11. Fission, Decay, Waste

Question 1

Briefly describe the two types fission

Answer 1

Spontaneous - Happens without external energy

Induced - Initiated by addition of energy

Question 2

What does SEMF predict about the splitting of nuclie in fission, and what is observed?

Answer 2

SEMF predicts equal size splitting

However asmmetry is observed due to shell structure

Question 3

From SEMF, what nucleus size can spontaneous fission occur

Answer 3

Typically A > 100

Question 4

What typically happens to daughter nuclei after spontaneous fission?

Answer 4

They are still neutron rich so undergo several beta decays until they reach a stable nuclide

Question 5

At which point does spontaneous fission have a larger probability, to where it competes with alpha decay?

Answer 5

When you have very heavy nuclei, A > 270

- Z^2 / A = 49 for an ellipsoid

Question 6

What type of problem is spontaneous fission, and describe it

Answer 6

A potential barrier problem like alpha decay

• Daughter nuclei needs to get through the barrier
• About 5-6MeV below the top potential (Activation energy)
• Spontaneous fission occurs when this disappears with a large probability

Question 7

What is the probability of a daughter nucleus tunnelling through the potential barrier and why?

Answer 7

Very small because we are dealing with very large objects

Question 8

How can we induce fission in terms of the activation energy?

Answer 8

Add energy to the nucleus typically by absorption of neutrons as they don’t feel the EM force

Question 9

Describe the energies involved in induced fission between even N and odd N nuclei

Answer 9

Odd - Adds the energy of the neutron as well as the pairing energy (often > activation energy)
Even - Capturing neutron movees to a less energetically favourable state by a change in pairing energy

Question 10

Describe and explain the differences in crosssections for U235 and U238

Answer 10

U235 is odd N so very low energy (thermal) neutrons can induce fission
U238 needs neutrons with 1.2MeV

Question 11

State the multiplication factor

Answer 11

k = (no. neutrons produced in n+1 stage) / (no. neutrons produced in n state)

Question 12

Describe what happens to the product nuclei after U235 Fission

Answer 12

• Most of the released energy is carried away by fragments
• 2.5 neutrons created which have a reasonable high energy
• Some fragments give off further neutrons with a mean delay time of 13s

Question 13

What are the k values of interest (multiplication factor)

Answer 13

k = 1: Critical, constant chain reaction rate
k < 1: Subscritical, rate goes down
k > 1: Supercritical, rate goes up

Question 14

What is the equation for the mean free path of a neutron between two collisions

Answer 14

L = 1/(ρ_nucleus * mean σ_total)

• Density of nucleus and mean total cross section
• Mean cross section if U235 and 238 present
• Typically 3cm

Question 15

Describe the critical mass for U235

Answer 15

1 in 6 neutrons cause fission, so will travel Lsqrt(6) = 7cm and then induce fission
- Critical mass corresponds to a radius of 7cm on fission starts

Question 16

What is the equation for the power output of a reactor?

Answer 16

W_f = J N σ_fission
J - Neutron flux
N - Number of nuclei that can undergo fission
W - Fission rate

Question 17

What is the energy released by a single fission?

Answer 17

200MeV for U235

Question 18

Why do we slow the neutrons down, and how are they slowed?

Answer 18

For U235, the cross section is much higher at low neutron energies
- Slow down with a moderator to increase fission efficiency

Question 19

What are actinides?

Answer 19

Radioactive elements with an atomic number between 89 and 103

• Mainly Uranium itself with other elements
• Have very long lifetimes (000s of years)

Question 20

What are the two forms of nuclear waste, and state their lifetimes

Answer 20

Actinides (> 000s of years) and fission products (decades)

Question 21

What is the general cycle of nuclear waste after it is removed from a reactor?

Answer 21

• Stored near reactor for cooling as it has a very high activity even without fission
• Once activity decreases, longer term storage

Question 22

What are the three forms of long term storage for nuclear waste?

Answer 22

1. Deep underground

2. Transmutation + induced fission in accelerator systems

Question 23

What must happen QMically for fusion to occur

Answer 23

The two nuclei have to overcome the Coulomb potential barrier in order to get close enough to fuse