Nuclear and particle physics

1. The nuclear atom:

• a) Alpha-particle scattering experiment (Rutherford experiment): Evidence of a small, charged nucleus:

• Overview: Rutherford’s gold foil experiment involved directing a beam of alpha particles (positively charged helium nuclei) at a thin gold foil.
• Observations:
• – Most alpha particles passed straight through the foil, suggesting that atoms are mostly empty space.
• – A small fraction of alpha particles was deflected at large angles, and a very few rebounded almost directly back.
• Conclusion:
• – These observations led to the conclusion that atoms have a small, dense, positively charged nucleus, where most of the atom’s mass is concentrated.

• b) Simple nuclear model of the atom: Protons, neutrons, and electrons:

• Model:
• – The atom consists of a nucleus (containing protons and neutrons) surrounded by electrons in orbitals.
• – Protons have a positive charge, neutrons are neutral, and electrons have a negative charge.
• Charge balance:
• – In a neutral atom, the number of protons equals the number of electrons.

• c) Relative sizes of the atom and the nucleus

• Atom size:
• – Approximately [math]10^{-10}[/math] m (or 1 Ångström).
• Nucleus size:
• – Approximately [math]10^{-15}[/math]  m (or 1 femtometer).
• Scale:
• – The nucleus is about 100,000 times smaller than the atom, yet it contains nearly all the mass.

• d) Proton number, nucleon number, isotopes, and nuclear notation ([math]{}^{A}_{Z}X[/math])

• Proton number (Z):
• – The number of protons in the nucleus of an atom.
• – Determines the element (e.g., Z=1 is hydrogen, Z=2 is helium).
• Nucleon number (A):
• – The total number of protons and neutrons in the nucleus
• – A=Z+N, where N is the number of neutrons.
• Isotopes:
• – Atoms of the same element with the same proton number (Z) but different nucleon numbers (A), due to different numbers of neutrons.
• – Example: [math]{}_1^1H, {}_1^2H, {}_1^3[/math]Hare isotopes of hydrogen.
• Notation ([math]{}^{A}_{Z}X[/math]):
• – X is the chemical symbol of the element.
• – Z is written as a subscript, and A as a superscript.
• – Example: [math]{}^{12}_{6}C[/math] for carbon-12, [math]{}^{12}_{6}C[/math] for carbon-14.

• e) Strong Nuclear Force

• Definition: The strong nuclear force is the fundamental force that binds protons and neutrons (nucleons) together in the nucleus, overcoming the electrostatic repulsion between positively charged protons.
• ⇒ Properties:
• Short-range nature:
• – The force is attractive between nucleons up to a distance of about 3 femtometers (fm).
• – It becomes repulsive at very short distances (less than 5 fm) to prevent the nucleons from collapsing into one another.
• Strength:
• – The strong nuclear force is much stronger than the electromagnetic force, but its influence is limited to within the nucleus.

• f) Radius of Nuclei ([math]R=r_0 A^{1⁄3}[/math])

• Formula:
• [math]R=r_0 A^{1⁄3}[/math]
• – R: Radius of the nucleus.
• – [math]r_0 [/math]: A constant (approximately 2 fm).
• – A: Nucleon number (number of protons + neutrons in the nucleus).
• Explanation:
• – This relationship shows that the nuclear radius increases with the cube root of the nucleon number.
• – The nucleus is approximately spherical, and its size grows as more nucleons are added.

• g) Mean Densities of Atoms and Nuclei:

• Mean density of a nucleus:
• – The nucleus is extremely dense because it contains almost all the mass of the atom within a very small volume.
• – Volume of nucleus:
• [math]V = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi r_0^3 A [/math]
• – Density of nucleus:
• [math] \rho_{\text{nucleus}} = \frac{\text{Mass of nucleus}}{\text{Volume of nucleus}} \approx \frac{A \cdot m_{\text{nucleon}}}{\frac{4}{3} \pi r_0^3 A} [/math]
• Simplifies to;
• [math] \rho_{\text{nucleus}} = \frac{A \cdot m_{\text{nucleon}}}{\frac{4}{3} \pi r_0^3 A}
  \approx 2.3 \times 10^{17} \, \text{kg/m}^3 [/math]
• Mean density of an atom:
• – The atomic volume is much larger than the nucleus due to the empty space where electrons reside.
• – Atomic densities are much lower, on the order of [math]10^3 kg/m^3 [/math] (comparable to that of solids and liquids).
• Comparison:
• The nucleus is about [math]10^4 [/math] times denser than the average density of an atom.

