## IB DP Physics 2025 Syllabus

The new DP Physics course was launched in February 2023 for first teaching in August 2023. First assessment will take place in May 2025. IBDP Physics courses are here as per new syllabus and guidelines provided by the board. Details of changes in pattern and syllabus are also mentioned on this page.

### A. Space, time and motion

#### A.1 Kinematics

- Motion Analysis:
- Motion is described in terms of position, velocity, and acceleration.

- Velocity & Acceleration:
- Velocity: Rate of change of position.
- Acceleration: Rate of change of velocity.

- Displacement:
- Change in position is termed displacement.

- Distance vs. Displacement:
- Distance: Total path length.
- Displacement: Shortest path between two points.

- Instantaneous vs. Average Values:
- Instantaneous: Values at a specific moment.
- Average: Values over a time interval.

- Equations of Motion:
- For uniformly accelerated motion:
- \( s = \frac{u+v}{2} t \)
- \( v = u + at \)
- \( s = ut + \frac{1}{2} at^2 \)
- \( v^2 = u^2 + 2as \)

- For uniformly accelerated motion:
- Uniform vs. Non-Uniform Acceleration:
- Uniform: Constant acceleration.
- Non-Uniform: Varying acceleration.

- Projectile Motion:
- Analyze by resolving motion into vertical and horizontal components, ignoring fluid resistance.

- Effect of Fluid Resistance:
- Fluid resistance affects projectile time of flight, trajectory, velocity, acceleration, range, and terminal speed.

**A.2 Forces and momentum**

- Newton’s Laws:
- First: An object remains in uniform motion unless acted on by a force.
- Second: Force equals mass times acceleration \((F = ma)\).
- Third: For every action, there’s an equal and opposite reaction.

- Free-Body Diagrams:
- Represents forces acting on a body; useful for finding the resultant force.

- Contact Forces:
- Normal Force \((F_N)\): Perpendicular to the surface.
- Frictional Force \((F_f)\): Opposes motion, with static \(F_f \leq \mu_sF_N\) and dynamic \(F_f = \mu_dF_N\) friction.
- Tension: Force in a stretched string/rope.
- Elastic Force \((F_H)\): Follows Hooke’s law \((F_H = -kx)\).
- Viscous Drag \((F_d)\): Opposes motion in fluids \((F_d = 6\pi \eta rv)\).
- Buoyancy \((F_b)\): Upward force by displaced fluid \((F_b = \rho Vg)\).

- Field Forces:
- Gravitational Force \((F_g = mg)\): Weight of a body.
- Electric and Magnetic Forces \((F_e, F_m)\).

- Linear Momentum:
- \(p = mv\) remains constant unless acted upon by an external force.

- Impulse:
- Impulse \(J = F \Delta t\) equals the change in momentum.

- Momentum Change:
- Impulse applied results in a change in momentum.

- Newton’s Second Law:
- \(F = ma\) assumes constant mass; \(F = \Delta p\) applies when mass changes.

- Collisions & Explosions:
- Elastic Collisions: Kinetic energy conserved.
- Inelastic Collisions: Some kinetic energy is lost.

- Centripetal Acceleration:
- Objects in circular motion experience acceleration towards the center \(a = \frac{v^2}{r}\).

- Centripetal Force:
- Acts perpendicular to velocity, causing change in direction.

- Angular Velocity:
- Circular motion described by angular velocity \(\omega\) related to linear speed \(v = \omega r\).

#### A.3 Work, energy and power

- Conservation of Energy:
- Energy cannot be created or destroyed, only transformed. Work done by a force transfers energy.

- Sankey Diagrams:
- Graphical representations of energy transfers in a system, showing useful energy output versus wasted energy.

- Work Done:
- Work \(W = F s \cos \theta\) depends on the force’s component in the direction of displacement.

- Resultant Force & Energy:
- Work done by the resultant force equals the change in the system’s energy.

- Mechanical Energy:
- Sum of kinetic, gravitational potential, and elastic potential energy. Conserved if no resistive forces.
- Mechanical Energy Conservation:
- Work transforms energy between kinetic \((E_k = \frac{1}{2} mv^2)\), gravitational potential \((\Delta E_p = mg\Delta h)\), and elastic potential \((E_H = \frac{1}{2} k(\Delta x)^2)\) forms.

- Power:
- Rate of work done or energy transfer, \(P = \frac{\Delta W}{\Delta t} = Fv\).

