Source: https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-4-2-nuclear-radius

[Revision notes](https://senecalearning.com/en-gb/revision-notes.md) › [IB Diploma](https://senecalearning.com/en-gb/revision-notes/ib-diploma.md) › [Physics](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics.md) › [Physics: IB Diploma Higher Level](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level.md) › Nuclear Radius

# Nuclear Radius

Physics: IB Diploma Higher Level, topic 5.4.2

## Rutherford Scattering Experiment

Rutherford first determined the radius of the nucleus in his famous alpha particle scattering experiment. The answer he arrived at was quite a surprise.

### Change in energy

![Change in energy](https://image-v2.cdn.app.senecalearning.com/courseImages/chemistry/10.3.1%20Using%20materials/gold-295936_640-min.jpg)

- The alpha particles in Rutherford’s experiment had a kinetic energy of 5.3 MeV.
- The gold nucleus in the experiment does work on the alpha particle to slow it down. Eventually, the alpha particle has zero kinetic energy (KE) and then is repelled.

### Distance of closest approach

![Distance of closest approach](https://image-v2.cdn.app.senecalearning.com/courseImages/chemistry/1.1.2%20-%20Model%20of%20the%20atom/atom-1674878_640-min%20-%20Edited.jpg)

- The closest point of approach is where the KE lost = electrostatic potential energy gained.
- The formula for electrostatic potential energy is:
 - PE $$ = \frac{Qq}{4\pi \epsilon_0r}$$ where r is the distance of separation of charges Q and q.

### Distance of closest approach 2

![Distance of closest approach 2](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/5.1.1.1a%20-%20Nucleus%20structure,%20protons,%20neutrons-min.png)

- So:
 - $$(5.3 \times 10^6) \times (1.6 \times 10^{-19}) = \frac{(79 \times 1.6 \times 10^{-19})(2 \times 1.6 \times 10^{-19})}{4\pi \epsilon_0 r}$$
- Which gives:
 - $$ r = \frac{79 \times 2 \times (1.6 \times 10^{-19})}{(5.3 \times 10^6) \times (4\pi \epsilon_0)} = 4.3 \times 10^{-14}$$ m
- This is an over-estimate for the radius of the nucleus. Rutherford was convinced that the alpha particles had not come into contact with the gold nucleus.

## Electron Diffraction Experiment

Electron diffraction experiments are an alternative method of finding the radius of the nucleus.

### De Broglie wavelength

![De Broglie wavelength](https://image-v2.cdn.app.senecalearning.com/2018-10/19fa8018-14c0-4ffa-966a-b53624838b3b/electron-diffraction-intensity-graph.png)

- The electron can behave like a wave, with de Broglie wavelength given by:
 - $$\lambda =\frac{h}{p}$$ 
    - Where h is the Planck constant and p is the momentum of the electron.
- The de Broglie wavelength is a wavelength associated with matter based on its mass and momentum.

### Intensity of electrons

![Intensity of electrons](https://image-v2.cdn.app.senecalearning.com/2018-10/19fa8018-14c0-4ffa-966a-b53624838b3b/electron-diffraction-intensity-graph.png)

- The graph of intensity of diffracted electrons against diffraction angle is shown here.

### Explanation of graph

![Explanation of graph](https://image-v2.cdn.app.senecalearning.com/2018-10/19fa8018-14c0-4ffa-966a-b53624838b3b/electron-diffraction-intensity-graph.png)

- The angle θ, where the intensity is a minimum, can be explained by assuming that the electrons have diffracted around a spherical object (i.e. the nucleus).
- The diameter of the nucleus, d,  can be found using the equation:
 - $$\sin \theta = 1.22 \frac{\lambda}{d}$$

## Liquid Drop Model of the Nucleus

We assume the nucleus is of constant density and spherical in the liquid drop model.

### Principle

![Principle](https://image-v2.cdn.app.senecalearning.com/courseImages/chemistry/10.4.1%20The%20Haber%20process/drops-2087006_640-min.jpg)

- The liquid drop model of the nucleus means that the volume of the nucleus is directly proportional to the number of nucleons present in that nucleus and that the nucleus is spherical.
- $$V = kA = \frac43 \pi r^3$$
- Where r is the radius of the nucleus with mass number A and volume V.