2. Fundamental particles:

• a) Particles and Antiparticles

• ⇒ Electron–Positron:
• The electron ([math]e^-[/math]) is a negatively charged particle.
• Its antiparticle is the positron ([math]e^+[/math]), which has the same mass but a positive charge.
• ⇒ Proton–Antiproton:
• The proton (p) is a positively charged particle found in the nucleus of an atom.
• The antiproton ([math]\overline{p}[/math]) has the same mass but a negative charge.
• ⇒ Neutron–Antineutron:
• The neutron (n) is a neutral particle found in the nucleus.
• The antineutron ([math]\overline{n}[/math]) has the same mass and no charge but opposite quantum numbers (such as baryon number).
• ⇒ Neutrino–Antineutrino:
• The neutrino (v) is a neutral, very low-mass particle.
• Its antiparticle is the antineutrino ([math]\overline{v}[/math]), which has the same mass but opposite lepton number.

• b) Particle and Antiparticle Properties

• Same mass:
• – Particles and their corresponding antiparticles always have identical mass.
• Opposite charge:
• – For charged particles, the antiparticle has an equal but opposite charge.
• – Example: An electron ([math]e^-[/math]) has a charge of −1, while a positron ([math]e^+[/math]) has a charge of +1.
• For neutral particles (like neutrons and neutrinos), their antiparticles differ in quantum numbers such as baryon or lepton number.

• c) Classification of Hadrons:

• Definition:
• – Hadrons are composite particles made of quarks held together by the strong nuclear force.
• Examples:
• Proton (p):
• – Made of two up quarks and one down quark (uud).
• Neutron (n):
• – Made of one up quark and two down quarks (udd).
• Forces involved:
• – Hadrons experience the strong nuclear force (binding quarks together) and the weak nuclear force (responsible for certain types of particle decay).
• Types:
• – Baryons: Hadrons made of three quarks (e.g., protons and neutrons).
• – Mesons: Hadrons made of one quark and one antiquark (e.g., pions).

• d) Classification of Leptons

• Definition:
• – Leptons are fundamental particles (not made of quarks) that do not experience the strong nuclear force.
• Examples:
• Electron ([math]e^-[/math]):
• – A negatively charged lepton.
• Neutrino ([math]v[/math]):
• – A neutral lepton with extremely low mass.
• Forces involved:
• – Leptons interact via the weak nuclear force (responsible for processes like beta decay).
• – Charged leptons (like electrons) also interact electromagnetically.
• – Leptons do not experience the strong nuclear force.
• Types:
• Charged leptons:
• – Electron ([math]e^-[/math]), muon ([math]μ^-[/math]), tau ([math]τ^-[/math]).
• Neutral leptons (neutrinos):
• – Electron neutrino (​[math]v_e[/math]), muon neutrino ([math]v_μ[/math]​), tau neutrino ([math]v_τ[/math]​).

• e) Quark Model of Hadrons

• ⇒ Quarks: Fundamental particles that make up hadrons. They experience the strong nuclear force.
• Types of quarks: up (u), down (d), and strange (s) (among others).
• Quarks have fractional charges in units of the elementary charge e.
• [math]\begin{gather}u & : +\frac{2}{3} \, e \\ d & : -\frac{1}{3} \, e \\ s & : -\frac{1}{3} \, e \end{gather} [/math]
• ⇒ Antiquarks: The antiparticles of quarks, with opposite charges:
• [math]\begin{gather} \overline{u} & : -\frac{2}{3} \, e \\ \overline{d} & : +\frac{1}{3} \, e \\ \overline{s} & : +\frac{1}{3} \, e \end{gather}[/math]

• f) Quark Structure of Protons and Neutrons

• Proton (uud):
• – Made of two up quarks and one down
• – Charge:
• [math]+\frac{2}{3}e + \frac{2}{3}e – \frac{1}{3}e = +1e[/math]
• Neutron (udd):
• – Made of one up quark and two down
• Charge:
• [math]+\frac{2}{3}e – \frac{1}{3}e – \frac{1}{3}e = 0e[/math]

• g) Charges of the up (u), down (d), strange (s), anti-up ([math]\overline{u}[/math]), anti-down ([math]\overline{d}[/math]) and the ant-strange ([math]\overline{s}[/math]) quarks as fractions of the elementary charge e:

• The charges of the quarks and antiquarks are expressed as fractions of the elementary charge e, which is the charge of a proton (+1e) or the negative of the charge of an electron (−1e):
• ⇒ Quarks:
• – Up quark (u): [math]+\frac{2}{3}e[/math]
• – Down quark (d):[math]-\frac{1}{3}e[/math]
• – Strange quark (s): [math]-\frac{1}{3}e[/math]
• ⇒ Antiquarks:
• – Anti-up quark([math]\overline{u}[/math]) [math]-\frac{2}{3}e[/math]
• – Anti-down quark ([math]\overline{d}[/math]): [math]+\frac{1}{3}e[/math]
• – Anti-strange quark([math]\overline{s}[/math]): [math]+\frac{1}{3}e[/math]
• These fractional charges are key properties of quarks and antiquarks in the Standard Model of particle physics.

• h)  Beta Decay and Quark Transformations

• Beta decay involves the transformation of quarks via the weak nuclear force, mediated by WWW-bosons:

• i) Beta-minus ([math]β^-[/math]) decay:

• A neutron transforms into a proton:
• [math]n \to p + e^- + \overline{\nu}_e[/math]
• In terms of quarks:
• – A down quark (d) converts into an up quark (u):
• [math]d \to u + W^-[/math]
• – The [math]W^-[/math] boson quickly decays:
• [math]W^- \to e^- + \overline{\nu}_e[/math]

• j) Beta-plus ([math]β^+[/math]) decay:

•  A proton transforms into a neutron:
• [math]p \to n + e^+ + \nu_e[/math]
•  In terms of quarks:
• – An up quark (u) converts into a down quark (d):
• [math]u \to d + W^+[/math]
• – The [math]W^+[/math]boson quickly decays:
• [math]W^+ \to e^+ + \nu_e[/math]

• k) Balancing Quark Transformations in Terms of Charge

• ⇒ [math]β^-[/math]decay: [math]d \to u + e^- + \overline{\nu}_e[/math]​
• Initial charge: [math]-\frac{1}{3} e[/math](down quark).
• Final charge: [math]+\frac{2}{3} e[/math](up quark) + −1e (electron) + 0e (antineutrino).
• Net charge: [math]-\frac{1}{3} e = -\frac{1}{3} e[/math](balanced).
• ⇒ [math]β+[/math]decay: [math]d \to u + e^- + \nu_e[/math]​
• Initial charge: [math]+\frac{2}{3} e[/math](up quark).
• Final charge: [math]-\frac{1}{3} e[/math](down quark) +  (positron) +  (neutrino).
• Net charge: [math]+\frac{2}{3} e = +\frac{2}{3} e[/math](balanced).

• l)   Decay of Particles in the Quark Model

• ⇒ Proton Decay:
• Protons are stable in the Standard Model. Hypothetical proton decay (in grand unified theories) might involve
• [math]p \to \pi^0 + e^+[/math]
• ⇒ Neutron Decay:
• A free neutron undergoes [math] \beta ^- [/math]decay:
• [math]n \to p + e^- + \overline{\nu}_e[/math]
• ⇒ Strange Particle Decay:
• Strange quarks can decay into up or down quarks via the weak force. For example:
• [math]\Delta^0 (uds) \to p (uud) + \pi^- (\overline{u}d)[/math]