- Efficiency:
- Efficiency \(\eta = \frac{E_{\text{output}}}{E_{\text{input}}} = \frac{P_{\text{output}}}{P_{\text{input}}}\).

- Energy Density:
- Amount of energy stored in a fuel source per unit volume or mass.

#### A.4 Rigid body mechanics

- Torque:
- Torque \(\tau\) is given by \(\tau = Fr \sin \theta\), where \(F\) is the force, \(r\) is the distance from the axis, and \(\theta\) is the angle between the force and lever arm.

- Rotational Equilibrium:
- In rotational equilibrium, the resultant torque is zero. Unbalanced torque causes angular acceleration.

- Rotational Motion:
- Described using angular displacement (\(\theta\)), angular velocity (\(\omega\)), and angular acceleration (\(\alpha\)).

- Equations of Motion:
- For uniform angular acceleration:
- \(\Delta \theta = \frac{\omega_f + \omega_i}{2} t\)
- \(\omega_f = \omega_i + \alpha t\)
- \(\Delta \theta = \omega_i t + \frac{1}{2} \alpha t^2\)
- \(\omega_f^2 = \omega_i^2 + 2\alpha \Delta \theta\)

- For uniform angular acceleration:
- Moment of Inertia:
- Depends on mass distribution about the axis. For point masses: \(I = \Sigma mr^2\).

- Newton’s Second Law for Rotation
- \(\tau = I\alpha\), where \(\tau\) is torque, \(I\) is moment of inertia, and \(\alpha\) is angular acceleration.

- Angular Momentum:
- \(L = I\omega\), constant unless acted upon by a resultant torque, where \(\Delta L = \tau \Delta t\).

- Rotational Kinetic Energy:
- \(E_k = \frac{1}{2} I \omega^2 = \frac{L^2}{2I}\).

#### A.5 Galilean and special relativity

- Reference Frames:
- Newton’s laws apply in all inertial reference frames, known as Galilean relativity.

- Galilean Transformations:
- For position: \( x’ = x – vt \)
- For time: \( t’ = t \)
- Velocity addition: \( u’ = u – v \)

- Special Relativity Postulates:
- The laws of physics are identical in all inertial frames.
- The speed of light in a vacuum is constant for all observers, regardless of their motion.

- Lorentz Transformations:
- For coordinates: \( x’ = \gamma(x – vt) \)
- For time: \( t’ = \gamma\left(t – \frac{vx}{c^2}\right) \)

- Relativistic Velocity Addition:
- \( u’ = \frac{u – v}{1 – \frac{uv}{c^2}} \)

- Space-Time Interval:
- The invariant space-time interval: \( (\Delta s)^2 = (c\Delta t)^2 – (\Delta x)^2 \)

- Proper Time & Length:
- Proper Time: The time interval measured by an observer at rest relative to the event.
- Proper Length: The length measured in the rest frame of the object.

- Time Dilation:
- \( \Delta t = \gamma \Delta t_0 \)

- Length Contraction:
- \( L = \frac{L_0}{\gamma} \)

- Relativity of Simultaneity:
- Events that are simultaneous in one frame may not be in another.

- Space-Time Diagrams:
- Interpret motion with world lines; the angle relates to speed: \( \tan \theta = \frac{v}{c} \)

- Experimental Evidence:
- Muon decay experiments confirm time dilation and length contraction.

### B. The particulate nature of matter

#### B.1 Thermal Energy Transfers

- Molecular Theory:
- Understand the behavior and structure of molecules in solids, liquids, and gases.

- Density:
- Density \( \rho = \frac{m}{V} \), where \( m \) is mass and \( V \) is volume.

- Temperature Scales:
- Temperature can be measured in Kelvin or Celsius; a change in temperature is the same in both scales.

- Kelvin Temperature:
- The average kinetic energy of particles is proportional to temperature in Kelvin, \( \overline{E_k} = \frac{3}{2} k_B T \).

- Internal Energy:
- Internal energy consists of total intermolecular potential energy and the total random kinetic energy of molecules.

- Temperature Difference:
- Determines the direction of thermal energy transfer between bodies.

- Phase Change:
- Involves energy changes that alter particle behavior without changing temperature.

- Thermal Energy Transfers:
- Use specific heat capacity \( Q = mc\Delta T \) and latent heat \( Q = mL \) for calculations.

