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DP IB Physics: HL

Revision Notes

Home / IB / Physics: HL / DP / Revision Notes / 12. Quantum & Nuclear Physics (HL only) / 12.1 The Interaction of Matter with Radiation / 12.1.1 Photons


12.1.1 Photons


Photons

  • In classical wave theory, electromagnetic (EM) radiation is assumed to behave as a wave
    • This is demonstrated by the fact EM radiation exhibits phenomena such as diffraction and interference

  • However, experiments from the last century, such as discovering the photoelectric effect and atomic line spectra, can only be explained if the EM radiation is thought of as behaving as particles

  • These experiments have formed the basis of quantum theory, which will be explored in detail in this section

Photons

  • Photons are fundamental particles which make up all forms of electromagnetic radiation
  • A photon is defined as

A massless ''packet'' or a ''quantum'' of electromagnetic energy

12-1-1-photons-ib-hl

A wave packet (photon)

  • It is also defined as:

A massless particle that possesses an energy equal to E = hf

  • This means is that the energy of a photon is not transferred continuously, but as discrete packets of energy
  • In other words, each photon carries a specific amount of energy, and transfers this energy all in one go, rather than supplying a consistent amount of energy

  • The energy of a photon can be calculated using the formula:

E italic equals h f

  • Substituting in from the wave equation, energy can also be equal to:

begin mathsize 16px style E italic equals fraction numerator h c over denominator lambda end fraction end style

  • Where:
    • E = energy of the photon (J)
    • h = Planck's constant (J s)
    • c = the speed of light (m s-1)
    • f = frequency in Hertz (Hz)
    • λ = wavelength (m)

  • This equation tells us:
    • The higher the frequency of EM radiation, the higher the energy of the photon
    • The energy of a photon is inversely proportional to the wavelength
    • A long-wavelength photon of light has a lower energy than a shorter-wavelength photon

 

Worked Example

Light of wavelength 490 nm is incident normally on a surface, as shown in the diagram.
The power of the light is 3.6 mW. The light is completely absorbed by the surface.

Calculate the number of photons incident on the surface in 2.0 s.

Step 1: Write down the known quantities

    • Wavelength, λ = 490 nm = 490 × 10−9 m
    • Power, P = 3.6 mW = 3.6 × 10−3 W
    • Time, t = 2.0 s

Step 2: Write the equations for wave speed and photon energy

begin mathsize 16px style w a v e space s p e e d colon space space space space space c space equals space f lambda space rightwards arrow space f space equals space c over lambda end style

    size 16px p size 16px h size 16px o size 16px t size 16px o size 16px n size 16px space size 16px e size 16px n size 16px e size 16px r size 16px g size 16px y size 16px colon size 16px space size 16px space size 16px space size 16px space size 16px space size 16px E size 16px space size 16px equals size 16px space size 16px h size 16px f size 16px space size 16px rightwards arrow size 16px space size 16px E size 16px space size 16px equals size 16px space fraction numerator size 16px h size 16px c over denominator size 16px lambda end fraction

Step 3: Calculate the energy of one photon

Step 4: Calculate the number of photons hitting the surface every second

fraction numerator size 16px p size 16px o size 16px w size 16px e size 16px r size 16px space size 16px o size 16px f size 16px space size 16px l size 16px i size 16px g size 16px h size 16px t size 16px space size 16px s size 16px o size 16px u size 16px r size 16px c size 16px e over denominator size 16px e size 16px n size 16px e size 16px r size 16px g size 16px y size 16px space size 16px o size 16px f size 16px space size 16px o size 16px n size 16px e size 16px space size 16px p size 16px h size 16px o size 16px t size 16px o size 16px n end fraction size 16px space size 16px equals fraction numerator size 16px 3 size 16px. size 16px 6 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px minus size 16px 3 end exponent over denominator size 16px 4 size 16px. size 16px 06 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px minus size 16px 19 end exponent end fraction size 16px space size 16px space size 16px equals size 16px space size 16px 8 size 16px. size 16px 9 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px 15 size 16px space size 16px s to the power of size 16px minus size 16px 1 end exponent