3. Radioactivity:

• a) Radioactive decay:
• Spontaneous Nature: Radioactive decay occurs without external influence. It is caused by the instability of the atomic nucleus.
• Random Nature: The exact moment when a particular nucleus decays cannot be predicted. However, the decay follows a statistical pattern.
• b) Types of Radiation:
• ⇒ α-particles (alpha particles):
• Nature: Helium nuclei ([math]{}^{4}_{2}\text{He}[/math]); consist of 2 protons and 2 neutrons.
• Penetration: Low; stopped by paper or a few centimeters of air.
• Range: Very short, typically a few millimeters in air.
• ⇒ β-particles (beta particles):
• Nature:
• – β⁻ (beta-minus): High-energy electrons emitted when a neutron transforms into a proton.
• – β⁺ (beta-plus): Positrons emitted when a proton transforms into a neutron.
• Penetration: Moderate; stopped by a few millimeters of aluminum.
• Range: Up to a meter in air.
• ⇒ γ-rays (gamma rays):
• Nature: High-energy electromagnetic radiation (photons) emitted from the nucleus.
• Penetration: Very high; requires dense materials like lead or several centimeters of concrete for significant absorption.
• Range: Practically infinite in air unless absorbed.
•  II) Techniques for Investigating Absorption of Radiation
• Setup:
• – Use a Geiger-Müller (G-M) tube or scintillation counter to detect radiation intensity.
• – Place absorbers (paper, aluminum, lead) between the source and detector.
• Procedure:
• – Measure background radiation (without a source).
• – Place the radioactive source and record counts without an absorber.
• – Introduce materials of varying thickness and note the change in radiation intensity.
• Observations:
• – Alpha particles are blocked by thin paper or air.
• – Beta particles penetrate paper but are absorbed by aluminum.
• – Gamma rays require dense materials for absorption.
• c) Nuclear Decay Equations
• Alpha Decay:
• – A nucleus emits an alpha particle ([math]{}^{4}_{2}\text{He}[/math]):
• [math]{}^{A}_{Z}X \rightarrow {}^{A-4}_{Z-2}Y + {}^{4}_{2}\text{He}[/math]
• Beta-minus Decay:
• – A neutron converts to a proton, emitting an electron ([math] e^-[/math]) and an antineutrino (​[math]\bar{\nu}_e[/math]):
• [math]{}^{A}_{Z}X \rightarrow {}^{A}_{Z+1}Y + e^- + \bar{\nu}_e[/math]
• ​Beta-plus Decay:
• – A proton converts to a neutron, emitting a positron ([math] e^+[/math]) and a neutrino ([math]\nu_e[/math]​):
• [math]{}^{A}_{Z}X \rightarrow {}^{A}_{Z-1}Y + e^+ + \nu_e[/math]
• d) Activity and Decay Constant
• ⇒ Activity (A):
• The rate of decay of a radioactive sample, measured in disintegrations per second (Becquerels, Bq).
• [math]A = \lambda N[/math]
• Where:
• – A: Activity
• – λ: Decay constant (probability of decay per unit time)
• – N: Number of undecayed nuclei.
• ⇒ Decay Law:
• The number of nuclei N decreases over time:
• [math]N = N_0 e^{-\lambda t}[/math]
• Where:
• – ​[math]N_0[/math]: Initial number of nuclei.
• – t: Time elapsed.
• e) I. Half-Life of an Isotope
• o Definition:
• – The time it takes for half of the undecayed nuclei in a radioactive sample to decay.
• Relationship with Decay Constant (λ):
• [math]t_{1/2} = \frac{\ln 2}{\lambda}[/math]
• Where:
• – ​[math]t_{1/2}[/math]: Half-life.
• – λ: Decay constant.
• II. Determining the Half-Life of an Isotope (e.g., Protactinium)
• ⇒ Techniques and Procedures:
• Apparatus:
• – A source of protactinium (often a solution containing uranium, which decays to protactinium).
• – A Geiger-Müller (G-M) tube to measure activity.
• – A stopwatch or timer to record time intervals.
• Method:
• – Shake the protactinium solution (to separate it from the solvent).
• – Record the count rate (activity) over fixed time intervals using the G-M tube.
• – Plot a graph of activity (A) versus time (t) on a logarithmic scale or fit an exponential curve.
• – Determine ​[math]t_{1/2}[/math] from the graph or using the formula
• [math]t_{1/2} = \frac{\ln 2}{\lambda}[/math]
• f) I) Exponential Decay Equations
• Activity (A):
• [math]A = A_0 e^{-\lambda t}[/math]
• Where:
• – [math]A_0[/math]​: Initial activity.
• – A: Activity at time t.
• Number of Undecayed Nuclei (N):
• [math]N = N_0 e^{-\lambda t}[/math]
• Where:
• – ​[math]N_0[/math]: Initial number of nuclei.
• – N: Remaining nuclei at time t.
• II. Simulation of Radioactive Decay Using Dice
• Concept:
• – Dice rolls simulate the random and probabilistic nature of decay.
• Procedure:
• – Start with a set number of dice (e.g., 100).
• – Assign a “decay condition” (e.g., a roll of 666 represents a decay event).
• – Roll all the dice and remove the ones that meet the decay condition.
• – Record the number of remaining dice (analogous to undecayed nuclei) after each roll (each roll represents a time step).
• – Repeat the process until all dice are “decayed.”
• – Plot the number of remaining dice versus time steps to observe exponential decay.
• g) Graphical Methods and Spreadsheet Modelling
• Equation for Decay:
• [math]\frac{\Delta N}{\Delta t} = -\lambda N[/math]
• Where:
• – [math]{\Delta N}[/math]: Change in the number of nuclei.
• – [math]{\Delta t}[/math]: Time interval.
• Graphical Approach:
• – Use experimental data (e.g., N t) to plot a decay curve.
• Fit the curve to [math]N = N_0 e^{-\lambda t}[/math] to extract
• Spreadsheet Modelling:
• – Create a column for time intervals (t).
• – Use the formula [math]N = N_0 e^{-\lambda t}[/math] to calculate N iteratively.
  • Plot N vs. t to simulate decay.
  • Alternatively, simulate decay step-by-step using [math]\Delta N = -\lambda N \Delta t[/math]

