Nuclear Fission (Part 1)

Question 1

What do we assume in the liquid drop model?

Answer 1

• Assume all nuclei is a continuous medium
• Hold together by strong force (surface tension)
• Pushed apart by electrostatic force

Question 2

What is neutron absorption?

Answer 2

When neutrons collide with nuclei and are absorbed, making the atom gain a neutron.

Question 3

What happens to Uranium-238 after it absorbs a neutron?

Answer 3

It can undergo beta decay twice to form Pu-239.

Question 4

What is the new U-239 like and what happens?

Answer 4

It is highly deformed and therefore there may be fission fragments which repel due to electrostatics.

Question 5

What is the average number of neutrons which are released?

Answer 5

~2.5

Question 6

What is an example of fission fragments?

Answer 6

Kr-92 and Ba-141, with 3 neutrons released.

Question 7

What is the approximate energy release of nuclear fission?

Answer 7

~200 MeV

Question 8

What is the chain reaction which happens in nuclear fission?

Answer 8

Since the number of neutrons which are released is > 1, a chain reaction occurs when these neutrons are absorbed by other atoms.

Question 9

What is the equation for the probability of hitting a nuclei?

Answer 9

P = #of nuclei*σ/A, where σ is the effective cross section area of nucleus

Question 10

What kind of ‘target’ does a neutron ‘see’ and why? What is the equation for the area of the target?

Answer 10

A spherical target as it is not effected by nuclear charge.

σ = π*R^2

Question 11

What happens in an elastic scattering event?

Answer 11

• Total KE is conserved
• If nuclear mass&raquo_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)

Question 12

What are the 3 possibilities after neutron absorption?

Answer 12

• n emitted with lower KE and some gamma rays
• n capture
• Fission with the reaction cross section σ(f)

Question 13

What happens in neutron capture?

Answer 13

• Nucleus relaxes by emitting gamma rays

- U is now unstable so beta decays to Np and then to Pu

Question 14

What happens in the fission reaction? What is the tot cross section of this reaction?

Answer 14

Atom divides into two new atoms and more neutrons.

σ(total) = σ(elastic)+σ(inelastic)+σ(gamma)+σ(fission)

Question 15

What are thermal neutrons?

Answer 15

Neutrons in thermal equilibrium with their surroundings.

Question 16

What does a graph of neutron energy against spectral shape look like?

Answer 16

Negative skew going off to zero on right

Question 17

What is the equation for the de Broglie wavelength?

Answer 17

λ = h/mv

Question 18

On a graph of σ(f) against neutron energy, what does the dotted line represent?

Answer 18

Resonance region dominated by spikes at resonant energies.

Question 19

What is σ(f) approximately equal to for neutrons with E<1 MeV?

Answer 19

~0

Question 20

What is σ(f) approximately equal to for neutrons with E>1 MeV?

Answer 20

~1/4* σ(g)

Question 21

About how many neutrons from the first fission initiate secondary fission?

Answer 21

0.46

Question 22

Why can’t you have reactors with only U-238 in it?

Answer 22

Because each reaction reduces the number of neutrons.

Question 23

Why is it better to slow neutrons down?

Answer 23

Because the cross section for fission increases with lower energy neutrons.

Question 24

What are 2 things which can power thermal nuclear reactors?

Answer 24

Fuel, moderator (used to slow neutrons down, thus increasing reaction rate), control rods, or coolant.

Question 25

What are 3 common moderators?

Answer 25

• Hydrogen (but can absorb neutrons)
• Deuterium (doesnt absorb neutrons)
• Graphite (less efficient than H)

Question 26

What are control rods used for? What are some example control rod materials?

Answer 26

Absorb n slowing the reaction down. Usually Cadmium and Boron.

Question 27

What are two types of coolant?

Answer 27

• Graphite moderator

- Water

Question 28

What is the equation for the rate of change of number of neutrons in time?

Answer 28

dФ/dt = (K-1)*Ф/τ, where K is factor increase after each fission, and τ is mean neutron lifetime, or time between fissions.

Question 29

What is the equation for the reactor period and what happens when this is +ve or -ve?

Answer 29

T = τ/(K-1)

T>0, # n exponentially increase
T<0, #n exponentially decrease

Question 30

What are delayed neutrons?

Answer 30

Where atoms beta decay to other nuclei before the release neutrons.

Question 31

What is the equation for τ, the average time between fission?

Answer 31

τ = (1-α)τ(prompt)+ατ(delayed), where α is the fraction of neutrons delayed.

Question 32

What are prompt neutrons?

Answer 32

Neutrons from direct fission.

Question 33

What are the isotopes separated through in a fision reaction?

Answer 33

• Gaseous diffusion

- Gas centrifugation