- Mechanisms of Heat Transfer:
- Conduction (via particle kinetic energy difference), convection (due to fluid density differences), and radiation (emission of electromagnetic waves).

- Rate of Thermal Conduction:
- Given by \( \frac{\Delta Q}{\Delta t} = kA \frac{\Delta T}{\Delta x} \).

- Thermal Convection:
- Described by fluid density differences and heat transfer.

- Thermal Radiation:
- Energy transfer by radiation, modeled by the Stefan-Boltzmann law \( L = \sigma AT^4 \)

- Apparent Brightness and Luminosity:
- \( b = \frac{L}{4\pi d^2} \), where \( b \) is brightness, \( L \) is luminosity, and \( d \) is the distance.

- Black Body Emission Spectrum:
- Temperature determined by Wien’s displacement law \( \lambda_{\text{max}}T = 2.9 \times 10^{-3} \, \text{mK} \).

- Solar Constant
- The amount of solar energy received per unit area at the Earth’s surface.

**B.2 The Greenhouse Effect**

- Energy Conservation:
- Conservation of energy principles apply.

- Emissivity:
- Ratio of radiated power per unit area to the power of a black body at the same temperature, \( \text{emissivity} = \frac{\text{power per unit area}}{\sigma T^4} \)

- Albedo:
- The reflectivity of a surface, \( \text{albedo} = \frac{\text{scattered power}}{\text{incident power}} \).

- Earth’s Albedo:
- Varies daily, influenced by cloud cover and latitude.

- Incoming Radiative Power:
- Dependent on the planet’s projected surface area; mean intensity \( S/4 \).

- Greenhouse Gases
- Main gases include CH₄, H₂O, CO₂, N₂O; origins are both natural and anthropogenic

- Infrared Absorption
- Greenhouse gases absorb infrared radiation, re-emitting it in all directions

- Greenhouse Effect:
- Explained by resonance models and molecular energy levels.

- Enhanced Greenhouse Effect:
- Human activities intensify the greenhouse effect, leading to climate change.

#### B.3 Gas Laws

- Pressure:
- Defined as \( P = \frac{F}{A} \), where \( F \) is force and \( A \) is area.

- Amount of Substance:
- \( n = \frac{N}{N_A} \), where \( N \) is the number of molecules, \( N_A \) is Avogadro’s number.

- Ideal Gases:
- Modeled by kinetic theory to approximate real gas behavior.

- Ideal Gas Law:
- Derived from empirical laws, \( \frac{PV}{T} = \text{constant} \).

- Ideal Gas Equations:
- \( PV = Nk_B T \) and \( PV = nRT \).

- Pressure and Kinetic Energy:
- Pressure is related to the average speed of molecules, \( P = \frac{1}{3}\rho v^2 \).

- Internal Energy of Gases:
- \( U = \frac{3}{2} Nk_B T \) or \( U = \frac{3}{2} RnT \).

- Ideal Gas Approximation:
- Works well under certain temperature, pressure, and density conditions.

**B.4 Current & Circuits**

- Emf and Circuits:
- Cells provide emf; circuit diagrams represent component arrangements.

- Direct Current (DC):
- \( I = \frac{\Delta q}{\Delta t} \), where \( I \) is current, \( \Delta q \) is charge, and \( \Delta t \) is time.

- Electric Potential Difference:
- \( V = \frac{W}{q} \), where \( V \) is potential difference, \( W \) is work, and \( q \) is charge.

- Conductors and Insulators:
- Differ in the mobility of charge carriers.

- Electric Resistance:
- \( R = \frac{V}{I} \), origin relates to material and temperature.

- Resistivity:
- \( \rho = \frac{RA}{L} \), where \( A \) is cross-sectional area, and \( L \) is length.

- Ohm’s Law:
- Linear relationship between \( V \) and \( I \) for ohmic conductors.

- Electrical Power:
- \( P = IV = I^2R = \frac{V^2}{R} \).

- Resistor Combinations:
- Series and parallel configurations.

- Electric Cells:
- Characterized by emf \( \epsilon \) and internal resistance \( r \), \( \epsilon = I(R + r) \).

- Variable Resistance:
- Resistors with adjustable resistance values.

**B.5 Thermodynamics **

- First Law of Thermodynamics:
- \( Q = \Delta U + W \), conservation of energy in closed systems.