4. Nuclear fusion and fission:

• a) Mass–Energy Equation
• The equation that relates mass and energy is:
• [math]\Delta E = \Delta m c^2[/math]
• Where:
• – [math]\Delta E[/math]: Energy released or absorbed.
• – [math]\Delta m[/math]: Mass defect (change in mass during a nuclear reaction, measured in kg).
• – c: Speed of light in a vacuum ([math]3 \times 10^8 \, \text{m/s}[/math]).
• ⇒ Significance:
• This equation explains how a small amount of mass can be converted into a large amount of energy, as observed in nuclear reactions and particle-antiparticle annihilations
• b) Energy Released (or Absorbed) in Simple Nuclear Reactions
• ⇒ Energy Release:
• In reactions like fusion or fission, the total mass of the products is less than the mass of the reactants. The “missing” mass ([math]\Delta m[/math]) is converted into energy ([math]\Delta E[/math]).
• Example:
• – Fusion of hydrogen nuclei in the Sun.
• ⇒ Energy Absorption:
• If the products have more mass than the reactants, energy must be absorbed to account for the mass increase.
• ⇒ Steps to Calculate Energy:
• Calculate the mass defect:
• [math]\Delta m = m_{\text{reactants}} – m_{\text{products}}[/math]
• Use [math]\Delta E = \Delta m c^2[/math] to find the energy released or absorbed.
• c) Creation and Annihilation of Particle–Antiparticle Pairs
• ⇒ Particle Creation:
• Energy can be converted into mass, creating a particle and its corresponding antiparticle.
• Example: A photon with sufficient energy produces an electron ([math]e^-[/math]) and a positron ([math]e^+[/math]) pair.
• [math]E_{\text{photon}} = 2 m_e c^2[/math]
• Where ​[math]m_e[/math] is the mass of an electron.
• ⇒ Annihilation:
• When a particle meets its antiparticle, they annihilate each other, converting their mass into energy (typically as photons).
• Energy released:
• [math]E_{\text{photon}} = 2 m c^2[/math]
• d) Mass Defect and Binding Energy
• ⇒ Mass Defect ([math]\Delta m[/math]):
• The difference between the total mass of individual nucleons (protons + neutrons) and the actual mass of the nucleus:
• [math]\Delta m = (Z m_p + N m_n) – m_{\text{nucleus}}[/math]
• Where:
• – Z: Number of protons.
• – N: Number of neutrons.
• – [math]m_p[/math]​: Mass of a proton.
• – [math]m_n[/math]: Mass of a neutron.
• ​- [math]m_{\text{nucleus}}[/math]: Mass of the nucleus.
• ⇒ Binding Energy (​[math]E_b[/math]):
• The energy required to completely separate a nucleus into its individual protons and neutrons.
• Calculated using:
• [math]E_b = 2mc^2[/math]
• e) Binding Energy Per Nucleon
• Defined as the binding energy divided by the total number of nucleons in the nucleus:
• [math]\text{Binding energy per nucleon} = \frac{E_b}{A}[/math]
• Where:
• – A=Z+N: Total number of nucleons.
• ⇒ Binding Energy Curve:
• Plot: Binding energy per nucleon (y-axis) vs. nucleon number (A, x-axis).
• – Peaks around iron (A≈56A), indicating it has the highest binding energy per nucleon and is the most stable.
• – For lighter nuclei (A<56): Fusion releases energy as nuclei combine to form a more stable nucleus.
• – For heavier nuclei (A>56): Fission releases energy as larger nuclei split into smaller, more stable nuclei.
• f) Energy Changes in Reactions
• ⇒ Fusion:
• Light nuclei combine to form heavier nuclei.
• Energy is released due to an increase in binding energy per nucleon.
• ⇒ Fission:
• Heavy nuclei split into smaller nuclei.
• Energy is released because the products have a higher binding energy per nucleon.
• Calculating Binding Energy Using [math]\Delta E = \Delta m c^2[/math]
• 1. Obtain the mass defect ([math]\Delta m[/math]) by calculating the difference between the total mass of nucleons and the nucleus.