### Radius

![Radius](https://image-v2.cdn.app.senecalearning.com/courseImages/chemistry/1.1.2%20-%20Model%20of%20the%20atom/(s)%201.1.3.2%20-%20atomic%20structure-min%20(1).png)

- Using the previous equation:
 - $$r = \sqrt[3]{\frac{3kA}{4\pi}}$$
- Or more conveniently:
 - $$r=r_0A^{1/3}$$
 - Where r0 is the radius of the proton.

### Validity of model

![Validity of model](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/OCR%20Gateway/atom%20arrangement.jpg)

- The idea on the previous slide and the subsequent experimental confirmation is evidence that the liquid drop model is correct. 
- The consequence of this is that nuclear material has a constant density.

## Test yourself on Nuclear Radius

- Which of these statements is true at the distance of closest approach?
- What is the equation for the De Broglie wavelength?
- What is the equation for the angle of diffraction?
- What can we conclude from the liquid drop model of the nucleus?
- According to the liquid drop model, the volume of a nucleus is proportional to what?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/d1080336-c86a-41e9-bd82-37d8d6e9f104/section/85b56755-e644-4600-b952-efcbce63dd7e/session)

- Previous topic: [5.4.1 Nuclear Instability & Radioactive Decay](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-4-1-nuclear-instability-and-radioactive-decay.md)
- Next topic: [5.4.3 IB Multiple Choice - Nuclear Physics](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-4-3-ib-multiple-choice-nuclear-physics.md)

## Physics: IB Diploma Higher Level contents

### 1 Space, Time & Motion
- 1.1 Motion
  - [1.1.1 Motion Basics](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-1-1-motion-basics.md)
  - [1.1.2 Graphs of Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-1-2-graphs-of-motion.md)
  - [1.1.3 Uniform Acceleration Equations](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-1-3-uniform-acceleration-equations.md)
  - [1.1.4 Projectile Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-1-4-projectile-motion.md)
  - [1.1.5 Bouncing Ball Example](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-1-5-bouncing-ball-example.md)
- 1.2 Forces
  - [1.2.1 Friction](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-2-1-friction.md)
  - [1.2.2 Terminal Speed](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-2-2-terminal-speed.md)
  - [1.2.3 Newton's Laws](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-2-3-newtons-laws.md)
  - [1.2.4 Exam-Style Question - Forces](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-2-4-exam-style-question-forces.md)
  - [1.2.5 End of Topic Test - Newton's Third Law](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-2-5-end-of-topic-test-newtons-third-law.md)
- 1.3 Momentum & Impulse
  - [1.3.1 Momentum](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-3-1-momentum.md)
  - [1.3.2 Momentum 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-3-2-momentum-2.md)
  - [1.3.3 End of Topic Test - Newton's Laws & Momentum](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-3-3-end-of-topic-test-newtons-laws-and-momentum.md)
- 1.4 Work, Energy & Power
  - [1.4.1 Work & Energy](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-4-1-work-and-energy.md)
  - [1.4.2 Conservation of Energy](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-4-2-conservation-of-energy.md)
  - [1.4.3 Power & Efficiency](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-4-3-power-and-efficiency.md)
  - [1.4.4 IB Multiple Choice- Work, Energy & Power](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/1-4-4-ib-multiple-choice-work-energy-and-power.md)

