Comprehensive Physics Study Guide: Grade 11 (National Curriculum of Pakistan)

PHYSICAL QUANTITIES AND MEASUREMENTS

Estimation of Physical Quantities

• Definition: An estimation is a rough educated guess of the value of a physical quantity by using prior experience and sound physical reasoning.
• Strategies for Estimation:
  • Length: Break a large object into smaller units of known length (e.g., floor heights for a building) or aggregate small units to find a bulk total (e.g., paper stack thickness).
  • Areas and Volumes: Introduce a simple geometric model (sphere or box), estimate linear dimensions, and apply standard formulas.
  • Mass from Volume and Density: Estimate volume first, then use average density ($\text{mass} = \text{density} \times \text{volume}$). Densities to remember: air $\approx 1\,kg\,m^{-3}$, water $\approx 10^{3}\,kg\,m^{-3}$, densest solids $\approx 10^{4}\,kg\,m^{-3}$.
• Standard Scales:
  • Diameter of proton: $10^{-15}\,m$.
  • Mass of electron: $10^{-30}\,kg$.
  • One year: $10^{7}\,s$.
  • Age of universe: $10^{18}\,s$.

Derived Units in Terms of Base Units

• Derived units are obtained by multiplying or dividing SI base units.
• Examples:
  • Force (Newton, N): $kg \times m\,s^{-2}$.
  • Work (Joule, J): $N\,m = kg\,m^{2}\,s^{-2}$.
  • Power (Watt, W): $J\,s^{-1} = kg\,m^{2}\,s^{-3}$.
  • Pressure (Pascal, Pa): $N\,m^{-2} = kg\,m^{-1}\,s^{-2}$.
  • Electric Charge (Coulomb, C): $A\,s$.

Dimensions of Physical Quantities

• Definition: Dimension denotes the qualitative nature of a physical quantity, represented by capital letters in square brackets [ ].
• Base Dimensions:
  • Mass: [M], Length: [L], Time: [T], Electric Current: [I], Temperature: [$\theta$], Intensity of Light: [J], Amount of Substance: [N].
• Categories:
  • Dimensional Variables: Have dimensions and variable magnitude (e.g., velocity, force).
  • Dimensional Constants: Have dimensions and constant magnitude (e.g., Planck's constant $h$, gravitational constant $G$).
  • Dimensionless Variables: No dimensions but variable magnitude (e.g., strain, plane angle).
  • Dimensionless Constants: No dimensions and constant magnitude (e.g., $\pi$, $e$, pure numbers).
• Dimensional Analysis Applications:
  • Homogeneity: Checking the correctness of an equation. Both sides must have the same dimensions (Principle of Homogeneity).
  • Formula Derivation: Predicting relations by equating powers of M, L, and T.
• Limitations:
  • Cannot distinguish between quantities with the same dimensions (e.g., work and torque).
  • Cannot derive formulas involving trigonometric, exponential, or logarithmic functions.
  • Cannot determine the value of dimensionless constants.

Precision and Accuracy

• Precision: Refers to the closeness of measured values to each other. It is associated with the least count of the instrument and absolute uncertainty.
• Accuracy: Refers to how closely a measurement agrees with the true/standard value. It is indicated by fractional or percentage uncertainty.
• Example: If a 160.0 lb person weighs 170.1, 169.9, and 170.0 lbs on a scale, the measurements are precise but not accurate.

Uncertainties

• Definition: The range of possible values within which the true value lies.
• Absolute Uncertainty: Equal to the least count of the measuring instrument.
• Fractional Uncertainty: $\frac{\text{Absolute Uncertainty}}{\text{Measured Value}}$.
• Percentage Uncertainty: $\text{Fractional Uncertainty} \times 100\%$.
• Rules for Calculation:
  • Addition/Subtraction: Absolute uncertainties are added: $\Delta z = \pm (\Delta x + \Delta y)$.
  • Multiplication/Division: Percentage uncertainties are added.
  • Power of a Quantity: Percentage uncertainty is multiplied by that power: for $z = x^{n}$, $\text{\% uncertainty in } z = n \times (\text{\% uncertainty in } x)$.
  • Average Values: Uncertainty is the mean deviation of the readings.
  • Timing Experiments: Uncertainty in time period $\Delta T = \frac{\text{Least Count}}{\text{No. of vibrations}}$.

