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5.2.4Nuclear Physics

Half-Life — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

5 min read 9 parts Lesson 14 of 17 1 quiz

📚 Cambridge IGCSE Physics 0625 Hub / Topical Revision
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Curriculum Equation Key Radioactive Decay & Half-Life FormulasFast Exam Solution
N(t) = N₀ × (1/2)t / t½ | λ = ln(2) / t½ ≈ 0.693 / t½ | E = Δm × c²
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Lesson summary

5.2.4 Half-Life — IGCSE PHYSICS notes: Define half-life, determine it from a decay curve or table, correct for background and relate half-life to the choice of isotope.Half-life = the time taken for half the nuclei of an isotope in a sample to decay, or for the activity or count …

  • After n half-lives
  • Equal intervals
  • Long half-life
  • Short half-life
  • Corrected count
  • Constant — each isotope has its own fixed half-life

Part 1 of 7Half-life

Half-life
Half-life the time taken for half the nuclei of an isotope in a sample to decay, or for the activity or count rate to halve.
Constant
  • Constant each isotope has its own fixed half-life.
Range
  • Range from fractions of a second to billions of years.
Decay curve
  • Decay curve an exponential curve that never quite reaches zero.

Part 2 of 7Fraction remaining

Half-livesFraction remainingPercentage remaining
01100%
11/250%
21/425%
31/812.5%
41/166.25%
After n half-lives
  • After n half-lives the fraction remaining is (1/2)n.
Equal intervals
  • Equal intervals the activity falls from 100% to 50% in the same time as from 50% to 25%.

Part 3 of 7Using half-life

Using half-life
Find the fraction remaining: final amount divided by initial amount.
Match it to a whole number of half-lives.
Multiply the number of half-lives by the half-life to get the time.
  • Units
    • use the same unit for the elapsed time and the half-life.

Part 4 of 7Finding half-life from a graph (Extended)

1
Subtract background from every reading and plot the corrected count rate against time.
2
Draw a smooth best-fit curve.
3
Read the initial count rate C0 and mark half this value on the y-axis.
4
Read across to the curve and down to the time axis: this time is one half-life.
5
Repeat from another starting value and average.
  • Background
    • measure the background count with no sources, then subtract it from each reading to get the corrected count.

Part 5 of 7Half-life and the choice of isotope (Extended)

UseRadiationHalf-life
Medical tracerGammaShort, a few hours (technetium-99m about 6 h)
Smoke alarmAlphaLong (americium-241 about 430 years)
Thickness monitoringBetaLong, 10–20 years
Radiotherapy and sterilisingGammaAbout 5 years (cobalt-60)
Carbon datingBeta (carbon-14)About 5700 years

Part 6 of 7Half-life and hazard

Long half-life
  • Long half-life waste stays hazardous for a very long time and must be stored securely.
Short half-life
  • Short half-life a source decays quickly, is very active, but soon becomes safe.

Part 7 of 7More from the specification

More from the specification
Radiation monitoring in transverse magnetic fields
  • Radiation monitoring in transverse magnetic fields sweeping decay products through magnetic fields provides an experimental means to track half-life count rates.
Half-life
  • Half-life the time for half of the unstable nuclei in a sample to decay, or for the activity to fall to half.
Radioactive decay
  • Radioactive decay an unstable nucleus emits ionising radiation at random, and which nucleus decays next cannot be predicted.
Decay curve
  • Decay curve activity or count rate falls exponentially, so equal time intervals give equal fractional drops.
Nuclear particles
  • Nuclear particles the nucleus contains protons and neutrons, with the atomic number as the proton number and mass number as total nucleons.
Half-life
  • Half-life the time for half of the unstable nuclei in a sample to decay, or for the activity to fall to half.
Radioactive decay
  • Radioactive decay an unstable nucleus emits ionising radiation at random, and which nucleus decays next cannot be predicted.
Decay curve
  • Decay curve activity or count rate falls exponentially, so equal time intervals give equal fractional drops.
Nuclear particles
  • Nuclear particles the nucleus contains protons and neutrons, with the atomic number as the proton number and mass number as total nucleons.
Penetrating power
  • How far radiation travels through a material.
Ionising power
  • How strongly radiation ionises atoms.
Unstable nucleus
  • A nucleus with an imbalance of protons and neutrons that may decay.
Electric field
  • Region of space in which a charge experiences a force.
Magnetic field
  • Area around a magnet where its effects can be detected.
Decay equation
  • An equation in nuclide notation with balanced nucleon and proton numbers.
Kinetic energy
  • K = ½mv2, energy of motion.
Neutron
  • Neutral particle in the nucleus, relative mass 1.
Radioactive
  • Describes a nucleus that decays spontaneously and randomly.
Proton
  • Positive particle in the nucleus, relative charge +1 and relative mass 1.
Charge
  • Quantity of electricity in coulombs, Q = It.
    What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Detector
  • An instrument that records the particles produced in collisions.

Key terms

TermMeaning
Half-lifeTime for half the nuclei of an isotope to decay.
ActivityNumber of decays per second of a sample.
Decay curveGraph of activity or count rate against time.
Corrected countMeasured count minus background count.
TracerShort-lived radioactive isotope used in medicine.

Avoid these mistakes

1
Using the half-life as the total decay time — the sample never fully disappears.
2
Forgetting to subtract background before finding half-life.
3
Saying that after 3 half-lives 25% remains — it is 12.5%.
4
Using different time units for the elapsed time and the half-life.

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