Step 5: Calculate the number of photons that hit the surface in 2 s

size 16px left parenthesis size 16px 8 size 16px. size 16px 9 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px 15 size 16px space size 16px cross times size 16px space size 16px 2 size 16px right parenthesis size 16px space size 16px equals size 16px space size 16px 1 size 16px. size 16px 8 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px 16

Photon Momentum

  • Einstein showed that a photon travelling in a vacuum has momentum, despite it having no mass
  • The momentum (p) of a photon is related to its energy (E) by the equation:

  • Where
    • c = the speed of light
    • p = the momentum of the photon (kg m s-1)
    • E = the energy of the photon (J)

Worked Example

A 5.0 mW laser beam is incident normally on a fixed metal plate. The cross-sectional area of the beam is 8.0 × 10-6 m2. The light from the laser has frequency 5.6 × 1014 Hz.

Assuming that all the photons are absorbed by the plate, calculate the momentum of the photon, and the pressure exerted by the laser beam on the metal plate.

Step 1: Write down the known quantities

    • Power, P = 5.0 mW = 5.0 × 10−3 W
    • Frequency, f = 5.6 × 1014 Hz
    • Cross-sectional area, A = 8.0 × 10−6 m2

Step 2: Write the equations for photon energy and momentum

begin mathsize 16px style p h o t o n space e n e r g y colon space E space equals space h f

p h o t o n space m o m e n t u m colon space p space equals space E over c space equals space fraction numerator h f over denominator c end fraction space end style

Step 3: Calculate the photon momentum

Step 4: Calculate the number of photons incident on the plate every second

      begin mathsize 16px style fraction numerator power space of space light space source over denominator energy space of space one space photon end fraction space equals space fraction numerator 5.0 space cross times space 10 to the power of negative 3 end exponent over denominator h f end fraction end style

begin mathsize 14px style space equals space space fraction numerator 5.0 space cross times space 10 to the power of negative 3 end exponent over denominator left parenthesis 6.63 space cross times space 10 to the power of negative 34 end exponent right parenthesis space cross times space left parenthesis 5.6 space cross times space 10 to the power of 14 right parenthesis end fraction space equals space 1.35 space cross times space 10 to the power of 16 space s to the power of negative 1 end exponent end style

Step 5: Calculate the force exerted on the plate in a 1.0 s time interval

begin mathsize 16px style f o r c e space equals space r a t e space o f space c h a n g e space o f space m o m e n t u m
rightwards arrow space f o r c e space equals space n u m b e r space o f space p h o t o n s space p e r space s e c o n d space space cross times space m o m e n t u m space o f space e a c h space p h o t o n end style

begin mathsize 16px style F space equals space left parenthesis 1.35 space cross times space 10 to the power of 16 right parenthesis space cross times space left parenthesis 1.24 space cross times space 10 to the power of negative 27 end exponent right parenthesis space equals space 1.67 space cross times space 10 to the power of negative 11 end exponent space N end style

 Step 6: Calculate the pressure

p r e s s u r e space equals space fraction numerator size 16px f size 16px o size 16px r size 16px c size 16px e over denominator size 16px a size 16px r size 16px e size 16px a end fraction size 16px space size 16px equals size 16px space fraction numerator size 16px 1 size 16px. size 16px 67 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px minus size 16px 11 end exponent over denominator size 16px 8 size 16px. size 16px 0 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px minus size 16px 6 end exponent end fraction size 16px space size 16px equals size 16px space size 16px 2 size 16px. size 16px 1 size 16px space size 16px cross times size 16px space size 16px 10 to the power of size 16px minus size 16px 6 end exponent size 16px space size 16px P size 16px a

Exam Tip

Make sure you learn the definition for a photon: discrete quantity / packet / quantum of electromagnetic energy are all acceptable definitions

The values of Planck’s constant and the speed of light will always be given to you in an exam, however, it helps to memorise them to speed up calculation questions!


