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
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
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-lives | Fraction remaining | Percentage remaining |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
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)
| Use | Radiation | Half-life |
|---|---|---|
| Medical tracer | Gamma | Short, a few hours (technetium-99m about 6 h) |
| Smoke alarm | Alpha | Long (americium-241 about 430 years) |
| Thickness monitoring | Beta | Long, 10–20 years |
| Radiotherapy and sterilising | Gamma | About 5 years (cobalt-60) |
| Carbon dating | Beta (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
| Term | Meaning |
|---|---|
| Half-life | Time for half the nuclei of an isotope to decay. |
| Activity | Number of decays per second of a sample. |
| Decay curve | Graph of activity or count rate against time. |
| Corrected count | Measured count minus background count. |
| Tracer | Short-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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