• 2. Convert  into energy using [math]c^2[/math](or use a conversion factor to directly calculate energy in MeV).
• 3. Use this energy to determine stability or energy changes in reactions.
• g) Induced Nuclear Fission and Chain Reaction
• ⇒ Induced Nuclear Fission:
• Fission occurs when a heavy nucleus (e.g., uranium-235 or plutonium-239) absorbs a neutron, becomes unstable, and splits into two smaller nuclei, releasing:
• – Energy (due to mass defect).
• – Neutrons (usually 2 or 3).
• ⇒ Chain Reaction:
• The released neutrons from one fission event can induce further fission in other nuclei, leading to a self-sustaining reaction.
• Critical Mass: The minimum amount of fissile material needed to maintain a chain reaction.
• h) Basic Structure of a Nuclear Fission Reactor
• ⇒ Fuel Rods:
• Contain fissile material, such as uranium-235 or plutonium-239.
• Serve as the source of energy through nuclear fission.
• ⇒ Control Rods:
• Made of neutron-absorbing materials (e.g., boron or cadmium).
• Inserted or withdrawn to control the rate of the chain reaction by absorbing excess neutrons.
• ⇒ Moderator:
• Slows down fast-moving neutrons to increase the likelihood of absorption by the fissile nuclei.
• Common moderators include water, heavy water, or graphite.
• ⇒ Coolant:
• Transfers the heat generated in the reactor to a heat exchanger or turbine.
• ⇒ Containment Structure:
• A thick shield of concrete and steel that prevents the escape of radiation.
• i) Environmental Impact of Nuclear Waste
• ⇒ Types of Waste:
• Low-Level Waste (LLW): Contaminated materials like gloves and tools.
• Intermediate-Level Waste (ILW): Reactor components or chemical sludges.
• High-Level Waste (HLW): Spent fuel rods and products of fission.
• ⇒ Challenges:
• Long Half-Lives: Some isotopes remain radioactive for thousands of years (e.g., plutonium-239 with a half-life of 24,000 years).
• Storage: Safe disposal methods include deep geological repositories, vitrification (encasing waste in glass), and interim storage.
• Environmental Risks: Leaks, groundwater contamination, or accidental exposure could have significant long-term effects.
• ⇒ Mitigation:
• Improve waste storage and containment technologies.
• Explore methods like transmutation to reduce the half-life of waste.
• j) Nuclear Fusion
• ⇒ Nuclear Fusion:
• Fusion occurs when two light nuclei combine to form a heavier nucleus, releasing energy due to mass defect.
• Example (common in stars):
• [math]{}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} + \text{energy}[/math]
• Energy released is much greater than fission due to higher binding energy per nucleon.
• ⇒ Conditions for Fusion:
• High Temperatures (∼10 million to 100 million K): To overcome electrostatic repulsion between positively charged nuclei.
• High Pressure: To force nuclei close together for fusion to occur.
• ⇒ Fusion Reactors:
• Experimental reactors, such as tokamaks (e.g., ITER), use magnetic confinement or inertial confinement to achieve the required conditions.
• ⇒ Advantages:
• Produces minimal radioactive waste.
• Abundant fuel (e.g., isotopes of hydrogen like deuterium and tritium).
• k) Balancing Nuclear Transformation Equations
• ⇒ Principles:
• Conservation of Mass Number (A):
• The total number of nucleons (protons + neutrons) must be the same before and after the reaction.
• Conservation of Atomic Number (Z):
• The total charge (number of protons) must remain constant.
• Examples:
• Alpha Decay:
• [math]{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}[/math]
• Beta-Minus Decay:
• [math]{}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + e^- + \bar{\nu}_e[/math]
• Fusion Reaction:
• [math]{}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} [/math]