AS level

1. Physical Quantities and Units

SI Units, Prefixes and Standard Form

• Physical Quantity: A property of an object or substance that can be measured, consisting of a numerical magnitude and a unit.

• Base Quantities and SI Units:

  • Mass: kilogram ($kg$)

  • Length: metre ($m$)

  • Time: second ($s$)

  • Electric current: ampere ($A$)

  • Thermodynamic temperature: kelvin ($K$)

  • Amount of substance: mole ($mol$)

• Derived Units: Units created by combining base units via multiplication or division.

  • Force (Newton, $N$): $1\,N = 1\,kg\,m\,s^{-2}$

  • Energy / Work (Joule, $J$): $1\,J = 1\,N\,m = 1\,kg\,m^2\,s^{-2}$

  • Power (Watt, $W$): $1\,W = 1\,J\,s^{-1} = 1\,kg\,m^2\,s^{-3}$

  • Pressure (Pascal, $Pa$): $1\,Pa = 1\,N\,m^{-2} = 1\,kg\,m^{-1}\,s^{-2}$

  • Electric Charge (Coulomb, $C$): $1\,C = 1\,A\,s$

  • Potential Difference (Volt, $V$): $1\,V = 1\,J\,C^{-1} = 1\,kg\,m^2\,s^{-3}\,A^{-1}$

• SI Prefixes:

  • Pico ($p$): $10^{-12}$

  • Nano ($n$): $10^{-9}$

  • Micro ($\mu$): $10^{-6}$

  • Milli ($m$): $10^{-3}$

  • Centi ($c$): $10^{-2}$

  • Deci ($d$): $10^{-1}$

  • Kilo ($k$): $10^{3}$

  • Mega ($M$): $10^{6}$

  • Giga ($G$): $10^{9}$

  • Tera ($T$): $10^{12}$

• Standard Form: Numbers written as $A \times 10^n$, where $1 \le A < 10$ and $n$ is an integer.

  • Example: $450\,nm = 450 \times 10^{-9}\,m = 4.5 \times 10^{-7}\,m$

Scalars and Vectors

• Scalar: A quantity with magnitude only (e.g., distance, speed, mass, time, energy, temperature, electric charge).

• Vector: A quantity with both magnitude and direction (e.g., displacement, velocity, acceleration, force, momentum).

• Vector Components (Resolving Vectors):

  • Horizontal component: $F_x = F \cos(\theta)$

  • Vertical component: $F_y = F \sin(\theta)$

  • Magnitude: $F = \sqrt{F<em>x^2 + F</em>y^2}$

  • Direction: $\theta = \tan^{-1}\left(\frac{F<em>y}{F</em>x}\right)$

  • Example: A force of $50\,N$ acts at $30^\circ$ to the horizontal:
    $F<em>x = 50 \cos(30^\circ) = 43.3\,N$ $F</em>y = 50 \sin(30^\circ) = 25.0\,N$

Measurements, Uncertainties and Percentage Errors

• Systematic Error: Consistent deviation from the true value in one direction across all measurements (e.g., zero offset, miscalibrated instrument). Cannot be eliminated by repeat readings.

• Random Error: Scatter in measurements around a mean value caused by uncontrollable environmental variations or human reaction time. Reduced by taking repeated measurements and calculating a mean.

• Precision: How close repeated measurements are to each other.

• Accuracy: How close a measured value is to the true value.

• Uncertainty Formulas:

  • Absolute uncertainty: $\Delta x$

  • Fractional uncertainty: $\frac{\Delta x}{x}$

  • Percentage uncertainty: $\frac{\Delta x}{x} \times 100\%$

• Combining Uncertainties:

  • Addition/Subtraction ($y = a + b$ or $y = a - b$):
    $\Delta y = \Delta a + \Delta b$

  • Multiplication/Division ($y = a \times b$ or $y = \frac{a}{b}$):
    $\frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b}$

  • Powers ($y = a^n$):
    $\frac{\Delta y}{y} = n \times \frac{\Delta a}{a}$

Significant Figures

• The result of a calculation should have the same number of significant figures as the raw measurement with the fewest significant figures.

2. Kinematics

Distance, Displacement, Speed and Velocity

• Distance ($s$ or $d$): Total path length travelled by an object (scalar, measured in $m$).

