Half Life

Half-Life

Although each nuclear decay is random, with a large collection of nuclei, we can statistically predict how many will decay in 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 half-life:
- $\lambda =\frac{ln (2)}{T_\frac{1}{2}}$ = 0.69 ÷ 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 × 10¹¹ s.

Half-Life

The half-life of a sample is the time taken for the number of radioactive counts to fall to half the initial value.

Half-life

Half-life is the time taken for half of the sample to decay.
This is the same as saying the time taken for the count rate to halve.
Knowing the half-life of a substance and the number of nuclei it has means we can find its age.

Uses of half-life

We can find the age of a material by considering the count rate of the material.
By knowing the original count rate, the current count rate, and the half-life of the material - we can use the following equation to calculate the time passed:
- $A={A_0}e^{-{\lambda}t}$

Graphical Method

Half life can be found in many ways, the easiest is to use a graph.

Graphical method

Firstly plot a graph of count rate or number of atoms against time.
The plot should show exponential decay.
Look for the initial count rate / number of atoms (the y-intercept).

Graphical method 2

Divide the initial count rate or number of atoms by two, this is the half count rate, or half the initial number of atoms.
Draw a line across from the half count rate to the decay curve.
Draw a line down to the time axis (x axis) and read off the time. This is the half-life.

Graphical method 3

Each half-life will be the same length.
So it will take two half-lives for the sample to decay to a quarter of the initial count, or a quarter of the initial atoms.

1Measurements & Errors

1.1Measurements & Errors

1.1.1Use of SI Units

1.1.2SI Prefixes, Standard Form & Converting Units

1.1.3End of Topic Test - Units & Prefixes

1.1.4Limitation of Physical Measurements

1.1.5Uncertainty

1.1.6Estimation

1.1.7End of Topic Test - Measurements & Errors

2Particles & Radiation

2.1Particles

2.1.1Atomic Model

2.1.2Specific Charge, Protons & Neutron Numbers

2.1.3End of Topic Test - Atomic Model

2.1.4Isotopes

2.1.5Stable & Unstable Nuclei

2.1.6End of Topic Test - Isotopes & Nuclei

2.1.7A-A* (AO3/4) - Stable & Unstable Nuclei

2.1.8Particles, Antiparticles & Photons

2.1.9Particle Interactions

2.1.10Classification of Particles

2.1.11End of Topic Test - Particles & Interactions

2.1.12Quarks & Antiquarks

2.1.13Application of Conservation Laws

2.1.14End of Topic Test - Leptons & Quarks

2.1.15Exam-Style Question - Radioactive Decay

2.2Electromagnetic Radiation & Quantum Phenomena

2.2.1The Photoelectric Effect

2.2.2The Photoelectric Effect Explanation

2.2.3End of Topic Test - The Photoelectric Effect

2.2.4Collisions of Electrons with Atoms

2.2.5Energy Levels & Photon Emission

2.2.6Wave-Particle Duality

2.2.7End of Topic Test - Absorption & Emission

3Waves

3.1Progressive & Stationary Waves

3.1.1Progressive Waves

3.1.2Wave Speed & Phase Difference

3.1.3Longitudinal & Transverse Waves

3.1.4End of Topic Test - Progressive Waves

3.1.5Polarisation

3.1.6Stationary Waves

3.1.7Stationary Waves 2

3.1.8End of Topic Test - Polarisation & Stationary Wave

3.1.9A-A* (AO3/4) - Stationary Waves

3.2Refraction, Diffraction & Interference

3.2.1Interference

3.2.2Interference 2

3.2.3End of Topic Test - Interference

3.2.4Diffraction

3.2.5Diffraction Gratings

3.2.6End of Topic Test - Diffraction

3.2.7Refraction at a Plane Surface

3.2.8Internal Reflection & Fibre Optics

3.2.9End of Topic Test - Refraction

3.2.10Exam-Style Question - Waves

4Mechanics & Materials

4.1Force, Energy & Momentum

4.2Materials

4.2.1Density

4.2.2Bulk Properties of Solids

4.2.3Energy in Materials

4.2.4Young Modulus

4.2.5End of Topic Test - Materials

5Electricity

5.1Current Electricity

5.1.1Basics of Electricity

5.1.2Current-Voltage Characteristics

5.1.3End of Topic Test - Basics of Electricity

5.1.4Resistivity

5.1.5Superconductivity

5.1.6A-A* (AO3/4) - Superconductivity

5.1.7End of Topic Test - Resistivity & Superconductors

5.1.8Circuits

5.1.9Power and Conservation

5.1.10Potential Divider

5.1.11Emf & Internal Resistance

5.1.12End of Topic Test - Power & Potential

5.1.13Exam-Style Question - Resistance

6Further Mechanics & Thermal Physics (A2 only)

6.1Periodic Motion (A2 only)

6.1.1Circular Motion

6.1.2Circular Motion 2

6.1.3End of Topic Test - Circular Motion

6.1.4Simple Harmonic Motion

6.1.5Simple Harmonic Systems

6.1.6Energy in Simple Harmonic Motion

6.1.7Resonance

6.1.8End of Topic Test - Simple Harmonic Motion

6.1.9A-A* (AO3/4) - Simple Harmonic Motion

6.2Thermal Physics (A2 only)

6.2.1Thermal Energy Transfer

6.2.2Thermal Energy Transfer Experiments

6.2.3Ideal Gases

6.2.4Ideal Gases 2

6.2.5Boyle's Law & Charles' Law

6.2.6Molecular Kinetic Theory Model

6.2.7Molecular Kinetic Theory Model 2

6.2.8End of Topic Test - Thermal Energy & Ideal Gases

6.2.9Exam-Style Question - Ideal Gases

7Fields & Their Consequences (A2 only)