VECTORS

Vector Resolution in 2-D

• Rectangular Components: Mutually perpendicular parts of a vector ($A_{x}$ and $A_{y}$).
• Formulas:
  • $A_{x} = A\cos(\theta)$.
  • $A_{y} = A\sin(\theta)$.
  • Magnitude: $A = \sqrt{A_{x}^{2} + A_{y}^{2}}$.
  • Direction: $\theta = \tan^{-1}(\frac{A_{y}}{A_{x}})$.
• Unit Vectors: $\mathbf{i}$ and $\mathbf{j}$ representing directions along +x and +y axes.

Product of Vectors

• Scalar (Dot) Product: Results in a scalar quantity.
  • Definition: $\mathbf{A} \cdot \mathbf{B} = AB\cos(\theta)$.
  • Properties:
    • Commutative: $\mathbf{A} \cdot \mathbf{B} = \mathbf{B} \cdot \mathbf{A}$.
    • Perpendicular ($\theta = 90^{\circ}$): $\mathbf{A} \cdot \mathbf{B} = 0$.
    • Parallel ($\theta = 0^{\circ}$): $\mathbf{A} \cdot \mathbf{B} = AB$.
    • Component form: $\mathbf{A} \cdot \mathbf{B} = A_{x}B_{x} + A_{y}B_{y} + A_{z}B_{z}$.
• Vector (Cross) Product: Results in a vector quantity perpendicular to the plane of the original vectors.
  • Definition: $\mathbf{A} \times \mathbf{B} = AB\sin(\theta)\hat{n}$.
  • Properties:
    • Anti-commutative: $\mathbf{A} \times \mathbf{B} = -(\mathbf{B} \times \mathbf{A})$.
    • Parallel ($\theta = 0^{\circ}$): $\mathbf{A} \times \mathbf{B} = 0$ (null vector).
    • Perpendicular ($\theta = 90^{\circ}$): maximum magnitude $AB$.
  • Physical Significance: The magnitude of $\mathbf{A} \times \mathbf{B}$ represents the area of a parallelogram formed by vectors A and B.

TRANSLATORY MOTION

Equations of Uniformly Accelerated Motion

1. $v_{f} = v_{i} + at$
2. $S = v_{i}t + \frac{1}{2}at^{2}$
3. $2aS = v_{f}^{2} - v_{i}^{2}$

• Free-Fall Motion: Substitutes $a = g = 9.81\,m/s^{2}$ and $S = h$.

Projectile Motion

• Definition: 2-D motion under the action of gravity only, neglecting air resistance.
• Assumptions:
  • Horizontal velocity ($v_{ix} = v_{i}\cos(\theta)$) remains constant ($a_{x} = 0$).
  • Vertical velocity ($v_{iy} = v_{i}\sin(\theta)$) changes due to gravity ($a_{y} = -g$).
• Key Parameters:
  • Maximum Height ($H$): $H = \frac{v_{i}^{2}\sin^{2}(\theta)}{2g}$.
  • Time of Flight ($T$): $T = \frac{2v_{i}\sin(\theta)}{g}$.
  • Range ($R$): $R = \frac{v_{i}^{2}\sin(2\theta)}{g}$.
  • Maximum Range: Occurs at $\theta = 45^{\circ}$.
  • Complementary Angles: Pairs like $(75^{\circ}, 15^{\circ})$ yield the same range.
• Air Resistance Effects: Reduces maximum height and range, increases time of flight, and alters the parabolic path.

Linear Momentum Conservation

• Law: The total momentum of an isolated system (net external force is zero) remains constant.
• Applications:
  • Explosions: Sum of final momenta of fragments equals the initial momentum (often zero).
  • Recoil of Gun: $m_{c}v_{c} + m_{b}v_{b} = 0$.
  • Rocket Propulsion: Ejection of hot gases with large momentum results in equal and opposite momentum for the rocket.

Collisions

• Elastic Collision: Both momentum and kinetic energy are conserved (e.g., subatomic particles).
  • Relative speed of approach = Relative speed of separation ($u_{1} - u_{2} = v_{2} - v_{1}$).
• Inelastic Collision: Momentum is conserved, but kinetic energy is not (transformed into heat, sound, or deformation).

ROTATIONAL AND CIRCULAR MOTION

Angular Kinematics

• Angular Displacement ($\Delta\theta$): Measured in radians. $1\,\text{rad} = 57.3^{\circ}$. Relation: $S = r\theta$.
• Angular Velocity ($\omega$): $\omega = \frac{\Delta\theta}{\Delta t}$. Relation: $v = r\omega$.
• Angular Acceleration ($\alpha$): $\alpha = \frac{\Delta\omega}{\Delta t}$. Relation: $a_{T} = r\alpha$.