• Displacement ($s$): Straight-line distance from the initial position to the final position in a specified direction (vector, measured in $m$).

• Speed ($v$): Rate of change of distance:
  $v = \frac{\Delta s}{\Delta t}$

• Velocity ($v$): Rate of change of displacement:
  $v = \frac{\Delta s}{\Delta t}$

Acceleration and Free Fall

• Acceleration ($a$): Rate of change of velocity:
  $a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$

• Free Fall: Motion under the influence of gravity alone, with constant downward acceleration $g = 9.81\,m\,s^{-2}$ (ignoring air resistance).

Equations of Motion (Constant Acceleration)

• Standard variables ($s, u, v, a, t$):
  $v = u + a t$
  $s = u t + \frac{1}{2} a t^2$
  $s = \frac{1}{2} (u + v) t$
  $v^2 = u^2 + 2 a s$
  $s = v t - \frac{1}{2} a t^2$

• Example: A car accelerates uniformly from rest ($u = 0\,m\,s^{-1}$) at $2.5\,m\,s^{-2}$ over a distance of $80\,m$:
  $v^2 = 0^2 + 2 \times 2.5 \times 80 = 400$
  $v = \sqrt{400} = 20\,m\,s^{-1}$

Graphs of Motion

• Displacement-Time Graph:

  • Gradient: Velocity ($v = \frac{\Delta s}{\Delta t}$

  • Straight line: Constant velocity

  • Curved line: Changing velocity (acceleration)

• Velocity-Time Graph:

  • Gradient: Acceleration ($a = \frac{\Delta v}{\Delta t}$

  • Area under curve: Total displacement ($s = \int v\,dt$ or geometric area)

• Acceleration-Time Graph:

  • Area under curve: Change in velocity ($\Delta v$)

3. Dynamics

Newton's Three Laws of Motion

• Newton's First Law: An object continues in a state of rest or uniform motion in a straight line unless acted upon by a resultant external force.

• Newton's Second Law: The resultant force acting on an object is proportional to the rate of change of momentum and acts in the direction of the change: $F = \frac{\Delta p}{\Delta t}$

  • For constant mass $m$:
    $F = m a$

• Newton's Third Law: When object A exerts a force on object B, object B exerts an equal in magnitude, opposite in direction force of the same type on object A.

Linear Momentum

• Momentum ($p$): Product of mass and velocity:
  $p = m v$

• Conservation of Linear Momentum: In an isolated system with no external forces, total initial momentum equals total final momentum:
  $m<em>1 u</em>1 + m<em>2 u</em>2 = m<em>1 v</em>1 + m<em>2 v</em>2$

• Elastic vs Inelastic Collisions:

  • Perfectly Elastic: Momentum and kinetic energy are conserved ($\Delta E_k = 0$).

  • Inelastic: Momentum is conserved, but kinetic energy is converted into other forms (e.g., heat, sound).

Forces and Equilibrium

• Weight ($W$): Gravitational pull on an object:
  $W = m g$

• Friction ($f$): Contact force resisting relative motion between surfaces.

• Tension ($T$): Pulling force exerted through a stretched string or cable.

• Normal Contact Force ($N$ or $R$): Force perpendicular to the contact surface.

• Equilibrium Conditions:

  • The resultant force in any direction is zero ($\Sigma F<em>x = 0$, $\Sigma F</em>y = 0$).

  • The resultant moment about any point is zero ($\Sigma \tau = 0$).

Terminal Velocity

• As an object falls through a fluid, drag increases with velocity:

  1. Initially: Drag is zero, downward force is $W$, acceleration is $g$.

  2. In motion: Velocity increases, drag force $D$ increases, resultant force $F_{net} = W - D$ decreases, so acceleration decreases.

  3. At terminal velocity: $D = W$, resultant force is zero ($F_{net} = 0$), acceleration is zero ($a = 0\,m\,s^{-2}$), velocity remains constant.

4. Forces, Density and Pressure

Moments and Equilibrium

• Moment of a Force: The turning effect of a force about a pivot:
  $\text{Moment} = F d$
  where $d$ is the perpendicular distance from the pivot to the line of action of force $F$.

• Principle of Moments: For an object in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that same point:
  $\Sigma \text{Clockwise Moments} = \Sigma \text{Anticlockwise Moments}$

• Couple: A pair of equal, opposite, and parallel forces whose lines of action do not coincide.

