Radioactive Decay

When an object is radioactive it releases radioactive particles but as time passes the rate of particles decreases. This is called decay.

Random decay

The decay of a radioactive substance is random and unpredictable.
To measure decay, we must look at the count rate over a long time to see if it decreases.

Probability

The probability that a given nucleus will decay in a given time is proportional to the number of nuclei. The equation for calculating the rate of decay is:
- The rate of decay of nuclei = decay constant x the number of nuclei
- $\frac{{\Delta}N}{{\Delta}t}=-{\lambda}N$
  - ${\lambda}$ is the decay constant.
  - $N$ is the number of nuclei.

The Exponential Law

The reduction in the rate of decay decreases according to an exponential pattern.

Exponential decay

From the equation for the rate of decay, we can find an exponential relationship between the number of nuclei and time.
The equation for the rate of decay of nuclei is:
- $\frac{{\Delta}N}{{\Delta}t}=-{\lambda}N$
The exponential relationship corresponding to this is:
- $N={N_0}e^{-{\lambda}t}$
  - ${N_0}$ is the initial number of nuclei.

Activity

The activity of a sample can be found by using the decay constant and the number of nuclei. The equation for activity is:
- Activity = decay constant x number of nuclei
- $A={\lambda}N$
The exponential relationship corresponding to the activity is:
- $A={A_0}e^{-{\lambda}t}$

Half-Life

Although each nuclear decay is random, with a large collection of nuclei, we can statistically predict how many will decay after a certain time.

Time taken to halve

Half-life, T_1/2, is the time taken:
- For the number of radioactive nuclei in a sample to halve.
- For the activity (the number of decays per second) to halve.

Activity

The activity of a sample is directly proportional to the number of nuclei remaining:
- Activity = decay constant, λ x number of nuclei remaining.
Activity is related to the half life:
- $λ =\frac{ \ln (2)}{T_{1/2}} = \frac{0.693}{T_{1/2}}$

Activity 2

By knowing the activity, we can infer how many nuclei are remaining.
Knowing the atomic mass of an isotope and the mass of a sample of isotope enables the number of nuclei and so the activity to be found.

Example

Find the half-life of a sample of plutonium-239, which has a mass of 1200 g and an activity of 2.8 × 10¹² Bq:
- Number of moles of Pu-239 = 1200 ÷ 239 = 5.021.
- Number of nuclei = number of moles × Avogadro’s constant = 3.02 × 10²⁴.
- λ = activity ÷ number of nuclei = 9.26 × 10^-13.
- So, half-life T_1/2 = ln(2) ÷ λ = 7.5 × 10¹⁰ s.

