Nuclear

Question 1

Nuclear binding energy

Answer 1

This is the energy needed to pull the nucleus apart. Minus Mass defect times the speed of light squared

Question 2

Graph of stability

Answer 2

This is a plot of proton number Z against neutron number N. The line of stability runs roughly down the middle with a small curvature going from (2,2) to (126,82)

Question 3

Binding energy graph

Answer 3

Binding energy per nucleon against number of nucleons A. Heavy nuclei binding energy about 8MeV/nucleon. Maximum at A=56 iron. Local peaks occur at A=4n

Question 4

Mass defect

Answer 4

The difference between the mass of the constituent elements minus the mass of the Nucleus.

Question 5

Cross section

Answer 5

The area around a particle another particle must exist in in order for there to be a collision.

Question 6

Fermis squared, barns and pico barns

Answer 6

10^-30, 10^-28 and 10^-40. All in m^2

Question 7

Rutherford

Answer 7

First scattering experiments. Nuclei are very small. Radii R=r_0A^1/3. r_0 nucleon radius, so incompressible

Question 8

Mott

Answer 8

Rutherford assumed alpha is point like. Mott used electrons instead as they are point like. This meant considering magnetic moment, relativistic effects and nuclear recoil

Question 9

Hofstadter

Answer 9

With his testing of mott is was seen that really the nucleus has a fussy edge and the density changes continuously at the edge

Question 10

Liquid drop model

Answer 10

Central density remains constant no matter the size. R is proportional to the cube root of A. Force binding is short range making it incompressible. All like a drop of water

Question 11

Liquid drop binding

Answer 11

Volume term (shört range force) minus surface term (nucleons on the surface are less tightly bound) minus coulomb (repulsion between protons) term. Two minus because they weaken the bounding.

Question 12

Semi empirical mass formula

Answer 12

The same as binding energy with two extra terms. The first term is the asymmetry term, it says that the most stable is N=Z the more asymmetric the less tightly bound. The second is the pairing term. It says the lowest energy state is when all the protons and neutrons are paired off. These are quantum effects

Question 13

Disadvantages with SEMF

Answer 13

Gets the general shape of binding energy graph right, predicts nuclear decay and tells us fission is possible. But it fails to explain the spikes at 4n, why some nuclei aren’t spherical and properties like nuclear spin, parity and magnetic moment

Question 14

She’ll model

Answer 14

Treating the nucleus as a quantum well with quantised energy levels that can exist certain numbers of nucleons.

Question 15

Shell model evidence

Answer 15

Peaks not seen at 4n and magic numbers. It’s not true the line of N=Z which is stable but in fact the magic numbers. High abundance for magic numbers as they are more stable. See peaks at magic numbers for neutron binding energy. Neutron capture energy is at lows at magic numbers as they are stable nuclei. The electric quadruple moment deforms the nuclei for unfolded shells. Takes a lot more energy to put the a nucleus into the first excited state when shells are full. If both protons and neutrons are a magic number then the stability increases further.

Question 16

Potential of shell model

Answer 16

The inverse of the Saxon woods mass distribution

Question 17

Spectroscopic notation

Answer 17

Basic energy level brackets angular momentum l the vector coupling j as a subscript

Question 18

Issue with Saxon wood potential

Answer 18

Didn’t take into account the spin orbit coupling. The alignment of l and s. This is done with a dot product of the two. This new model reduces degeneracy

Question 19

Sources of neutrons

Answer 19

Elastic scatter, inelastic scatter, neutron capture and spallation

Question 20

Reactors

Answer 20

First reaction is set off releasing three neutrons. Often to energetic so a moderator is use. Control rod containing boron or cadmium. Large cross section for thermal neutron interactions.

Question 21

Nonelactic

Answer 21

Secondary particle isn’t a neutron

Question 22

Capture

Answer 22

Disappearance at low neutron energy. New isotope formed and may be radioactive and make it good to test properties

Question 23

Neutron spallation

Answer 23

After neutron capture the nucleus fragments.

Question 24

Endothermic reactions

Answer 24

Need to overcome negative Q, has a threshold energy

Question 25

Collective treatment

Answer 25

Bringing together many ideas to deal with the issue of large nuclei which aren't properly described by the shell model. Helps describe rotational and vibrational modes in non spherical nuclei

Question 26

Nuclear spin equal to zero for an even-even nuclei

Answer 26

No magnetic moments

Question 27

Nuclear magnetic moment

Answer 27

mu is equal to the g factor times e hbar/ 2m_p times nuclear spin. Or g_j j mu_N

Question 28

Electric quadrupole moment

Answer 28

Describes the nuclear charge distribution. Filled shells mean spherical shape with EQM=0 and with unfilled a finite EQM

Question 29

Odd protons in outer shell

Answer 29

An extra proton leads to oblate Q<0. A proton hole leads to prolate for Q>0

Question 30

Decay constant

Answer 30

Lambda is ln(2) over half life

Question 31

Number of particle after time t

Answer 31

The starting number of particles times the exponential of minus decay constant times time

Question 32

Shape of nuclear potential

Answer 32

Starts high crosses the r axis hits a minimum values and the goes towards the r axis

Question 33

Deuteron

Answer 33

The spins are aligned to increase nuclear potential. Leading to a spin component of the wave function with this there is a isospin term. This is because two fermions can't exist in the same state and space. So they must be different