• Torque of a Couple:
  $\tau = F d$
  where $F$ is the magnitude of one force and $d$ is the perpendicular separation between the lines of action of the two forces.

Density and Volume

• Density ($\rho$): Mass per unit volume: $\rho = \frac{m}{V}$

  • Base SI unit: $kg\,m^{-3}$

Pressure in Solids and Fluids

• Pressure ($p$): Normal force per unit cross-sectional area: $p = \frac{F}{A}$

  • Unit: Pascal ($Pa$), where $1\,Pa = 1\,N\,m^{-2}$

• Hydrostatic Pressure: Pressure exerted by a static column of fluid of density $\rho$ and depth $\Delta h$:
  $\Delta p = \rho g \Delta h$

• Upthrust (Archimedes' Principle): Any object wholly or partially immersed in a fluid experiences an upward force equal to the weight of the fluid displaced:
  $F_{up} = \rho g V$
  where $V$ is the volume of fluid displaced and $\rho$ is fluid density.

• Example: A diver descends $15\,m$ below freshwater ($\rho = 1000\,kg\,m^{-3}$):
  $\Delta p = 1000 \times 9.81 \times 15 = 1.47 \times 10^5\,Pa$

5. Work, Energy and Power

Work Done

• Work Done ($W$): The product of the magnitude of the displacement and the component of the force in the direction of the displacement: $W = F s \cos(\theta)$ where $\theta$ is the angle between force vector $F$ and displacement vector $s$.

  • If force is parallel to displacement ($\theta = 0^\circ$): $W = F s$

  • Unit: Joule ($J$), where $1\,J = 1\,N\,m$

Kinetic and Potential Energy

• Kinetic Energy ($E<em>k$): Energy due to motion:
  $E</em>k = \frac{1}{2} m v^2$

• Gravitational Potential Energy ($E<em>p$): Energy stored in an object due to its position in a gravitational field:
  $E</em>p = m g \Delta h$

• Principle of Conservation of Energy: Energy cannot be created or destroyed; it can only be transformed from one form to another. Total energy of a closed system remains constant.
  $\Delta E<em>p = \Delta E</em>k + W_{\text{friction}}$

Power and Efficiency

• Power ($P$): Rate of transfer of energy or rate of doing work: $P = \frac{W}{t} = \frac{\Delta E}{t}$

  • For an object moving at constant velocity $v$ under constant driving force $F$:
    $P = F v$

  • Unit: Watt ($W$), where $1\,W = 1\,J\,s^{-1}$

• Efficiency: The ratio of useful energy/power output to total energy/power input:
  $\text{Efficiency} = \frac{\text{Useful Power Output}}{\text{Total Power Input}} \times 100\%$

• Example: An electric winch lifts a $200\,kg$ crate by $5.0\,m$ in $10\,s$ with a power input of $1200\,W$:
  $W = m g h = 200 \times 9.81 \times 5.0 = 9810\,J$
  $P_{out} = \frac{9810}{10} = 981\,W$
  $\text{Efficiency} = \frac{981}{1200} \times 100\% = 81.8\%$

6. Deformation of Solids

Hooke's Law and Spring Constant

• Hooke's Law: Extension is directly proportional to applied force, provided the limit of proportionality is not exceeded:
  $F = k x$
  where $k$ is the spring constant (stiffness, in $N\,m^{-1}$) and $x$ is the extension ($m$).

• Spring Combinations:

  • In Series:
    $\frac{1}{k<em>{total}} = \frac{1}{k</em>1} + \frac{1}{k_2}$

  • In Parallel:
    $k<em>{total} = k</em>1 + k_2$

Force-Extension Graphs and Energy

• Limit of Proportionality: Point beyond which force is no longer proportional to extension.

• Elastic Limit: Maximum stress/force from which the material returns to original dimensions upon unloading.

• Elastic Strain Energy ($E<em>p$): Area under the force-extension graph:
  $E</em>p = \frac{1}{2} F x = \frac{1}{2} k x^2$

Stress, Strain and Young Modulus

• Tensile Stress ($\sigma$): Force per unit cross-sectional area: $\sigma = \frac{F}{A}$

  • Unit: Pascal ($Pa$) or $N\,m^{-2}$

• Tensile Strain ($\epsilon$): Fractional change in length: $\epsilon = \frac{\Delta L}{L}$

  • Dimensionless ratio (no units).