Centripetal Force

• Definition: The net force keeping an object in a circular path, directed toward the center.
• Formula: $F_{c} = \frac{mv^{2}}{r} = mr\omega^{2}$.
• Providers: Tension, friction (on banked/unbanked roads), or gravity (for orbits).
• Banked Curves: $\tan(\theta) = \frac{v^{2}}{rg}$, independent of vehicle mass.
• Centrifuge: Device using high-speed rotation to separate substances of different densities based on inertia and centripetal requirements.

Moment of Inertia ($I$)

• Definition: Rotational equivalent of mass, resisting changes in rotational motion.
• Generic Form: $I = \sum m_{i}r_{i}^{2}$.
• Torque Relation: $\tau = I\alpha$.

Angular Momentum ($L$)

• General Formula: $\mathbf{L} = \mathbf{r} \times \mathbf{p}$.
• Magnitude (Point Mass): $L = mvr = mr^{2}\omega = I\omega$.
• Law of Conservation: In the absence of external torque, $L_{i} = L_{f}$. Examples: Ice skaters pulling arms in to spin faster; gyroscopes maintaining orientation.

Weightlessness and Artificial Gravity

• Weightlessness: Occurs during free-fall (e.g., in a satellite) where the gravity provides centripetal acceleration, causing zero apparent weight.
• Artificial Gravity: Created by rotating a space station. Acceleration $a_{c} = \frac{v^{2}}{R}$. To mimic Earth gravity ($a_{c} = g$), required angular velocity is $\omega = \sqrt{\frac{g}{R}}$.

WORK AND ENERGY

Work

• Definition: Dot product of force and displacement: $W = \mathbf{F} \cdot \mathbf{d} = Fd\cos(\theta)$.
• Graphical Analysis: Work is the area under the force-displacement graph.
• Variable Force: Total work is the integral or sum of small intervals: $W = \sum F_{i}\cos(\theta_{i})\Delta d_{i}$.

Conservative and Non-Conservative Fields

• Conservative Field: Work done is independent of the path taken; work done around a closed path is zero (e.g., gravitational, electric fields).
• Non-Conservative Field: Work done depends on the path; work done around a closed path is non-zero (e.g., friction, viscous drag).

Kinetic Energy and Work-Energy Principle

• Kinetic Energy ($K.E$): $K.E = \frac{1}{2}mv^{2}$.
• Work-Energy Theorem: The net work done on an object equals its change in kinetic energy: $W_{net} = \Delta K.E$.
• Resistive Medium: Work done by applied force = Gain in K.E + Work done against resistive forces ($W_{r}$).

Efficiency

• Formula: $\text{Efficiency} = \frac{\text{Useful energy output}}{\text{Energy input}} \times 100\%$.
• No real machine is 100% efficient due to thermal energy losses.

FLUID MECHANICS

Upthrust and Archimedes' Principle

• Principle: When an object is immersed in fluid, it experiences an upward force equal to the weight of the displaced liquid.
• Formula: $\text{Upthrust} = \rho g V$.
• Applications: Floating of ships, submarines (using ballast tanks to adjust weight), balloons.

Viscosity and Terminal Velocity

• Viscosity ($\eta$): Measure of fluid resistance to flow.
• Stoke's Law: Drag force on a sphere $F_{d} = 6\pi\eta r v$.
• Terminal Velocity ($v_{t}$): Reached when drag force equals weight. For a sphere: $v_{t} = \frac{2\rho g r^{2}}{9\eta}$.

Fluid Flow and Continuity

• Streamline (Laminar): Smooth flow where every particle follows the same path.
• Turbulent: Irregular flow with whirlpools.
• Equation of Continuity: Based on conservation of mass. For an incompressible fluid: $A_{1}v_{1} = A_{2}v_{2} = \text{constant}$.

Bernoulli's Equation

• Formula: $P + \frac{1}{2}\rho v^{2} + \rho gh = \text{constant}$.
• Interpretation: Sum of pressure, K.E per unit volume, and P.E per unit volume is constant.
• Applications:
  • Torricelli's Theorem: Efflux speed $v = \sqrt{2gh}$.
  • Venturi Meter: Used to measure flow speed via pressure difference.
  • Aerofoil: Higher velocity above the wing creates low pressure, resulting in lift.
  • Magnus Effect: Spinning ball deflects due to pressure differences.
  • Atomizer: Fast air over a tube creates low pressure, sucking up liquid.