### 2 The Particulate Nature of Matter
- 2.1 Thermal Concepts
  - [2.1.1 Molecular Kinetic Theory Model](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-1-molecular-kinetic-theory-model.md)
  - [2.1.2 Molecular Kinetic Theory Model 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-2-molecular-kinetic-theory-model-2.md)
  - [2.1.3 Thermal Energy Transfer](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-3-thermal-energy-transfer.md)
  - [2.1.4 Thermal Energy Transfer Experiments](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-4-thermal-energy-transfer-experiments.md)
  - [2.1.5 Thermal Equilibrium](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-5-thermal-equilibrium.md)
  - [2.1.6 Thermal Conductivity](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-6-thermal-conductivity.md)
  - [2.1.7 Heat Energy Transfer](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-1-7-heat-energy-transfer.md)
- 2.2 Modelling a Gas
  - [2.2.1 Ideal Gases](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-2-1-ideal-gases.md)
  - [2.2.2 Ideal Gases 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-2-2-ideal-gases-2.md)
  - [2.2.3 End of Topic Test - Thermal Energy & Ideal Gases](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-2-3-end-of-topic-test-thermal-energy-and-ideal-gases.md)
  - [2.2.4 Exam-Style Question - Ideal Gases](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/2-2-4-exam-style-question-ideal-gases.md)

### 3 Wave Behaviour
- 3.1 Oscillations
  - [3.1.1 Progressive Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-1-1-progressive-waves.md)
  - [3.1.2 Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-1-2-simple-harmonic-motion.md)
- 3.2 Travelling Waves
  - [3.2.1 Wave Speed & Phase Difference](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-2-1-wave-speed-and-phase-difference.md)
  - [3.2.2 Longitudinal & Transverse Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-2-2-longitudinal-and-transverse-waves.md)
  - [3.2.3 Electromagnetic Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-2-3-electromagnetic-waves.md)
  - [3.2.4 Electromagnetic Waves 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-2-4-electromagnetic-waves-2.md)
  - [3.2.5 Sound Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-2-5-sound-waves.md)
- 3.3 Wave Characteristics
  - [3.3.1 Polarisation](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-3-1-polarisation.md)
- 3.4 Wave Behaviour
  - [3.4.1 Reflection & Absorption](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-4-1-reflection-and-absorption.md)
  - [3.4.2 Reflection of Light](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-4-2-reflection-of-light.md)
  - [3.4.3 Refraction](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-4-3-refraction.md)
  - [3.4.4 Refractive index](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-4-4-refractive-index.md)
- 3.5 Standing Waves
  - [3.5.1 Standing Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-5-1-standing-waves.md)
  - [3.5.2 Standing Waves 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-5-2-standing-waves-2.md)
  - [3.5.3 End of Topic Test - Standing Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-5-3-end-of-topic-test-standing-waves.md)
  - [3.5.4 IB Multiple Choice - Waves](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-5-4-ib-multiple-choice-waves.md)
- 3.6 Simple Harmonic Motion
  - [3.6.1 Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-6-1-simple-harmonic-motion.md)
  - [3.6.2 Simple Harmonic Systems](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-6-2-simple-harmonic-systems.md)
  - [3.6.3 Energy in Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-6-3-energy-in-simple-harmonic-motion.md)
  - [3.6.4 End of Topic Test - Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-6-4-end-of-topic-test-simple-harmonic-motion.md)
  - [3.6.5 End of Topic Test - Simple Harmonic Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-6-5-end-of-topic-test-simple-harmonic-motion.md)
- 3.7 Single Slit Diffraction
  - [3.7.1 Diffraction](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-7-1-diffraction.md)
- 3.8 Interference
  - [3.8.1 Interference](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-8-1-interference.md)
  - [3.8.2 Interference 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-8-2-interference-2.md)
  - [3.8.3 Diffraction Gratings](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-8-3-diffraction-gratings.md)
  - [3.8.4 End of Topic Test - Diffraction](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-8-4-end-of-topic-test-diffraction.md)
- 3.9 Doppler Effect
  - [3.9.1 Doppler Effect](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/3-9-1-doppler-effect.md)