  • 1. Measurement & Uncertainties
    • 1.1 Measurements in Physics
      • 1.1.1 SI Units
        • 1.1.2 Using Scientific Notation
          • 1.1.3 Estimating Physical Quantities
          • 1.2 Uncertainties & Errors
            • 1.2.1 Random & Systematic Errors
              • 1.2.2 Calculating Uncertainties
                • 1.2.3 Determining Uncertainties from Graphs
                • 1.3 Vectors & Scalars
                  • 1.3.1 Vector & Scalar Quantities
                    • 1.3.2 Combining & Resolving Vectors
                      • 1.3.3 Solving Vector Problems
                    • 2. Mechanics
                      • 2.1 Motion
                        • 2.1.1 Distance & Displacement
                          • 2.1.2 Speed & Velocity
                            • 2.1.3 Acceleration
                              • 2.1.4 Graphs Describing Motion
                                • 2.1.5 Uniform Acceleration
                                  • 2.1.6 Acceleration of Free Fall Experiment
                                    • 2.1.7 Projectile Motion
                                      • 2.1.8 Terminal Speed
                                      • 2.2 Forces
                                        • 2.2.1 Free-Body Diagrams
                                          • 2.2.2 Newton’s First Law
                                            • 2.2.3 Newton’s Second Law
                                              • 2.2.4 Newton’s Third Law
                                                • 2.2.5 Applying Newton’s Laws of Motion
                                                  • 2.2.6 Friction
                                                  • 2.3 Work, Energy & Power
                                                    • 2.3.1 Kinetic Energy
                                                      • 2.3.2 Gravitational Potential Energy
                                                        • 2.3.3 Elastic Potential Energy
                                                          • 2.3.4 Work Done
                                                            • 2.3.5 Power
                                                              • 2.3.6 Principle of Conservation of Energy
                                                                • 2.3.7 Efficiency
                                                                • 2.4 Momentum & Impulse
                                                                  • 2.4.1 Force & Momentum
                                                                    • 2.4.2 Impulse
                                                                      • 2.4.3 Conservation of Linear Momentum
                                                                        • 2.4.4 Collisions & Explosions
                                                                      • 3. Thermal Physics
                                                                        • 3.1 Thermal Concepts
                                                                          • 3.1.1 Solids, Liquids & Gases
                                                                            • 3.1.2 Temperature
                                                                              • 3.1.3 Internal Energy
                                                                                • 3.1.4 Specific Heat Capacity
                                                                                  • 3.1.5 Specific Latent Heat
                                                                                    • 3.1.6 Phase Change
                                                                                      • 3.1.7 Investigating Thermal Energy
                                                                                      • 3.2 Modelling a Gas
                                                                                        • 3.2.1 Ideal Gas Laws
                                                                                          • 3.2.2 Ideal Gas Equation
                                                                                            • 3.2.3 Kinetic Model of an Ideal Gas
                                                                                              • 3.2.4 Mole Calculations
                                                                                                • 3.2.5 Investigating Gas Laws
                                                                                              • 4. Waves
                                                                                                • 4.1 Oscillations
                                                                                                  • 4.1.1 Properties of Oscillations
                                                                                                    • 4.1.2 Simple Harmonic Oscillations
                                                                                                      • 4.1.3 SHM Graphs
                                                                                                        • 4.1.4 Energy in SHM
                                                                                                        • 4.2 Travelling Waves
                                                                                                          • 4.2.1 Properties of Waves
                                                                                                            • 4.2.2 Transverse & Longitudinal Waves
                                                                                                              • 4.2.3 Electromagnetic Waves
                                                                                                                • 4.2.4 Sound Waves
                                                                                                                • 4.3 Wave Characteristics
                                                                                                                  • 4.3.1 Wavefronts
                                                                                                                    • 4.3.2 Amplitude & Intensity
                                                                                                                      • 4.3.3 Superposition
                                                                                                                        • 4.3.4 Polarisation
                                                                                                                          • 4.3.5 Malus’s Law
                                                                                                                          • 4.4 Wave Behaviour
                                                                                                                            • 4.4.1 Reflection, Refraction & Transmission
                                                                                                                              • 4.4.2 Reflection
                                                                                                                                • 4.4.3 Refraction
                                                                                                                                  • 4.4.4 Determining Refractive Index
                                                                                                                                    • 4.4.5 Single-Slit Diffraction
                                                                                                                                      • 4.4.6 Interference & Path Difference
                                                                                                                                        • 4.4.7 Double-Slit Equation
                                                                                                                                        • 4.5 Standing Waves
                                                                                                                                          • 4.5.1 The Nature of Standing Waves
                                                                                                                                            • 4.5.2 Nodes & Antinodes
                                                                                                                                              • 4.5.3 Boundary Conditions for Standing Waves
                                                                                                                                                • 4.5.4 Harmonics
                                                                                                                                              • 5. Electricity & Magnetism
                                                                                                                                                • 5.1 Electric Fields
                                                                                                                                                  • 5.1.1 Charge & Current
                                                                                                                                                    • 5.1.2 Drift Speed
                                                                                                                                                      • 5.1.3 Potential Difference & DC
                                                                                                                                                        • 5.1.4 Electric Fields
                                                                                                                                                          • 5.1.5 Coulomb’s Law
                                                                                                                                                          • 5.2 Heating Effect of Electric Currents
                                                                                                                                                            • 5.2.1 Circuits
                                                                                                                                                              • 5.2.2 Resistance & Resistors
                                                                                                                                                                • 5.2.3 Kirchhoff’s Circuit Laws
                                                                                                                                                                  • 5.2.4 I-V Characteristics
                                                                                                                                                                    • 5.2.5 Resistivity
                                                                                                                                                                      • 5.2.6 Investigating Resistivity
                                                                                                                                                                        • 5.2.7 Series & Parallel Circuits