- Work Done:
- \( W = P\Delta V \), work related to pressure and volume changes.

- Internal Energy:
- Change in internal energy: \( \Delta U = \frac{3}{2} Nk_B \Delta T = \frac{3}{2} nR \Delta T \).

- Entropy:
- Entropy \( S \) relates to the disorder of a system.

- Entropy Calculation:
- \( \Delta S = \frac{\Delta Q}{T} \) or \( S = k_B \ln \Omega \).

- Second Law of Thermodynamics:
- Entropy of isolated systems always increases.

- Irreversibility:
- Real processes are irreversible, leading to entropy increase.

- Non-Isolated Systems:
- Entropy can decrease locally but increases in surroundings.

- Thermodynamic Processes:
- Isovolumetric, isobaric, isothermal, and adiabatic processes.

- Adiabatic Processes:
- Modeled by \( PV^{5/3} = \text{constant} \).

- Cyclic Gas Processes:
- Used in heat engines.

- Heat Engine Efficiency:
- \( \eta = \frac{\text{useful work}}{\text{input energy}} \).

- Carnot Cycle:
- Sets the efficiency limit, \( \eta_{\text{Carnot}} = 1 – \frac{T_c}{T_h} \).

### C. Wave behaviour

#### C.1 Simple Harmonic Motion

- Conditions for SHM:
- SHM occurs when a system experiences a restoring force proportional to its displacement and directed towards its equilibrium position.

- Defining Equation:
- The acceleration \( a \) is given by \( a = -\omega^2 x \), where \( \omega \) is the angular frequency, and \( x \) is the displacement.

- Descriptive Parameters:
- SHM can be described by time period \( T \), frequency \( f \), angular frequency \( \omega \), amplitude, equilibrium position, and displacement.

- Time Period Relationships:
- The time period \( T \) is related to frequency \( f \) by \( T = \frac{1}{f} \) and to angular frequency \( \omega \) by \( T = \frac{2\pi}{\omega} \).

- Mass-Spring System:
- The time period \( T \) for a mass-spring system is \( T = 2\pi \sqrt{\frac{m}{k}} \), where \( m \) is mass, and \( k \) is the spring constant.

- Simple Pendulum:
- The time period \( T \) of a simple pendulum is \( T = 2\pi \sqrt{\frac{l}{g}} \), where \( l \) is the length of the pendulum, and \( g \) is the acceleration due to gravity.

- Energy Changes:
- Energy in SHM oscillates between kinetic and potential energy. At maximum displacement, potential energy is maximal, and kinetic energy is zero; at equilibrium, kinetic energy is maximal, and potential energy is zero.

AHL

- Phase Angle in SHM:
- SHM can be described using a phase angle \( \phi \).

- SHM Equations:
- Position: \( x = x_0 \sin(\omega t + \phi) \), Velocity: \( v = \omega x_0 \cos(\omega t + \phi) \), Energy: \( E_T = \frac{1}{2} m\omega^2 x_0^2 \), Potential Energy: \( E_p = \frac{1}{2} m\omega^2 x^2 \)

**C.2 Wave Models**

- Wave Types:
- Transverse waves oscillate perpendicular to the direction of propagation, while longitudinal waves oscillate parallel.

- Wave Properties:
- Wavelength \( \lambda \), frequency \( f \), time period \( T \), and wave speed \( v \) are related by \( v = f\lambda = \frac{\lambda}{T} \).

- Sound & Electromagnetic Waves:
- Sound waves are mechanical, needing a medium, while electromagnetic waves can propagate in a vacuum.

- Wave Differences:
- Mechanical waves require a medium, whereas electromagnetic waves do not.

#### C.3 Wave Phenomena

- Wavefronts and Rays:
- Waves in 2D and 3D can be described by wavefronts and rays.

- Boundary Behavior:
- Waves reflect, refract, or transmit when encountering boundaries.

- Diffraction:
- Waves bend around obstacles and through apertures, described by diffraction.

- Wave Diagrams:
- Refraction and diffraction can be represented using wavefront-ray diagrams.

- Snell’s Law & TIR:
- Refraction is governed by Snell’s Law \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \). The critical angle and total internal reflection are key concepts.

- Superposition:
- When waves overlap, their amplitudes add up, creating constructive or destructive interference.

- Double-Source Interference:
- Coherent sources produce interference patterns. Constructive interference occurs at path differences of \( n\lambda \), destructive at \( (n + \frac{1}{2})\lambda \).