### 4 Fields
- 4.1 Circular Motion
  - [4.1.1 Circular Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-1-1-circular-motion.md)
  - [4.1.2 Centripetal Force](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-1-2-centripetal-force.md)
  - [4.1.3 IB Multiple Choice - Circular Motion](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-1-3-ib-multiple-choice-circular-motion.md)
- 4.2 Newton's Law of Gravitation
  - [4.2.1 Newton's Law](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-2-1-newtons-law.md)
  - [4.2.2 Orbits of Planets & Satellites](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-2-2-orbits-of-planets-and-satellites.md)
  - [4.2.3 Escape Velocity & Synchronous Orbits](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-2-3-escape-velocity-and-synchronous-orbits.md)
  - [4.2.4 End of Topic Test - Gravitational Fields](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-2-4-end-of-topic-test-gravitational-fields.md)
- 4.3 Fields
  - [4.3.1 Fields](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-1-fields.md)
  - [4.3.2 Gravitational Field Strength](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-2-gravitational-field-strength.md)
  - [4.3.3 Gravitational Potential](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-3-gravitational-potential.md)
  - [4.3.4 Electric Field Strength](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-4-electric-field-strength.md)
  - [4.3.5 Electrostatic & Gravitational Forces](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-5-electrostatic-and-gravitational-forces.md)
  - [4.3.6 Electric Potential](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-6-electric-potential.md)
  - [4.3.7 IB Multiple Choice - Gravitational Fields](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-3-7-ib-multiple-choice-gravitational-fields.md)
- 4.4 Fields at Work
  - [4.4.1 Radial Field Strength](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-4-1-radial-field-strength.md)
  - [4.4.2 Orbits of Planets & Satellites](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-4-2-orbits-of-planets-and-satellites.md)
  - [4.4.3 Escape Velocity & Synchronous Orbits](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-4-3-escape-velocity-and-synchronous-orbits.md)
  - [4.4.4 End of Topic Test - Gravitational Fields](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-4-4-end-of-topic-test-gravitational-fields.md)
  - [4.4.5 Uniform Electric Fields](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-4-5-uniform-electric-fields.md)
  - [4.4.6 IB Multiple Choice - Electric Field & Potential](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-4-6-ib-multiple-choice-electric-field-and-potential.md)
- 4.5 Electric Fields
  - [4.5.1 Electric Charge](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-5-1-electric-charge.md)
  - [4.5.2 Conservation of Charge](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-5-2-conservation-of-charge.md)
  - [4.5.3 Coulomb's Law](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-5-3-coulombs-law.md)
  - [4.5.4 Current](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-5-4-current.md)
  - [4.5.5 Potential Difference](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-5-5-potential-difference.md)
  - [4.5.6 IB Multiple Choice - Electric Charge](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-5-6-ib-multiple-choice-electric-charge.md)
- 4.6 Magnetic Effect of Electric Currents
  - [4.6.1 Magnetism](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-6-1-magnetism.md)
  - [4.6.2 Magnetic Field](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-6-2-magnetic-field.md)
  - [4.6.3 Magnetic Force](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-6-3-magnetic-force.md)
  - [4.6.4 Moving Charges in a Magnetic Field](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-6-4-moving-charges-in-a-magnetic-field.md)
  - [4.6.5 IB Multiple Choice - Magnetism](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-6-5-ib-multiple-choice-magnetism.md)
- 4.7 Heating Effect of Currents
  - [4.7.1 Circuits](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-7-1-circuits.md)
  - [4.7.2 Resistance](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-7-2-resistance.md)
  - [4.7.3 Power and Conservation](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-7-3-power-and-conservation.md)
  - [4.7.4 IB Multiple Choice - DC Circuits](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-7-4-ib-multiple-choice-dc-circuits.md)
- 4.8 Electromagnetic Induction
  - [4.8.1 Electromagnetic Induction](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-8-1-electromagnetic-induction.md)
  - [4.8.2 Electromagnetic Induction 2](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-8-2-electromagnetic-induction-2.md)
  - [4.8.3 Magnetic Flux & Flux Linkage](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-8-3-magnetic-flux-and-flux-linkage.md)
  - [4.8.4 End of Topic Test - Electromagnetic Induction](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-8-4-end-of-topic-test-electromagnetic-induction.md)
- 4.9 Power Generation & Transmission
  - [4.9.1 Alternating Currents](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-9-1-alternating-currents.md)
  - [4.9.2 Operation of a Transformer](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-9-2-operation-of-a-transformer.md)
- 4.10 Capacitance
  - [4.10.1 Capacitance](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-1-capacitance.md)
  - [4.10.2 Parallel Plate Capacitor](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-2-parallel-plate-capacitor.md)
  - [4.10.3 Energy Stored by a Capacitor](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-3-energy-stored-by-a-capacitor.md)
  - [4.10.4 Capacitor Discharge](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-4-capacitor-discharge.md)
  - [4.10.5 Capacitor Charge](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-5-capacitor-charge.md)
  - [4.10.6 Magnetic Flux Density](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-6-magnetic-flux-density.md)
  - [4.10.7 End of Topic Test - Capacitance & Flux Density](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/4-10-7-end-of-topic-test-capacitance-and-flux-density.md)