                                                                                                                                                                          • 5.2.8 Heating Effect of Current
                                                                                                                                                                            • 5.2.9 Potential Divider Circuits
                                                                                                                                                                            • 5.3 Electric Cells
                                                                                                                                                                              • 5.3.1 Primary & Secondary Cells
                                                                                                                                                                                • 5.3.2 Investigating Electric Cells
                                                                                                                                                                                  • 5.3.3 Terminal Potential Difference
                                                                                                                                                                                    • 5.3.4 Electromotive Force & Internal Resistance
                                                                                                                                                                                    • 5.4 Magnetic Effects of Electric Currents
                                                                                                                                                                                      • 5.4.1 Magnetic Fields
                                                                                                                                                                                        • 5.4.2 Magnetic Force on a Charge
                                                                                                                                                                                          • 5.4.3 Magnetic Force on a Current-Carrying Conductor
                                                                                                                                                                                            • 5.4.4 Solving Problems Involving Magnetic Forces
                                                                                                                                                                                          • 6. Circular Motion & Gravitation
                                                                                                                                                                                            • 6.1 Circular Motion
                                                                                                                                                                                              • 6.1.1 Circular Motion
                                                                                                                                                                                                • 6.1.2 Centripetal Force
                                                                                                                                                                                                  • 6.1.3 Centripetal Acceleration
                                                                                                                                                                                                    • 6.1.4 Applications of Circular Motion
                                                                                                                                                                                                    • 6.2 Newton’s Law of Gravitation
                                                                                                                                                                                                      • 6.2.1 Newton’s Law of Gravitation
                                                                                                                                                                                                        • 6.2.2 Circular Orbits
                                                                                                                                                                                                          • 6.2.3 Gravitational Field Strength
                                                                                                                                                                                                        • 7. Atomic, Nuclear & Particle Physics
                                                                                                                                                                                                          • 7.1 Discrete Energy & Radioactivity
                                                                                                                                                                                                            • 7.1.1 Discrete Energy Levels
                                                                                                                                                                                                              • 7.1.2 Calculating Discrete Energies
                                                                                                                                                                                                                • 7.1.3 Emission & Absorption Spectrum
                                                                                                                                                                                                                  • 7.1.4 Isotopes & Radioactive Decay
                                                                                                                                                                                                                    • 7.1.5 Background Radiation
                                                                                                                                                                                                                      • 7.1.6 Alpha, Beta & Gamma Particles
                                                                                                                                                                                                                        • 7.1.7 Decay Equations
                                                                                                                                                                                                                          • 7.1.8 Half-Life
                                                                                                                                                                                                                            • 7.1.9 Investigating Half-Life
                                                                                                                                                                                                                            • 7.2 Nuclear Reactions
                                                                                                                                                                                                                              • 7.2.1 Atomic Mass Unit
                                                                                                                                                                                                                                • 7.2.2 Mass Defect & Nuclear Binding Energy
                                                                                                                                                                                                                                  • 7.2.3 Nuclear Fission & Fusion
                                                                                                                                                                                                                                    • 7.2.4 Binding Energy per Nucleon Curve
                                                                                                                                                                                                                                    • 7.3 The Structure of Matter
                                                                                                                                                                                                                                      • 7.3.1 Discovery of the Nucleus
                                                                                                                                                                                                                                        • 7.3.2 Quarks & Leptons
                                                                                                                                                                                                                                          • 7.3.3 Hadrons, Baryons & Mesons
                                                                                                                                                                                                                                            • 7.3.4 Particle Conservation Laws
                                                                                                                                                                                                                                              • 7.3.5 Fundamental Forces
                                                                                                                                                                                                                                                • 7.3.6 Feynman Diagrams & Confinement
                                                                                                                                                                                                                                                  • 7.3.7 The Standard Model of Particle Physics
                                                                                                                                                                                                                                                • 8. Energy Production
                                                                                                                                                                                                                                                  • 8.1 Energy Sources