7.1Fields (A2 only)

7.1.1Fields

7.2Gravitational Fields (A2 only)

7.2.1Newton's Law

7.2.2Gravitational Field Strength

7.2.3Gravitational Potential

7.2.4Orbits of Planets & Satellites

7.2.5Escape Velocity & Synchronous Orbits

7.2.6End of Topic Test - Gravitational Fields

7.3Electric Fields (A2 only)

7.3.1Coulomb's Law

7.3.2Electric Field Strength

7.3.3Electric Field Strength 2

7.3.4Electric Potential

7.3.5End of Topic Test - Electric Fields

7.3.6A-A* (AO3/4) - Electric and Gravitational Field

7.4Capacitance (A2 only)

7.4.1Capacitance

7.4.2Parallel Plate Capacitor

7.4.3Energy Stored by a Capacitor

7.4.4Capacitor Discharge

7.4.5Capacitor Charge

7.5Magnetic Fields (A2 only)

7.5.1Magnetic Flux Density

7.5.2End of Topic Test - Capacitance & Flux Density

7.5.3Moving Charges in a Magnetic Field

7.5.4Magnetic Flux & Flux Linkage

7.5.5Electromagnetic Induction

7.5.6Electromagnetic Induction 2

7.5.7Alternating Currents

7.5.8Operation of a Transformer

7.5.9Magnetic Flux Density

7.5.10End of Topic Test - Electromagnetic Induction

8Nuclear Physics (A2 only)

8.1Radioactivity (A2 only)

8.1.1Rutherford Scattering

8.1.2Alpha & Beta Radiation

8.1.3Gamma Radiation

8.1.4Radioactive Decay

8.1.5Half Life

8.1.6End of Topic Test - Radioactivity

8.1.7Nuclear Instability

8.1.8Nuclear Radius

8.1.9Mass & Energy

8.1.10Binding Energy

8.1.11Induced Fission

8.1.12Safety Aspects of Nuclear Reactors

8.1.13End of Topic Test - Nuclear Physics

8.1.14A-A* (AO3/4) - Nuclear Fusion

9Option: Astrophysics (A2 only)

9.1Telescopes (A2 only)

9.1.1Astronomical Telescopes

9.1.2Reflecting Telescopes

9.1.3Single Dish Radio Telescopes

9.1.4Large Diameter Telescopes

9.2Classification of Stars (A2 only)

9.2.1Classification by Luminosity

9.2.2Absolute Magnitude

9.2.3Black Body Radiation

9.2.4Stellar Spectral Classes

9.2.5Hertzsprung-Russell Diagrams

9.2.6Astronomical Objects

9.3Cosmology (A2 only)

9.3.1Doppler Effect

9.3.2Hubble's Law

9.3.3Quasars

9.3.4Detecting Exoplanets

10Option: Medical Physics (A2 only)

10.1Physics of the Eye (A2 only)

10.1.1Physics of Vision

10.1.2Defects of Vision

10.1.3Lenses

10.1.4Correcting Defects of Vision

10.2Physics of the Ear (A2 only)

10.2.1Structure of the Ear

10.2.2Sensitivity of the Ear

10.2.3Hearing Defects

10.3Biological Measurement (A2 only)

10.3.1Electrocardiography (ECG)

10.4Non-Ionising Imaging (A2 only)

10.4.1Ultrasound Imaging

10.4.2Ultrasound Imaging 2

10.4.3Fibre Optics & Endoscopy

10.4.4Magnetic Resonance Scanning

10.5X-Ray Imaging (A2 only)

10.5.1Diagnostic X-Rays

10.5.2X-Ray Image Processing

10.5.3Absorption of X-Rays

10.5.4CT Scanners

10.6Radionuclide Imaging & Therapy (A2 only)

10.6.1Imaging Techniques

10.6.2Half Life

10.6.3Gamma Camera

10.6.4High Energy X-Rays

10.6.5Radioactive Implants

10.6.6Imaging Comparisons

11Option: Engineering Physics (A2 only)

11.1Rotational Dynamics (A2 only)

11.1.1Moment of Inertia

11.1.2Rotational Kinetic Energy

11.1.3Rotational Motion

11.1.4Torque & Angular Acceleration

11.1.5Angular Momentum

11.1.6Angular Work & Power

11.2Thermodynamics & Engines (A2 only)

11.2.1First Law of Thermodynamics

11.2.2Non-Flow Processes

11.2.3p-V Diagrams

11.2.4Engine Cycles

11.2.5Second Law & Engines

11.2.6Reversed Heat Engines

12Option: Turning Points in Physics (A2 only)

12.1Discovery of the Electron (A2 only)

12.1.1Cathode Rays

12.1.2Thermionic Electron Emission

12.1.3Electron Specific Charge

12.1.4Millikan's Experiment

12.2Wave-Particle Duality (A2 only)

12.2.1Newton's & Huygen's Theories of Light

12.2.2Electromagnetic Waves

12.2.3Photoelectricity

12.2.4Wave-Particle Duality

12.2.5Electron Microscopes

12.3Special Relativity (A2 only)

12.3.1Michelson-Morley Experiment

12.3.2Einstein's Theory of Special Relativity

12.3.3Time Dilation

12.3.4Length Contraction

12.3.5Mass & Energy

Jump to other topics