Superfluidity

• Definition: A state where a liquid (like Helium-4 below 2.17 K) has zero viscosity.
• Properties: Flows without friction through any surface; creeps over container walls; forms quantized vortices when stirred.

PHYSICS OF SOLIDS

Classification of Solids

• Crystalline: Regular atoms/ions arrangement (e.g., salts, metals), sharp melting points, anisotropic.
• Polycrystalline (Polymeric): Many small crystals (grains) with random orientation (e.g., synthetic polymers like Zylon).
• Amorphous (Glassy): Random arrangement, no definite geometric shape (e.g., glass, rubber), softens over a temperature range.
• Crystal Lattice: Repetition of the Unit Cell (smallest basic portion).
  • Simple Cubic (SC): 1 atom/cell.
  • Body-Centered Cubic (BCC): 2 atoms/cell.
  • Face-Centered Cubic (FCC): 4 atoms/cell.

Stress and Strain

• Stress ($\sigma$): $\frac{\text{Force}}{\text{Area}}$. Types: Tensile, Shear, Volume.
• Strain ($\epsilon$): Qualitative measure of deformation. No units.
  • Tensile strain: $\frac{\Delta L}{L}$.
  • Shear strain: $\tan(\theta) \approx \theta$.
  • Volume strain: $\frac{\Delta V}{V}$.
• Modulus of Elasticity: $\frac{\text{Stress}}{\text{Strain}}$.
  • Young's Modulus ($Y$): For linear deformation ($Y = \frac{F/A}{\Delta L/L}$).
  • Bulk Modulus ($B$): For volumetric deformation ($B = -\frac{\Delta P}{\Delta V/V}$).
  • Shear Modulus ($S$): For shape deformation ($S = \frac{F/A}{\theta}$).

Stress-Strain Curve

• Proportional Limit: Stress is linear to strain (Hooke's law).
• Elastic Limit: Max stress before permanent deformation.
• Plasticity: Material does not regain shape after stress removal.
• Ultimate Tensile Strength: Max stress a material can withstand.
• Ductile vs Brittle: Ductile materials undergo plastic deformation before breaking; brittle materials break shortly after the elastic limit.

Elastic Potential (Strain) Energy

• Definition: Work done to deform a material. Area under Force-Extension graph.
• Formula: $P.E = \frac{1}{2}Fx = \frac{1}{2}kx^{2}$.
• In terms of modulus: $P.E = \frac{1}{2} \frac{YA}{L} x^{2}$.

HEAT AND THERMODYNAMICS

Basic Concepts

• Thermal Equilibrium: Two systems at the same temperature have no net heat flow.
• Internal Energy ($U$): Sum of molecular K.E and P.E. For an ideal gas: $U \propto T$.
• Ideal Gas Equation: $PV = nRT = NkT$. (Boltzmann constant $k = R/N_{A} = 1.38 \times 10^{-23}\,J/K$).
• Work Done by Gas: $W = P\Delta V$. Area under P-V graph.

Laws of Thermodynamics

• First Law: Law of conservation of energy. $Q = \Delta U + W$.
• Second Law:
  • Kelvin Statement: Impossible to convert heat from a single reservoir entirely into work.
  • Clausius Statement: Heat cannot flow from cold to hot body without external work.

Thermodynamic Processes

• Isothermal: Constant temperature ($\Delta U = 0$, so $Q = W$). Slow process.
• Adiabatic: No heat exchange ($Q = 0$, so $W = -\Delta U$). Fast process. $PV^{\gamma} = \text{constant}$.
• Isochoric: Constant volume ($W = 0$, so $Q = \Delta U$).
• Isobaric: Constant pressure ($Q = \Delta U + P\Delta V$).

Heat Engines and Refrigerators

• Heat Engine: Converts heat from hot reservoir ($Q_{1}$) into work, rejecting waste heat ($Q_{2}$) to cold reservoir.
  • Efficiency $\eta = \frac{W}{Q_{1}} = 1 - \frac{Q_{2}}{Q_{1}}$.
• Carnot Engine: Ideal reversible engine. Max efficiency $\eta = 1 - \frac{T_{2}}{T_{1}}$.
• Refrigerator: Extracts heat from cold body using work. Coefficient of Performance ($CP$) for cooling: $CP = \frac{Q_{2}}{W} = \frac{T_{2}}{T_{1} - T_{2}}$.