                                                                                                                                                                                                                                                    • 8.1.1 Specific Energy
                                                                                                                                                                                                                                                      • 8.1.2 Sankey Diagrams
                                                                                                                                                                                                                                                        • 8.1.3 Primary & Secondary Energy Sources
                                                                                                                                                                                                                                                          • 8.1.4 Energy Resources
                                                                                                                                                                                                                                                            • 8.1.5 Energy Generation
                                                                                                                                                                                                                                                              • 8.1.6 Safety Issues in Nuclear Power
                                                                                                                                                                                                                                                              • 8.2 Thermal Energy Transfer
                                                                                                                                                                                                                                                                • 8.2.1 Conduction, Convection & Thermal Radiation
                                                                                                                                                                                                                                                                  • 8.2.2 Black-Body Radiation
                                                                                                                                                                                                                                                                    • 8.2.3 The Solar Constant, Albedo & Emissivity
                                                                                                                                                                                                                                                                      • 8.2.4 The Greenhouse Effect
                                                                                                                                                                                                                                                                        • 8.2.5 Earth's Surface–Atmosphere System
                                                                                                                                                                                                                                                                      • 9. Wave Phenomena (HL only)
                                                                                                                                                                                                                                                                        • 9.1 Simple Harmonic Motion
                                                                                                                                                                                                                                                                          • 9.1.1 The Defining Equation of SHM
                                                                                                                                                                                                                                                                            • 9.1.2 Energy Changes in SHM
                                                                                                                                                                                                                                                                              • 9.1.3 Calculating Energy Changes in SHM
                                                                                                                                                                                                                                                                                • 9.1.4 Examples of SHM
                                                                                                                                                                                                                                                                                • 9.2 Single-Slit Diffraction
                                                                                                                                                                                                                                                                                  • 9.2.1 The Nature of Single-Slit Diffraction
                                                                                                                                                                                                                                                                                    • 9.2.2 Intensity of Interference Maxima & Minima
                                                                                                                                                                                                                                                                                    • 9.3 Interference
                                                                                                                                                                                                                                                                                      • 9.3.1 Young’s Double-Slit Experiment
                                                                                                                                                                                                                                                                                        • 9.3.2 Two-Slit Interference Patterns
                                                                                                                                                                                                                                                                                          • 9.3.3 Diffraction Grating Patterns
                                                                                                                                                                                                                                                                                            • 9.3.4 The Diffraction Grating Equation
                                                                                                                                                                                                                                                                                              • 9.3.5 Thin Film Interference
                                                                                                                                                                                                                                                                                              • 9.4 Resolution
                                                                                                                                                                                                                                                                                                • 9.4.1 The Rayleigh Criterion
                                                                                                                                                                                                                                                                                                  • 9.4.2 Rayleigh Criterion Calculations
                                                                                                                                                                                                                                                                                                    • 9.4.3 Resolvance of Diffraction Gratings
                                                                                                                                                                                                                                                                                                    • 9.5 Doppler Effect
                                                                                                                                                                                                                                                                                                      • 9.5.1 The Doppler Effect
                                                                                                                                                                                                                                                                                                        • 9.5.2 Uses of The Doppler Effect
                                                                                                                                                                                                                                                                                                          • 9.5.3 The Doppler Equation
                                                                                                                                                                                                                                                                                                        • 10. Fields (HL only)
                                                                                                                                                                                                                                                                                                          • 10.1 Describing Fields