1Space, Time & Motion

1.1Motion

1.1.1Motion Basics

1.1.2Graphs of Motion

1.1.3Uniform Acceleration Equations

1.1.4Projectile Motion

1.1.5Bouncing Ball Example

1.2Forces

1.2.1Friction

1.2.2Terminal Speed

1.2.3Newton's Laws

1.2.4Exam-Style Question - Forces

1.2.5End of Topic Test - Newton's Third Law

1.3Momentum & Impulse

1.3.1Momentum

1.3.2Momentum 2

1.3.3End of Topic Test - Newton's Laws & Momentum

1.4Work, Energy & Power

1.4.1Work & Energy

1.4.2Conservation of Energy

1.4.3Power & Efficiency

1.4.4IB Multiple Choice- Work, Energy & Power

2The Particulate Nature of Matter

2.1Thermal Concepts

2.1.1Molecular Kinetic Theory Model

2.1.2Molecular Kinetic Theory Model 2

2.1.3Thermal Energy Transfer

2.1.4Thermal Energy Transfer Experiments

2.1.5Thermal Equilibrium

2.1.6Thermal Conductivity

2.1.7Heat Energy Transfer

2.2Modelling a Gas

2.2.1Ideal Gases

2.2.2Ideal Gases 2

2.2.3End of Topic Test - Thermal Energy & Ideal Gases

2.2.4Exam-Style Question - Ideal Gases

3Wave Behaviour

3.1Oscillations

3.1.1Progressive Waves

3.1.2Simple Harmonic Motion

3.2Travelling Waves

3.2.1Wave Speed & Phase Difference

3.2.2Longitudinal & Transverse Waves

3.2.3Electromagnetic Waves

3.2.4Electromagnetic Waves 2

3.2.5Sound Waves

3.3Wave Characteristics

3.3.1Polarisation

3.4Wave Behaviour

3.4.1Reflection & Absorption

3.4.2Reflection of Light

3.4.3Refraction

3.4.4Refractive index

3.5Standing Waves

3.5.1Standing Waves

3.5.2Standing Waves 2

3.5.3End of Topic Test - Standing Waves

3.5.4IB Multiple Choice - Waves

3.6Simple Harmonic Motion

3.6.1Simple Harmonic Motion

3.6.2Simple Harmonic Systems

3.6.3Energy in Simple Harmonic Motion

3.6.4End of Topic Test - Simple Harmonic Motion

3.6.5End of Topic Test - Simple Harmonic Motion

3.7Single Slit Diffraction

3.7.1Diffraction

3.8Interference

3.8.1Interference

3.8.2Interference 2

3.8.3Diffraction Gratings

3.8.4End of Topic Test - Diffraction

3.9Doppler Effect

3.9.1Doppler Effect

4Fields

4.1Circular Motion

4.1.1Circular Motion

4.1.2Centripetal Force

4.1.3IB Multiple Choice - Circular Motion

4.2Newton's Law of Gravitation

4.2.1Newton's Law

4.2.2Orbits of Planets & Satellites

4.2.3Escape Velocity & Synchronous Orbits

4.2.4End of Topic Test - Gravitational Fields

4.3Fields

4.3.1Fields

4.3.2Gravitational Field Strength

4.3.3Gravitational Potential

4.3.4Electric Field Strength

4.3.5Electrostatic & Gravitational Forces

4.3.6Electric Potential

4.3.7IB Multiple Choice - Gravitational Fields

4.4Fields at Work

4.4.1Radial Field Strength

4.4.2Orbits of Planets & Satellites

4.4.3Escape Velocity & Synchronous Orbits

4.4.4End of Topic Test - Gravitational Fields

4.4.5Uniform Electric Fields

4.4.6IB Multiple Choice - Electric Field & Potential

4.5Electric Fields

4.5.1Electric Charge

4.5.2Conservation of Charge

4.5.3Coulomb's Law

4.5.4Current

4.5.5Potential Difference

4.5.6IB Multiple Choice - Electric Charge

4.6Magnetic Effect of Electric Currents

4.6.1Magnetism

4.6.2Magnetic Field

4.6.3Magnetic Force

4.6.4Moving Charges in a Magnetic Field

4.6.5IB Multiple Choice - Magnetism

4.7Heating Effect of Currents

4.7.1Circuits

4.7.2Resistance

4.7.3Power and Conservation

4.7.4IB Multiple Choice - DC Circuits

4.8Electromagnetic Induction

4.8.1Electromagnetic Induction

4.8.2Electromagnetic Induction 2

4.8.3Magnetic Flux & Flux Linkage

4.8.4End of Topic Test - Electromagnetic Induction

4.9Power Generation & Transmission

4.9.1Alternating Currents

4.9.2Operation of a Transformer

4.10Capacitance

4.10.1Capacitance

4.10.2Parallel Plate Capacitor

4.10.3Energy Stored by a Capacitor

4.10.4Capacitor Discharge

4.10.5Capacitor Charge

4.10.6Magnetic Flux Density

4.10.7End of Topic Test - Capacitance & Flux Density

5Nuclear & Quantum Physics

5.1Discrete Energy & Radioactivity

5.1.1Atomic Spectra

5.1.2Atomic Structure

5.1.3Photons

5.1.4Discrete Energy Levels

5.1.5Alpha, Beta & Gamma Radiation

5.1.6Scientific Practices - Unstable Nuclei

5.1.7Radioactive Decay

5.1.8IB Multiple Choice - Atomic Physics

5.2Nuclear Reactions

5.2.1Mass & Energy

5.2.2Nuclear Fission

5.3The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons

5.3.2Particle Interactions

5.3.3Classification of Particles

5.3.4Wave-Particle Duality

5.3.5Wave Functions & Probability

5.3.6IB Multiple Choice - Quantum Physics

5.4Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay

5.4.2Nuclear Radius

5.4.3IB Multiple Choice - Nuclear Physics

6Measurements

6.1Measurements & Errors

6.1.1Fundamental Units

6.1.2SI Prefixes, Standard Form & Converting Units

6.1.3End of Topic Test - Units & Prefixes

6.2Uncertainties & Errors

6.2.1Limitation of Physical Measurements

6.2.2Uncertainty

6.2.3Estimation

6.2.4End of Topic Test - Measurements & Errors

6.3Vectors & Scalars

6.3.1Scalars & Vectors

6.3.2Vector Problems

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