- Young’s Double-Slit:
- Interference pattern spacing \( s = \frac{\lambda D}{d} \), where \( D \) is distance to the screen, and \( d \) is slit separation.

AHL

- Single-Slit Diffraction:
- Intensity patterns are given by \( \theta = \frac{b}{\lambda} \).

- Pattern Modulation:
- The single-slit pattern modulates the double-slit interference pattern

- Multiple Slits & Diffraction Gratings:
- Interference patterns are given by \( n\lambda = d \sin \theta \).

#### C.4 Standing Waves & Resonance

- Standing Wave Formation:
- Formed by the superposition of two identical waves traveling in opposite directions.

- Nodes and Antinodes:
- Nodes are points of zero amplitude, antinodes are points of maximum amplitude.

- Strings & Pipes:
- Standing waves in strings and pipes depend on boundary conditions.

- Resonance:
- Occurs when a system is driven at its natural frequency, leading to maximum amplitude.

- Damping:
- Damping reduces amplitude and affects resonant frequency. Light, critical, and heavy damping have distinct impacts on oscillatory systems.

Doppler Effect

- Doppler Effect:
- The apparent change in frequency or wavelength of a wave due to relative motion between the source and observer.

- Wavefront Diagrams:
- Representations of the Doppler effect show wavefront compression or elongation due to motion.

- Relative Change in Frequency:
- For light waves, the change in frequency \( \Delta f \) or wavelength \( \Delta \lambda \) is approximately \( \frac{v}{c} \), where \( v \) is relative speed, and \( c \) is the speed of light.

- Spectral Lines:
- Shifts in spectral lines indicate the motion of astronomical objects like stars and galaxies.

AHL

- Observed Frequency:
- Moving source:
- \( f’ = f \left(\frac{v}{v \pm u_s}\right) \),

- Moving observer:
- \( f’ = f \left(\frac{v \pm u_o}{v}\right) \). \( u_s \) and \( u_o \) are the speeds of the source and observer, respectively.

- Moving source:

#### C.5 Doppler Effect

- Doppler Effect:
- The apparent change in frequency or wavelength of a wave due to relative motion between the source and observer.

- Wavefront Diagrams:
- Representations of the Doppler effect show wavefront compression or elongation due to motion.

- Relative Change in Frequency:
- For light waves, the change in frequency \( \Delta f \) or wavelength \( \Delta \lambda \) is approximately \( \frac{v}{c} \), where \( v \) is relative speed, and \( c \) is the speed of light.

- Spectral Lines:
- Shifts in spectral lines indicate the motion of astronomical objects like stars and galaxies.

AHL

- Observed Frequency:
- Moving source:
- \( f’ = f \left(\frac{v}{v \pm u_s}\right) \),

- Moving observer:
- \( f’ = f \left(\frac{v \pm u_o}{v}\right) \). \( u_s \) and \( u_o \) are the speeds of the source and observer, respectively.

- Moving source:

### D. Fields

#### D.1 Gravitational Fields

- Kepler’s Three Laws:
- 1st: Planets orbit the Sun in ellipses with the Sun at one focus.
- 2nd: A line from a planet to the Sun sweeps out equal areas in equal times.
- 3rd: The square of a planet’s orbital period is proportional to the cube of the semi-major axis.

- Newton’s Law of Gravitation:
- \( F = G \frac{m_1 m_2}{r^2} \), where \( F \) is the gravitational force, \( G \) is the gravitational constant, and \( r \) is the distance between masses \( m_1 \) and \( m_2 \).
- Point Masses:

- Extended bodies can be treated as point masses when their size is negligible compared to the distance between them.
- Gravitational Field Strength:
- \( g = \frac{F}{m} = \frac{GM}{r^2} \), where \( g \) is the field strength, \( M \) is the mass of the attracting body, and \( r \) is the distance from the center.

- Gravitational Field Lines:
- These lines indicate the direction of the gravitational force, with density proportional to field strength.

AHL

- Gravitational Potential Energy:
- \( E_p \) is the work done to assemble a system from infinity.

- Two-Body System:
- \( E_p = -G \frac{m_1 m_2}{r} \), where \( r \) is the distance between the masses.

- Gravitational Potential:
- \( V_g = -\frac{GM}{r} \), the work done per unit mass to bring a mass from infinity to a point.