                                                                                                                                                                                                                                                                                                            • 10.1.1 Gravitational & Electrostatic Fields
                                                                                                                                                                                                                                                                                                              • 10.1.2 Gravitational & Electrostatic Field Lines
                                                                                                                                                                                                                                                                                                                • 10.1.3 Gravitational & Electrostatic Potential
                                                                                                                                                                                                                                                                                                                  • 10.1.4 Equipotential Surfaces
                                                                                                                                                                                                                                                                                                                  • 10.2 Fields at Work
                                                                                                                                                                                                                                                                                                                    • 10.2.1 Potential & Potential Energy
                                                                                                                                                                                                                                                                                                                      • 10.2.2 Potential Energy Calculations
                                                                                                                                                                                                                                                                                                                        • 10.2.3 Potential Gradient & Difference
                                                                                                                                                                                                                                                                                                                          • 10.2.4 Potential in a Charged Sphere
                                                                                                                                                                                                                                                                                                                            • 10.2.5 Escape Speed
                                                                                                                                                                                                                                                                                                                              • 10.2.6 Orbital Motion, Speed & Energy
                                                                                                                                                                                                                                                                                                                                • 10.2.7 Forces & Inverse-Square Law Behaviour
                                                                                                                                                                                                                                                                                                                                  • 10.2.8 Forces on Charges & Masses
                                                                                                                                                                                                                                                                                                                                • 11. Electromagnetic Induction (HL only)
                                                                                                                                                                                                                                                                                                                                  • 11.1 Electromagnetic Induction
                                                                                                                                                                                                                                                                                                                                    • 11.1.1 Emf, Magnetic Flux & Magnetic Flux Linkage
                                                                                                                                                                                                                                                                                                                                      • 11.1.2 Induced Emf
                                                                                                                                                                                                                                                                                                                                        • 11.1.3 Faraday’s Law
                                                                                                                                                                                                                                                                                                                                          • 11.1.4 Lenz’s Law
                                                                                                                                                                                                                                                                                                                                          • 11.2 Power Generation & Transmission
                                                                                                                                                                                                                                                                                                                                            • 11.2.1 AC Generators
                                                                                                                                                                                                                                                                                                                                              • 11.2.2 Root-Mean-Square Current & Voltage
                                                                                                                                                                                                                                                                                                                                                • 11.2.3 Step-Up & Step-Down Transformers
                                                                                                                                                                                                                                                                                                                                                  • 11.2.4 Transformer Calculations
                                                                                                                                                                                                                                                                                                                                                    • 11.2.5 AC Electrical Power Distribution
                                                                                                                                                                                                                                                                                                                                                      • 11.2.6 Diode Bridges
                                                                                                                                                                                                                                                                                                                                                        • 11.2.7 Investigating Diode Bridges
                                                                                                                                                                                                                                                                                                                                                          • 11.2.8 Rectification
                                                                                                                                                                                                                                                                                                                                                            • 11.2.9 Capacitors & Diode Bridges
                                                                                                                                                                                                                                                                                                                                                            • 11.3 Capacitance
                                                                                                                                                                                                                                                                                                                                                              • 11.3.1 Capacitance
                                                                                                                                                                                                                                                                                                                                                                • 11.3.2 Dielectric Materials