• Young Modulus ($E$): Ratio of tensile stress to tensile strain within the limit of proportionality: $E = \frac{\sigma}{\epsilon} = \frac{F L}{A \Delta L}$

  • Unit: Pascal ($Pa$)

• Deformation Regimes:

  • Elastic Deformation: Material returns to original shape and length when load is removed.

  • Plastic Deformation: Material suffers permanent deformation and does not return to original length when load is removed.

7. Waves

Wave Characteristics

• Progressive Wave: A disturbance that transfers energy through a medium or space without the net transfer of matter.

• Transverse Wave: Oscillations are perpendicular to the direction of wave energy propagation (e.g., electromagnetic waves, surface water waves, S-waves).

• Longitudinal Wave: Oscillations are parallel to the direction of wave energy propagation, consisting of compressions and rarefactions (e.g., sound waves, P-waves).

• Key Quantities:

  • Amplitude ($A$): Maximum displacement of an oscillating particle from its equilibrium position.

  • Wavelength ($\lambda$): Minimum distance between two points in phase on adjacent wave cycles.

  • Period ($T$): Time taken for one complete cycle:
    $T = \frac{1}{f}$

  • Frequency ($f$): Number of complete wave cycles passing a point per second ($Hz$).

  • Phase Difference ($\phi$): Angular difference between two points on a wave, given by $\phi = \frac{2 \pi x}{\lambda}$.

• Wave Speed Equation:
  $v = f \lambda$

• Wave Intensity ($I$): Radiant power per unit area normal to propagation direction: $I = \frac{P}{A}$

  • Proportionality: Intensity is proportional to the square of the amplitude:
    $I \propto A^2$

Wave Behaviors

• Reflection: Wave bounces off a boundary, satisfying $\theta<em>i = \theta</em>r$.

• Refraction: Change in wave speed and direction when entering a medium with a different refractive index:
  $n<em>1 \sin(\theta</em>1) = n<em>2 \sin(\theta</em>2)$
  $\frac{\sin(\theta<em>1)}{\sin(\theta</em>2)} = \frac{v<em>1}{v</em>2} = \frac{\lambda<em>1}{\lambda</em>2}$

• Diffraction: Spreading of wave fronts when passing around an obstacle or through an aperture, maximum when aperture size $w \approx \lambda$.

Electromagnetic Spectrum

• In a vacuum, all EM waves travel at the speed of light $c \approx 3.00 \times 10^8\,m\,s^{-1}$.

• Ordered by decreasing wavelength / increasing frequency:

  1. Radio waves: $\lambda > 10^{-1}\,m$

  2. Microwaves: $10^{-3}\,m < \lambda < 10^{-1}\,m$

  3. Infrared: $700\,nm < \lambda < 10^{-3}\,m$

  4. Visible light: $400\,nm \le \lambda \le 700\,nm$

  5. Ultraviolet: $10\,nm < \lambda < 400\,nm$

  6. X-rays: $10^{-11}\,m < \lambda < 10\,nm$

  7. Gamma rays: $\lambda < 10^{-11}\,m$

8. Superposition

Principle of Superposition and Interference

• Principle of Superposition: When two or more waves meet at a point, the resultant displacement is the algebraic sum of the individual displacements of the waves at that point:
  $y<em>{total} = y</em>1 + y_2$

• Coherent Waves: Waves with a constant phase difference and the same frequency.

• Constructive Interference: Waves arrive in phase (phase difference $\Delta \phi = 2 n \pi$):
  $\text{Path Difference} = n \lambda \quad (n = 0, 1, 2, \dots)$

• Destructive Interference: Waves arrive in antiphase (phase difference $\Delta \phi = (2 n + 1) \pi$):
  $\text{Path Difference} = \left(n + \frac{1}{2}\right) \lambda \quad (n = 0, 1, 2, \dots)$

Double-Slit and Diffraction Grating

• Young's Double-Slit Equation:
  $\lambda = \frac{a x}{D}$
  where $a$ is slit separation, $x$ is fringe spacing, and $D$ is distance from slits to screen.

• Diffraction Grating Equation:
  $d \sin(\theta) = n \lambda$
  where $d$ is line spacing ($d = \frac{1}{N}$ for $N$ lines per metre), $n$ is the diffraction order, and $\theta$ is the angle from the central maximum.

