
- Deuterium (doesnt absorb neutrons)
- Graphite (less efficient than H)
What are control rods used for? What are some example control rod materials?
Absorb n slowing the reaction down. Usually Cadmium and Boron.
What are two types of coolant?
- Graphite moderator
- Water
What is the equation for the rate of change of number of neutrons in time?
dФ/dt = (K-1)*Ф/τ, where K is factor increase after each fission, and τ is mean neutron lifetime, or time between fissions.
What is the equation for the reactor period and what happens when this is +ve or -ve?
T = τ/(K-1)
T>0, # n exponentially increase
T<0, #n exponentially decrease
What are delayed neutrons?
Where atoms beta decay to other nuclei before the release neutrons.
What is the equation for τ, the average time between fission?
τ = (1-α)τ(prompt)+ατ(delayed), where α is the fraction of neutrons delayed.
What are prompt neutrons?
Neutrons from direct fission.
What are the isotopes separated through in a fision reaction?
- Gaseous diffusion
- Gas centrifugation