                                                                                                                                                                                                                                                                                                                                                                  • 11.3.3 Capacitors in Series & Parallel
                                                                                                                                                                                                                                                                                                                                                                    • 11.3.4 The Time Constant
                                                                                                                                                                                                                                                                                                                                                                      • 11.3.5 Energy Stored in a Capacitor
                                                                                                                                                                                                                                                                                                                                                                        • 11.3.6 Capacitor Charge & Discharge
                                                                                                                                                                                                                                                                                                                                                                          • 11.3.7 Discharge Calculations
                                                                                                                                                                                                                                                                                                                                                                        • 12. Quantum & Nuclear Physics (HL only)
                                                                                                                                                                                                                                                                                                                                                                          • 12.1 The Interaction of Matter with Radiation
                                                                                                                                                                                                                                                                                                                                                                            • 12.1.1 Photons
                                                                                                                                                                                                                                                                                                                                                                              • 12.1.2 The Photoelectric Effect
                                                                                                                                                                                                                                                                                                                                                                                • 12.1.3 Observing the Photoelectric Effect
                                                                                                                                                                                                                                                                                                                                                                                  • 12.1.4 Solving Photoelectric Problems
                                                                                                                                                                                                                                                                                                                                                                                    • 12.1.5 Matter Waves
                                                                                                                                                                                                                                                                                                                                                                                      • 12.1.6 Pair Production & Annihilation
                                                                                                                                                                                                                                                                                                                                                                                        • 12.1.7 Quantization of Angular Momentum
                                                                                                                                                                                                                                                                                                                                                                                          • 12.1.8 The Wave Function
                                                                                                                                                                                                                                                                                                                                                                                            • 12.1.9 The Uncertainty Principle
                                                                                                                                                                                                                                                                                                                                                                                              • 12.1.10 Tunnelling
                                                                                                                                                                                                                                                                                                                                                                                              • 12.2 Nuclear Physics
                                                                                                                                                                                                                                                                                                                                                                                                • 12.2.1 Rutherford Scattering & Nuclear Radius
                                                                                                                                                                                                                                                                                                                                                                                                  • 12.2.2 Nuclear Scattering
                                                                                                                                                                                                                                                                                                                                                                                                    • 12.2.3 Deviations from Rutherford Scattering
                                                                                                                                                                                                                                                                                                                                                                                                      • 12.2.4 Nuclear Energy Levels
                                                                                                                                                                                                                                                                                                                                                                                                        • 12.2.5 The Neutrino
                                                                                                                                                                                                                                                                                                                                                                                                          • 12.2.6 The Law of Radioactive Decay
                                                                                                                                                                                                                                                                                                                                                                                                            • 12.2.7 Measuring Half-Life
                                                                                                                                                                                                                                                                                                                                                                                                          Katie Moon

                                                                                                                                                                                                                                                                                                                                                                                                          Author: Katie

                                                                                                                                                                                                                                                                                                                                                                                                          Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.


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