14.2.12

Half Life

Test yourself on Half Life

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

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

Time taken to halve

  • Half-life, T1/2, 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

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:
    • λ=ln(2)T12\lambda =\frac{ln (2)}{T_\frac{1}{2}} = 0.69 ÷ T1/2
Activity 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

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 T1/2 = ln(2) ÷ λ = 7.5 × 1010 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

  • 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

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=A0e−λtA={A_0}e^{-{\lambda}t}

Graphical Method

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

Graphical method

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

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

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.
Jump to other topics
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Half Life

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    A radioactive sample initially weighs 4 g. After 2 half-lives, what is the mass of the radioactive sample?Multiple choice
  2. 2
    What do half-lives allow us to do?Multiple choice
  3. 3
    What equation can be used to calculate the age of an object?Multiple choice
  4. 4
    Which of the following statements are true:<br/><br/> A) Half-life is the time taken for half of the nuclei to decay.<br/> B) Half-life is the time taken for the count rate to halve.<br/>Multiple choice
  5. 5
    Finding half life using a graphPut in order
Answer all questions on Half Life

Unlock your full potential with Seneca Premium

  • Unlimited access to 10,000+ open-ended exam questions

  • Mini-mock exams based on your study history

  • Unlock 800+ premium courses & e-books

Get started with Seneca Premium

Radioactive Decay

End of Topic Test - Radioactivity