Stationary (Standing) Waves

• Formation: Formed by the superposition of two progressive waves of equal amplitude, frequency, and speed travelling in opposite directions.

• Nodes: Points of zero displacement (complete destructive interference).

• Antinodes: Points of maximum displacement (constructive interference).

• Distance Rules:

  • Separation between adjacent nodes: $\frac{\lambda}{2}$

  • Separation between node and adjacent antinode: $\frac{\lambda}{4}$

• Comparison with Progressive Waves:

  • Progressive: Transfers energy, all particles have the same amplitude, phase varies continuously.

  • Stationary: Stores energy (no net transfer), amplitude varies from zero at nodes to maximum at antinodes, all particles between adjacent nodes vibrate in phase.

9. Electricity

Charge, Current, Potential Difference and EMF

• Electric Charge ($Q$): Measured in Coulombs ($C$). Elementary charge $e = 1.60 \times 10^{-19}\,C$.

• Electric Current ($I$): Rate of flow of electric charge:
  $I = \frac{\Delta Q}{\Delta t}$

• Microscopic Drift Equation:
  $I = n A v q$
  where $n$ is charge carrier number density, $A$ is cross-sectional area, $v$ is drift velocity, and $q$ is carrier charge.

• Potential Difference ($V$): Energy converted from electrical form to other forms per unit charge:
  $V = \frac{W}{Q}$

• Electromotive Force (EMF, $\mathcal{E}$): Energy converted from chemical or mechanical form to electrical form per unit charge:
  $\mathcal{E} = \frac{W}{Q}$

Resistance and Ohm's Law

• Resistance ($R$): Ratio of potential difference to current:
  $R = \frac{V}{I}$

• Ohm's Law: Current through a metallic conductor is directly proportional to potential difference across it, provided physical conditions (such as temperature) remain constant.

• Resistivity ($\rho$):
  $R = \frac{\rho L}{A}$
  where $\rho$ is resistivity ($\Omega\,m$), $L$ is length ($m$), and $A$ is cross-sectional area ($m^2$).

Electrical Power and Energy

• Electrical Power:
  $P = V I = I^2 R = \frac{V^2}{R}$

• Electrical Work / Energy:
  $W = P t = V I t = I^2 R t = \frac{V^2}{R} t$

I-V Characteristics

• Ohmic Conductor: Straight line passing through the origin ($I \propto V$, constant $R$).

• Filament Lamp: Curve with decreasing gradient as $V$ increases; higher current causes heating, increasing lattice vibrations and resistance.

• Semiconductor Diode: Negligible current in reverse bias; in forward bias, conducts strongly once threshold voltage ($\sim 0.7\,V$) is reached.

10. D.C. Circuits

Kirchhoff's Laws

• Kirchhoff's First Law: The algebraic sum of currents entering a junction is equal to the sum of currents leaving the junction (Conservation of Charge):
  $\Sigma I<em>{in} = \Sigma I</em>{out}$

• Kirchhoff's Second Law: In any closed loop of a circuit, the sum of electromotive forces is equal to the sum of potential drops (Conservation of Energy):
  $\Sigma \mathcal{E} = \Sigma (I R)$

Combination of Resistors

• Resistors in Series:
  $R<em>{total} = R</em>1 + R<em>2 + R</em>3 + \dots$
  Current is identical through each resistor; potential differences add.

• Resistors in Parallel:
  $\frac{1}{R<em>{total}} = \frac{1}{R</em>1} + \frac{1}{R<em>2} + \frac{1}{R</em>3} + \dots$
  Potential difference is identical across each branch; branch currents add.

Potential Dividers

• Two resistors $R<em>1$ and $R</em>2$ connected in series across supply voltage $V<em>{in}$: $V</em>{out} = \left(\frac{R<em>2}{R</em>1 + R<em>2}\right) V</em>{in}$

• Sensor Circuits:

  • Light Dependent Resistor (LDR): Resistance decreases as light intensity increases.

  • Negative Temperature Coefficient (NTC) Thermistor: Resistance decreases as temperature increases.