Entropy ($S$)

• Definition: Quantitative measure of disorder. $\Delta S = \frac{\Delta Q}{T}$.
• Principle: In all natural processes, entropy of the universe increases (Law of Degradation of Energy).

WAVES

Intensity

• Definition: Power per unit area ($I = \frac{P}{A}$). Unit: $W/m^{2}$.
• $I \propto (\text{amplitude})^{2}$.

Doppler's Effect

• Definition: Apparent change in frequency due to relative motion of source and observer.
• Formulas (Source speed $v_{s}$, observer speed $v_{L}$, sound speed $v$):
  • Observer moves toward stationary source: $f' = \frac{v + v_{L}}{v} f$.
  • Observer moves away from stationary source: $f' = \frac{v - v_{L}}{v} f$.
  • Source moves toward stationary observer: $f' = \frac{v}{v - v_{s}} f$.
  • Source moves away from stationary observer: $f' = \frac{v}{v + v_{s}} f$.
• Applications: SONAR, Radar speed traps, Redshift/Blueshift in astronomy, Doppler echocardiography.

Superposition and Interference

• Principle: Net displacement is the vector sum of individual wave displacements.
• Interference: Superposition of coherent waves.
  • Constructive: Waves in phase; path difference $d = m\lambda$.
  • Destructive: Waves $180^{\circ}$ out of phase; path difference $d = (m + \frac{1}{2})\lambda$.
• Beats: Superposition of waves with slightly different frequencies ($f_{1}, f_{2}$). Beat frequency: $f_{b} = |f_{1} - f_{2}|$.

Stationary Waves

• Produced by two identical waves traveling in opposite directions.
• Nodes: Zero displacement; Antinodes: Max displacement.
• Stretched String: Fundamental frequency $f_{1} = \frac{1}{2L}\sqrt{\frac{T}{m}}$. All harmonics ($nf_{1}$) are present.
• Open Organ Pipe: $f_{1} = \frac{v}{2L}$. All harmonics are present.
• Closed Organ Pipe: $f_{1} = \frac{v}{4L}$. Only odd harmonics ($f_{1}, 3f_{1}, 5f_{1}\dots$) are present.

Polarization

• Definition: Restricting wave vibrations to a single plane. Only occurs in transverse waves.
• Malus's Law: Transmitted intensity $I = I_{\circ}\cos^{2}(\theta)$.
• Uses: Reduced glare in sunglasses, sky photography, stress analysis in plastics.

Gravitational Waves

• Predicted by Einstein; ripples in spacetime caused by accelerated masses (e.g., merging black holes).
• Detected by Interferometers (like LIGO) which measure minute length changes ($1/10,000^{\text{th}}$ width of a proton).

ELECTROSTATICS

Coulomb's Law

• Formula: $F = k\frac{q_{1}q_{2}}{r^{2}}$, where $k = \frac{1}{4\pi\epsilon_{\circ}} \approx 9 \times 10^{9}\,N\,m^{2}\,C^{-2}$.
• Applies to point charges. Vector form obeys Newton's third law.

Electric Field Intensity ($E$)

• Definition: Force per unit positive test charge ($E = F/q$).
• For point charge: $E = k\frac{Q}{r^{2}}$.
• Field Lines: Outward from positive, inward to negative; never cross; density indicates strength.

Potential Gradient

• Formula: $E = -\frac{\Delta V}{\Delta r}$.
• Electric field strength is equal to the negative potential gradient.

Ferrofluids and Faraday Cage

• Ferrofluids: Liquid with nanometer particles that magnetize in an external field; used in MRI and electronics.
• Faraday Cage: Conducting enclosure that shields internal volume from external electric fields; charges reside on the external surface.

ELECTRICITY

Drift Velocity and Current

• Drift Velocity ($v$): Average velocity of free electrons in an electric field ($\approx 10^{-3}\,m/s$).
• Current Equation: $I = nAev$, where $n$ is free electron density.

Resistance and Resistivity

• Resistivity ($\rho$): Intrinsic property. $R = \rho \frac{L}{A}$.
• Conductivity ($\sigma$): $\sigma = 1/\rho$.
• Temperature dependence: $R_{T} = R_{\circ}[1 + \alpha(T - T_{\circ})]$. $\alpha$ is positive for metals, negative for semiconductors.