- Gravitational Field Strength:
- \( g = -\frac{\Delta V_g}{\Delta r} \), the potential gradient.

- Work in Gravitational Field:
- \( W = m \Delta V_g \), where \( W \) is work done and \( \Delta V_g \) is the change in gravitational potential.

- Equipotential Surfaces:
- Surfaces where the gravitational potential is the same, indicating no work is required to move along them.

- Equipotential Surfaces & Field Lines:
- Field lines are perpendicular to equipotential surfaces.

- Escape Speed:
- \( v_{esc} = \sqrt{\frac{2GM}{r}} \), the minimum speed needed to escape a gravitational field.

- Orbital Speed:
- \( v_{orbital} = \sqrt{\frac{GM}{r}} \), the speed needed for a stable orbit.

- Viscous Drag:
- A small drag force reduces the height and speed of an orbiting body

**D.2 Electric and magnetic fields**

- Electric Forces:
- Opposite charges attract, like charges repel.

- Coulomb’s Law:
- \( F = k \frac{q_1 q_2}{r^2} \), where \( k = \frac{1}{4 \pi \epsilon_0} \) and \( \epsilon_0 \) is the permittivity of free space.

- Conservation of Charge:
- Electric charge is conserved in any physical process.

- Millikan’s Experiment:
- Demonstrated the quantization of electric charge.

- Charge Transfer Methods:
- Charges can transfer via friction, induction, and contact, with grounding preventing charge buildup.

- Electric Field Strength:
- \( E = \frac{F}{q} \), where \( E \) is field strength, \( F \) is force, and \( q \) is charge.

- Electric Field Lines:
- Lines represent the direction of force on a positive charge, with density indicating field strength.

- Uniform Electric Field:
- Between parallel plates, \( E = \frac{V}{d} \), where \( V \) is voltage and \( d \) is the distance between plates

- Magnetic Field Lines:
- Lines indicate the direction of the magnetic force, showing the orientation of the field.

AHL

- Electric Potential Energy:
- \( E_p \) is the work done to assemble a system of charges from infinity.

- Two-Body System:
- \( E_p = k \frac{q_1 q_2}{r} \), where \( k \) is Coulomb’s constant.

- Electric Potential:
- \( V_e = \frac{kQ}{r} \), the work done per unit charge to bring a charge from infinity to a point.

- Electric Field Strength:
- \( E = -\frac{\Delta V_e}{\Delta r} \), the potential gradient.

- Work in Electric Field:
- \( W = q \Delta V_e \), where \( W \) is work done and \( \Delta V_e \) is the change in electric potential.

- Equipotential Surfaces:
- Surfaces where the electric potential is the same, indicating no work is required to move along them.

- Equipotential Surfaces & Field Lines:
- Field lines are perpendicular to equipotential surfaces.

#### D.3 Motion in electromagnetic fields

- Charged Particles in Fields:
- A charged particle moves in circular or helical paths in a magnetic field, depending on its initial velocity relative to the field.

- Perpendicular Fields:
- A particle moving in both electric and magnetic fields perpendicularly experiences a force that can result in a helical trajectory.

- Force on Moving Charge:
- \( F = qvB \sin \theta \), where \( F \) is the magnetic force, \( q \) is the charge, \( v \) is velocity, and \( B \) is the magnetic field strength.

- Force on Current-Carrying Conductor:
- \( F = BIL \sin \theta \), where \( I \) is current, \( L \) is length, and \( \theta \) is the angle between \( I \) and \( B \).

- Force Between Parallel Wires:
- \( \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi r} \), where \( \mu_0 \) is the permeability of free space, \( I_1 \) and \( I_2 \) are the currents, and \( r \) is the distance between wires.

#### D.4 Induction

- Magnetic Flux:
- \( \Phi = BA \cos \theta \), where \( \Phi \) is magnetic flux, \( B \) is magnetic field strength, \( A \) is area, and \( \theta \) is the angle between \( B \) and the normal to the area.

- Faraday’s Law:
- \( \epsilon = -N \frac{\Delta \Phi}{\Delta t} \), where \( \epsilon \) is induced emf, \( N \) is the number of turns in the coil, and \( \Delta \Phi/\Delta t \) is the rate of change of magnetic flux.

- Induced emf in Moving Conductor:
- \( \epsilon = BvL \), where \( v \) is the velocity of the conductor and \( L \) is its length.