EMF, Internal Resistance and Lost Volts

• Real power sources possess an internal resistance ($r$):
  $\mathcal{E} = V + I r = I (R + r)$

• Terminal Potential Difference ($V$):
  $V = \mathcal{E} - I r$

• Lost Volts ($V<em>{lost}$): Potential difference dropped across internal resistance:
  $V</em>{lost} = I r$

• Graph of $V$ vs $I$:

  • $y$-intercept: EMF ($\mathcal{E}$

  • Gradient: $-r$

• Example: A battery with $\mathcal{E} = 12.0\,V$ and internal resistance $r = 0.50\,\Omega$ is connected to a load resistor $R = 5.5\,\Omega$:
  $I = \frac{\mathcal{E}}{R + r} = \frac{12.0}{5.5 + 0.50} = 2.0\,A$
  $V = \mathcal{E} - I r = 12.0 - (2.0 \times 0.50) = 11.0\,V$
  $V_{lost} = 2.0 \times 0.50 = 1.0\,V$

11. Particle Physics

Nuclear Notation and Subatomic Structure

• Nuclide Representation:
  $^A_Z X$
  where $A$ is the nucleon number (mass number, $A = Z + N$), and $Z$ is the proton number (atomic number).

• Isotopes: Nuclei of the same element containing the same number of protons ($Z$) but different numbers of neutrons ($N$).

• Constituent Particles:

  • Proton ($p$): Charge $+1\,e$, relative mass $1$

  • Neutron ($n$): Charge $0$, relative mass $1$

  • Electron ($e^-$): Charge $-1\,e$, relative mass $\frac{1}{1836}$

Classification of Particles

• Hadrons: Particles subject to the strong nuclear force, composed of quarks:

  • Baryons: Composed of three quarks ($q q q$). (e.g., Proton = $u u d$, Neutron = $u d d$). Baryon number $B = +1$.

  • Antibaryons: Composed of three antiquarks ($\bar{q} \bar{q} \bar{q}$). Baryon number $B = -1$.

  • Mesons: Composed of one quark and one antiquark ($q \bar{q}$) (e.g., Pions, Kaons). Baryon number $B = 0$.

• Leptons: Fundamental particles not subject to the strong nuclear force:

  • Electrons ($e^-$), Muons ($\mu^-$), Tau ($\tau^-$) and their respective neutrinos ($\nu<em>e, \nu</em>\mu, \nu_\tau$).

  • Lepton number $L = +1$ for leptons, $L = -1$ for antileptons.

• Quark Properties:

  • Up ($u$): Charge $+\frac{2}{3}e$, Strangeness $0$, Baryon number $+\frac{1}{3}$

  • Down ($d$): Charge $-\frac{1}{3}e$, Strangeness $0$, Baryon number $+\frac{1}{3}$

  • Strange ($s$): Charge $-\frac{1}{3}e$, Strangeness $-1$, Baryon number $+\frac{1}{3}$

  • Corresponding antiquarks ($\bar{u}, \bar{d}, \bar{s}$) possess opposite sign charges, strangeness, and baryon numbers.

Fundamental Interactions

• Strong Interaction: Mediated by gluons/pions; acts over short range ($\sim 10^{-15}\,m$); binds quarks and holds nucleons together.

• Electromagnetic Interaction: Mediated by virtual photons; infinite range; acts on all charged particles.

• Weak Interaction: Mediated by $W^+$ and $W^-$ bosons; very short range ($\sim 10^{-18}\,m$); responsible for flavor changes and beta decay.

• Gravitational Interaction: Infinite range; acts on all mass-energy; negligible at the subatomic scale.

Beta Decay and Conservation Laws

• Beta-minus ($\beta^-$) Decay: Occurs in neutron-rich nuclei: $n \rightarrow p + e^- + \bar{\nu}_e$

  • Quark transformation:
    $d \rightarrow u + e^- + \bar{\nu}_e$

• Beta-plus ($\beta^+$) Decay: Occurs in proton-rich nuclei: $p \rightarrow n + e^+ + \nu_e$

  • Quark transformation:
    $u \rightarrow d + e^+ + \nu_e$

• Strict Conservation Laws: In every particle interaction, the following quantities are conserved:

  • Electric charge ($Q$

  • Baryon number ($B$

  • Lepton number ($L<em>e, L</em>\mu, L_\tau$

  • Mass-energy and momentum

• Strangeness ($S$): Conserved in strong and electromagnetic interactions, but can change by $\pm 1$ in weak interactions.