### 5 Nuclear & Quantum Physics
- 5.1 Discrete Energy & Radioactivity
  - [5.1.1 Atomic Spectra](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-1-atomic-spectra.md)
  - [5.1.2 Atomic Structure](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-2-atomic-structure.md)
  - [5.1.3 Photons](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-3-photons.md)
  - [5.1.4 Discrete Energy Levels](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-4-discrete-energy-levels.md)
  - [5.1.5 Alpha, Beta & Gamma Radiation](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-5-alpha-beta-and-gamma-radiation.md)
  - [5.1.6 Scientific Practices - Unstable Nuclei](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-6-scientific-practices-unstable-nuclei.md)
  - [5.1.7 Radioactive Decay](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-7-radioactive-decay.md)
  - [5.1.8 IB Multiple Choice - Atomic Physics](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-1-8-ib-multiple-choice-atomic-physics.md)
- 5.2 Nuclear Reactions
  - [5.2.1 Mass & Energy](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-2-1-mass-and-energy.md)
  - [5.2.2 Nuclear Fission](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-2-2-nuclear-fission.md)
- 5.3 The Interaction of Matter with Radiation
  - [5.3.1 Particles, Antiparticles & Photons](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-3-1-particles-antiparticles-and-photons.md)
  - [5.3.2 Particle Interactions](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-3-2-particle-interactions.md)
  - [5.3.3 Classification of Particles](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-3-3-classification-of-particles.md)
  - [5.3.4 Wave-Particle Duality](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-3-4-wave-particle-duality.md)
  - [5.3.5 Wave Functions & Probability](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-3-5-wave-functions-and-probability.md)
  - [5.3.6 IB Multiple Choice - Quantum Physics](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-3-6-ib-multiple-choice-quantum-physics.md)
- 5.4 Nuclear Physics
  - [5.4.1 Nuclear Instability & Radioactive Decay](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-4-1-nuclear-instability-and-radioactive-decay.md)
  - [5.4.2 Nuclear Radius](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-4-2-nuclear-radius.md)
  - [5.4.3 IB Multiple Choice - Nuclear Physics](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/5-4-3-ib-multiple-choice-nuclear-physics.md)

### 6 Measurements
- 6.1 Measurements & Errors
  - [6.1.1 Fundamental Units](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-1-1-fundamental-units.md)
  - [6.1.2 SI Prefixes, Standard Form & Converting Units](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-1-2-si-prefixes-standard-form-and-converting-units.md)
  - [6.1.3 End of Topic Test - Units & Prefixes](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-1-3-end-of-topic-test-units-and-prefixes.md)
- 6.2 Uncertainties & Errors
  - [6.2.1 Limitation of Physical Measurements](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-2-1-limitation-of-physical-measurements.md)
  - [6.2.2 Uncertainty](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-2-2-uncertainty.md)
  - [6.2.3 Estimation](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-2-3-estimation.md)
  - [6.2.4 End of Topic Test - Measurements & Errors](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-2-4-end-of-topic-test-measurements-and-errors.md)
- 6.3 Vectors & Scalars
  - [6.3.1 Scalars & Vectors](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-3-1-scalars-and-vectors.md)
  - [6.3.2 Vector Problems](https://senecalearning.com/en-gb/revision-notes/ib-diploma/physics/physics-ib-diploma-higher-level/6-3-2-vector-problems.md)