- Lenz’s Law:
- The direction of induced emf opposes the change in magnetic flux, conserving energy.

- Sinusoidal emf:
- Induced in a coil rotating in a uniform magnetic field, with frequency affecting the magnitude of emf.

### E. Nuclear and quantum physics

#### E.1 Structure of the atom

- Geiger–Marsden–Rutherford Experiment:
- Demonstrated the existence of a small, dense nucleus within the atom by observing the deflection of alpha particles.

- Nuclear Notation:
- Represents atoms using \( _{Z}^{A}X \), where \( Z \) is the atomic number, \( A \) is the mass number, and \( X \) is the element symbol.

- Spectra and Energy Levels:
- Emission and absorption spectra show discrete energy levels in atoms, where photons are emitted or absorbed during transitions between levels.

- Photon Energy:
- The energy \( E \) of emitted or absorbed photons is related to the frequency \( f \) by \( E = hƒ \), where \( h \) is Planck’s constant.

- Chemical Composition:
- Spectra analysis provides insights into the chemical composition of substances.

AHL

- Nuclear Radius & Nucleon Number:
- The nuclear radius \( R \) is related to nucleon number \( A \) by \( R = R_0 A^{1/3} \), affecting nuclear density.

- Rutherford Scattering:
- Deviations at high energies indicate limitations of the Rutherford model.

- Closest Approach:
- The minimum distance between an alpha particle and nucleus in scattering experiments, indicating nuclear size.

- Bohr Model Energy Levels:
- For hydrogen, energy levels are quantized, with \( E = -\frac{13.6}{n^2} \) eV.

- Quantized Orbits:
- The Bohr model predicts quantized orbits from angular momentum quantization \( mvr = \frac{nh}{2\pi} \).

Fission

- Energy Release:
- Energy is released during both spontaneous and neutron-induced fission.

- Chain Reactions:
- In fission, neutrons released can induce further fission, creating a self-sustaining reaction.

- Nuclear Power Plant Components:
- Control rods (absorb neutrons), moderators (slow neutrons), heat exchangers, and shielding are key components.

- Fission Products Management:
- Fission produces radioactive byproducts that require careful management due to their harmful nature.

Fusion & Stars

- Stellar Stability:
- Stars are stable due to the balance between radiation pressure (outward) and gravitational forces (inward).

- Fusion as Energy Source:
- Fusion reactions within stars release energy by fusing lighter elements into heavier ones.

- Conditions for Fusion:
- High temperature and density are required for fusion to occur in stars.

- Stellar Evolution:
- The mass of a star significantly influences its lifecycle and eventual fate.

- Hertzsprung–Russell Diagram:
- A graphical representation that shows the relationship between stars’ luminosity and temperature, with different regions corresponding to different types of stars.

- Stellar Parallax:
- A method for determining the distance \( d \) to stars using parallax angle \( p \), given by \( d = \frac{1}{p} \) parsecs.

- Stellar Radii:
- Can be determined from the star’s luminosity and temperature.

**E.2 Quantum Physics**

- Photoelectric Effect:
- Demonstrates the particle nature of light, where photons of sufficient energy eject electrons from a metal.

- Threshold Frequency:
- The minimum frequency needed for photons to release photoelectrons.

- Einstein’s Explanation:
- The maximum kinetic energy of photoelectrons is given by \( E_{\text{max}} = hƒ – \Phi \), where \( \Phi \) is the work function.

- Diffraction of Particles:
- Shows the wave nature of matter, supporting wave-particle duality.

- de Broglie Wavelength:
- For particles, wavelength \( \lambda = \frac{h}{p} \), where \( p \) is momentum.

- Compton Scattering:
- Provides additional evidence for the particle nature of light, where photons scatter off electrons, increasing in wavelength.

- Wavelength Shift:
- The shift \( \Delta \lambda = \frac{h}{m_e c}(1-\cos \theta) \) shows the change in photon wavelength after scattering.

#### E.3 Radioactive Decay

- Isotopes:
- Variants of elements with the same number of protons but different numbers of neutrons.

- Nuclear Binding Energy and Mass Defect:
- The energy needed to bind nucleons together; mass defect refers to the difference between the total mass of individual nucleons and the mass of the nucleus.

- Binding Energy Per Nucleon:
- Varies with nucleon number; higher binding energy per nucleon means more stable nuclei.