Circuit Components

• LDR (Light Dependent Resistor): Resistance decreases as light intensity increases.
• Thermistor: Heat-sensitive resistor. NTC (negative temperature coefficient) or PTC (positive).
• Potential Divider: Uses LDR/Thermistor to provide output voltage dependent on environment.

Kirchhoff's Laws

• KCL (First Law): Sum of currents entering a junction equals zero ($\sum I = 0$). Conservation of charge.
• KVL (Second Law): Algebraic sum of potential changes in a closed loop is zero ($\sum V = 0$). Conservation of energy.

Null Methods

• Wheatstone Bridge: Balanced when $P/Q = R/S$. Galvanometer reads zero.
• Potentiometer: Used to compare emf or measure potential difference without drawing current. $\frac{\epsilon_{1}}{\epsilon_{2}} = \frac{l_{1}}{l_{2}}$.

ELECTROMAGNETISM

Magnetic Force

• On Conductor: $F = BIL\sin(\theta)$ (Fleming's Left Hand Rule).
• On Moving Charge: $F = qvB\sin(\theta)$. (Right Hand Rule).

Motion in Magnetic Field

• Charge moving perpendicular to B follows a circular path: $r = \frac{mv}{qB}$.
• Velocity Selector: Mutually perpendicular E and B fields permit undeflected travel only at $v = E/B$.
• Lorentz Force: $\mathbf{F} = q\mathbf{E} + q(\mathbf{v} \times \mathbf{B})$.

Field Patterns

• Straight Wire: Concentric circles. $B = \frac{\mu_{\circ}I}{2\pi r}$.
• Solenoid: Uniform internal field. $B = \mu_{\circ}nI$. Inserting a ferrous core increases field strength via relative permeability $\mu_{r}$.

Faraday's and Lenz's Laws

• Magnetic Flux (\Phi): $\Phi = BA\cos(\theta)$. Unit: Weber (Wb).
• Faraday's Law: $\epsilon = -N \frac{\Delta\Phi}{\Delta t}$.
• Lenz's Law: Induced current direction opposes the change in flux (Conservation of Energy).
• Seismometer: Relative motion between a coil and magnet during an earthquake induces emf proportional to displacement.

RELATIVITY

Frames of Reference

• Inertial: Constant velocity; Newton's laws hold.
• Non-Inertial: Accelerating; Newton's laws seem not to hold.

Postulates of Special Relativity

1. Laws of physics are the same in all inertial frames.
2. Speed of light ($c$) is constant for all observers regardless of relative motion.

Consequences

• Simultaneity: Events simultaneous in one frame may not be in another.
• Mass-Energy Equivalence: $E = mc^{2}$.
• Length Contraction: $L = L_{\circ}\sqrt{1 - \frac{v^{2}}{c^{2}}}$.
• Time Dilation: $t = \frac{t_{\circ}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$.
• Relativistic Mass: $m = \frac{m_{\circ}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$.

Spacetime

• 4-D continuum merging 3-D space with 1-D time. Minkowski space describes gravity as space curvature.

PARTICLE PHYSICS

Conservation and Radiation

• Conservation: Nucleon number and charge are conserved in nuclear processes.
• Radiation Types:
  • Alpha (\alpha): He-4 nucleus, charge +2e.
  • Beta (\beta): Electrons (\beta^{-}) or Positrons (\beta^{+}), charge \pm 1e.
  • Gamma (\gamma): High energy photons, neutral.

Particles and Antiparticles

• Antiparticles have same mass but opposite charge (e.g., electron/positron).
• Beta Decay:
  • $\beta^{-}$: Neutron $\rightarrow$ Proton + Electron + Antineutrino.
  • $\beta^{+}$: Proton $\rightarrow$ Neutron + Positron + Neutrino.
• Annihilation: Particle and antiparticle meet, converting all mass to photons ($2\gamma$) or new subatomic particles.

Standard Model

• Quarks: Fundamental constituents of hadrons. Six flavors: up, down, charm, strange, top, bottom.
  • Protons: $uud$. Neutrons: $udd$.
• Leptons: Electrons, muons, taus, and their respective neutrinos.
• Force Carriers (Bosons):
  • Photon (Electromagnetic), Gluon (Strong), W and Z Bosons (Weak).
• Higgs Boson: Scalar particle responsible for mass via interactions with the Higgs field.

Particle Accelerators

• Linear (LINAC): Straight path acceleration.
• Synchrotron: Circular ring, uses magnetic fields to bend path (e.g., LHC).
• Cyclotron: Spiral path acceleration in circular metal 'dees'.