Physics - Nuclear Physics

Mass Energy Equivalence Relation

E=mc²

Mass Defect

The difference between the mass of a nucleus and the sum of the individual masses of its protons and neutrons at infinite separation
Mass defect = deltam = Zmp + (A-Z)mn - mtotal
Due to the equivalence of mass and energy, this suggests some energy is released in the process meaning some energy is required to hold nucleons together in the nucleus

Binding Energy

The energy required to break a nucleus into its constituent protons and neutrons at infinite separation

Binding Energy per Nucleon

The binding energy of a nucleus divided by the number of nucleons in the nucleus
Higher binding energy per nucleon = higher stability

Impact of Binding Energy Per Nucleon on Fission and Fusion

At low A values: nuclei have lower binding E per nucleon, stay stable when N=Z, so lighter nuclei will undergo fusion
At high A values: nuclei have higher binding E per nucleon, so undergo fission
Gradient is less steep for heavier nuclei hence fission releases less energy
Iron is the most stable nucleus

Nuclear Fusion

Two nuclei combine to form a single nucleus
For fusion to occur, both nuclei must have high enough KE to overcome electrostatic repulsion and get close enough for the strong nuclear force to take effect

Nuclear Fission

A single large nucleus divides to form smaller nuclei
Fission must be induced by firing neutrons at a nucleus, causing it to split into 2 or more daughter nuclei and neutrons. These neutrons can collide with further nuclei, causing a chain reaction, which only stops when all material has undergone fission or a moderator halts the reaction. If uncontrolled this can go on to cause the effects of a nuclear bomb.

Forces at Low Nucleon Number

The strong force dominates over electrostatic repulsion, so under the right conditions fusion occurs
Mass Defect = Binding Energy Released = deltamc²

Forces at high Nucleon Number

The electrostatic repulsion forces dominate over strong nuclear, so under right conditions fission occurs
Mass Defect = Binding Energy Released = deltamc²

Radioactive Decay

The spontaneous, random disintegration of a nucleus to a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle

Random

Exact time of decay of a nucleus cannot be predicted
This can be demonstrated using a GM tube. Near a radioactive source count rate is irrregular and unpredictable showing randomness

Spontaneous

Cannot be influenced by environmental factors

Decay Constant

The probability that an individual nucleus will decay per unit time
A=deltaN/deltat = -lamdaN

Radioactive Decay Equations

N=N0e^-lamdat
A=A0e^-lamdat
C=C0e^-lamdat
Smaller lamda means shallow slope

Half Life

The amount of time taken for the activity of a sample to decrease by half

Derivation of half life equation

At t1/2, N=1/2N0
1/2N0=N0e^-lamdat1/2
ln(1/2) = -lamdat1/2
t1/2 = ln2/lamda