- Mass-Energy Equivalence:
- Expressed by \( E = mc^2 \), illustrating the conversion between mass and energy in nuclear reactions.

- Strong Nuclear Force:
- A short-range force that holds nucleons together within the nucleus.

- Radioactive Decay:
- A random and spontaneous process that changes the nucleus’s state, involving alpha, beta, and gamma decay.

- Radioactive Decay Equations:
- Equations describe changes during alpha (α), beta-minus (β−), beta-plus (β+), and gamma (γ) decay.

- Neutrinos:
- Neutral particles, \( \nu \) (neutrinos) and \( \bar{\nu} \) (antineutrinos), are involved in beta decay.

- Penetration and Ionization:
- Alpha particles have low penetration but high ionization, beta particles have moderate penetration and ionization, and gamma rays have high penetration but low ionization.

- Activity, Count Rate, and Half-Life:
- Activity is the rate of decay, count rate is the number of decays detected, and half-life is the time required for half the radioactive nuclei to decay.

- Background Radiation:
- Must be considered in experiments to ensure accurate measurements of radioactive decay.

AHL

- Strong Nuclear Force Evidence:
- Experimental evidence shows the existence of a force stronger than electromagnetism at short ranges.

- Neutron-Proton Ratio:
- Stability of nuclei depends on the balance between neutrons and protons.

- Binding Energy Curve:
- Binding energy per nucleon remains relatively constant for nucleon numbers above 60, indicating stable nuclei.

- Alpha and Gamma Radiation:
- Discrete energy levels within the nucleus can be inferred from the emission spectra.

- Beta Decay & Neutrinos:
- The continuous beta spectrum suggests the presence of neutrinos.

- Decay Constant & Law:
- \( N = N_0 e^{-\lambda t} \) describes the number of undecayed nuclei over time.

- Decay Constant Approximation:
- The decay constant \( \lambda \) represents the probability of decay over a small time interval.

- Activity & Decay Rate:
- Activity \( A = \lambda N \) measures the decay rate, decreasing over time as \( A = \lambda N_0 e^{-\lambda t} \).

- Half-Life & Decay Constant:
- Half-life \( T_{1/2} \) is related to the decay constant by \( T_{1/2} = \frac{\ln 2}{\lambda} \).

#### E.4 Fission

- Energy Release:
- Energy is released during both spontaneous and neutron-induced fission.

- Chain Reactions:
- In fission, neutrons released can induce further fission, creating a self-sustaining reaction.

- Nuclear Power Plant Components:
- Control rods (absorb neutrons), moderators (slow neutrons), heat exchangers, and shielding are key components.

- Fission Products Management:
- Fission produces radioactive byproducts that require careful management due to their harmful nature.

Fusion & Stars

- Stellar Stability:
- Stars are stable due to the balance between radiation pressure (outward) and gravitational forces (inward).

- Fusion as Energy Source:
- Fusion reactions within stars release energy by fusing lighter elements into heavier ones.

- Conditions for Fusion:
- High temperature and density are required for fusion to occur in stars.

- Stellar Evolution:
- The mass of a star significantly influences its lifecycle and eventual fate.

- Hertzsprung–Russell Diagram:
- A graphical representation that shows the relationship between stars’ luminosity and temperature, with different regions corresponding to different types of stars.

- Stellar Parallax:
- A method for determining the distance \( d \) to stars using parallax angle \( p \), given by \( d = \frac{1}{p} \) parsecs.

- Stellar Radii:
- Can be determined from the star’s luminosity and temperature.

#### E.4 Fusion & Stars

- Stellar Stability:
- Stars are stable due to the balance between radiation pressure (outward) and gravitational forces (inward).

- Fusion as Energy Source:
- Fusion reactions within stars release energy by fusing lighter elements into heavier ones.

- Conditions for Fusion:
- High temperature and density are required for fusion to occur in stars.

- Stellar Evolution:
- The mass of a star significantly influences its lifecycle and eventual fate.

- Hertzsprung–Russell Diagram:
- A graphical representation that shows the relationship between stars’ luminosity and temperature, with different regions corresponding to different types of stars.

- Stellar Parallax:
- A method for determining the distance \( d \) to stars using parallax angle \( p \), given by \( d = \frac{1}{p} \) parsecs.

- Stellar Radii:
- Can be determined from the star’s luminosity and temperature.