#### Particle and Nuclear Physics

**Balanced Equations**

- α-decay:
^{4}_{2}α- Nucleon number decreases by 4
- Proton number decreases by 2

- β
^{–}-decay:^{0}_{-1}β^{–}- Proton number increases by 1

- β
^{+}-decay:^{0}_{+1}β^{+}- Proton number decreases by 1

- γ-decay:
^{0}_{0}γ- Proton and nucleon number are unchanged

**Mass-Energy Equivalence**

**Einstein’s Mass-energy relation:**E = mc². “Mass of a system increases when energy is supplied to it”- where c is the velocity of light in free space

**Mass Defect (ΔM):**The difference between the total mass of the individual, separate nucleons and the mass of the nucleus.**Binding Energy (ΔE):**The minimum external energy required to separate all the neutrons and protons of a nucleus. It is also the energy released when the nucleus is assembled from its constituent nucleons- The binding energy of a nucleus is a measure of how tightly the nucleus is bound and hence how stable it is
**Binding Energy per Nucleon**of a nucleus is the ratio of the total binding energy to tits nucleon number- The higher the binding energy per nucleon, the most stable the atom is

**Atomic Mass Unit**

- 1u is defined as
^{1}/_{12}of the mass of a neutral atom of carbon-12 — approximately equal to

1.661 × 10^{-27}kg - Mass excess = mass (in u) – nucleon number

**Nuclear Fission and Fusion**

**Fission**is a process in which a massive nucleus splits to form two smaller fragments- The large nucleus has a lower binding energy per nucleon so splits into
*fission fragments*which have higher binding energy per nucleon, therefore, more stable

- The large nucleus has a lower binding energy per nucleon so splits into
**Fusion**is a process by which two very light nuclei join together to form a heavier nucleus- Two light nuclei fuse so the final binding energy per nucleon will be greater than the original value

- In general, if energy is released in a nuclear reaction, then it shows that the binding energy of the product nuclei is greater than that of the reactants

**Spontaneous and Random Nature**

- Radioactive processes are random and spontaneous
**Random:**Impossible to predict and each nucleus has the same probability of decaying per unit time**Spontaneous:**Not affected by external factors such as the presence of other nuclei, temperature and pressure**Evidence on a graph:**- Random: The graph will have fluctuations in count rate
- Spontaneous: The graph has the same shape even at different temperatures, pressures ,etc.

**Radioactive Decay**

- The rate of decay of a given nuclide at any time is proportional to the number (N) of nuclei present at that time
^{dN}/_{dt}= -λN

- The
**activity****(A)**of a radioactive sample is the rate at which nuclei decay or disintegrate - the
**decay constant (λ)**is the probability that an individual nucleus will decay per unit time interval- A = λN

- The above relationship can also be written as:
- x = x
_{0}e^{-λt}- where x could represent activity, number of undecayed nuclei or received count

- x = x

**Exponential Nature**

- The activity of a radioactive substance represents an exponential decay
- The half-life (t
_{½}) of a radioactive substance is the mean time taken for half of the active nuclei in a sample to decay- Assuming the initial activity is 1, at half-life, the activity would be ½, so:
- ½ = (1)e
^{-λt} - Take ln of both sides: ln(½) = -λt
_{½} - Calculate and rearrange: λ =
^{0.693}/_{t½}

- ½ = (1)e

- Assuming the initial activity is 1, at half-life, the activity would be ½, so:
- Thus, decay constant is inversely proportional to its half-life