Key term
CCEA A-Level Physics 1210
Physical Quantities, Scalars and Vectors
Moments and Equilibrium
Linear Motion and Dynamics
Newton's Laws of Motion
Linear Momentum and Impulse
Work, Energy and Power
Current, Charge and Potential Difference
Resistance and Resistivity
Topic overviewResistance and Ohm's lawOhmic and non-ohmic behaviourResistors in series and in parallelInvestigating current, voltage and resistance in series and parallel circuitsElectrical power and energy in resistive circuitsResistivity and the equation R = ρl/AMeasuring the resistivity of a metalCurrent–voltage characteristics of a conductor, a lamp and a diodeResistance, temperature and superconductivity
Internal Resistance and Potential Dividers
Topic overviewInternal resistance and terminal potential differenceConsequences of internal resistance for external circuitsMeasuring electromotive force and internal resistanceThe potential divider and variable outputPotential dividers in lighting and heating control circuitsLoaded potential dividers and output voltage calculations
Waves
Refraction
Lenses
Superposition, Interference and Diffraction
Topic overviewSuperposition of wavesStanding waves, nodes and antinodesStanding waves on stretched stringsStanding waves in a pipe closed at one endMeasuring the speed of sound with a resonance tubeConditions for observable interferencePath difference and phase differenceYoung's double slitDiffraction at a single slitThe diffraction grating
Quantum Physics
Wave-Particle Duality
Astronomy
Practical Skills and Data Analysis
Topic overviewChoosing and using measuring instrumentsPrecision, accuracy and recording measurementsUsing the cathode ray oscilloscope to measure voltage and frequencyTables, graphs and presenting resultsLinearising a relationship and using the gradientAbsolute and percentage uncertaintyCombining uncertainties and uncertainty on a graphRandom and systematic error, reliability and refining an experiment
Deformation of Solids
Thermal Physics
Topic overviewBoyle's law, Charles's law and the pressure lawThe ideal gas equation pV = nRTThe Avogadro constant, the mole and pV = NkTInternal energy and the distribution of molecular energyThe kinetic theory equation pV = ⅓Nm⟨c²⟩Average molecular kinetic energy and temperatureAbsolute zero and the kelvin scaleSpecific heat capacity and the electrical method
Uniform Circular Motion
Simple Harmonic Motion
Topic overviewDefining simple harmonic motion and a = −ω²xDisplacement, velocity and acceleration: x = A cos ωtThe simple pendulum and T = 2π√(l/g)The loaded spiral spring and T = 2π√(m/k)SHM graphs and finding velocity from a gradientFree vibrations, forced vibrations and resonanceDamping: light, critical and over-damping
The Nucleus and Radioactive Decay
Topic overviewAlpha-particle scattering and the nuclear atomNuclear radius and nucleon numberThe density of nuclear matterAlpha, beta and gamma radiation: nature, penetration and rangeNuclear equations and changes in nucleon and proton numberThe random and exponential nature of radioactive decayActivity, the decay constant and A = −λNExponential decay calculations with A = A₀e^(−λt)Half-life and measuring it
Nuclear Energy, Fission and Fusion
Gravitational Fields
Electric Fields
Capacitors
Magnetic Fields
Charged Particles and Accelerators
The Nucleus and Radioactive Decay
Half-life and measuring it
- 3 things to know
- Unit A2 1
Overview
Recall questions on the definition of half-life, the relation t½ = ln2/λ and conversions both ways, worked calculations of the fraction remaining after several half-lives, measuring a short half-life from a decay curve, correcting for background count rate, and why the measurement is a statistical one.
What you need to know
Answer each one before you reveal it.
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Key term
Describe how the half-life of a source of a few minutes' half-life can be measured.
Key term
How is the half-life obtained more reliably from a logarithmic graph of the decay data?
Questions from this subtopic
Each one with the model answer underneath.
- 1
Define half-life.
Model answer
The half-life of a radioactive nuclide is the average time taken for half of the undecayed nuclei in a sample to decay, which is also the time for its activity to fall to half its value.
- 2
State the equation relating half-life to the decay constant and define every symbol.
Model answer
t½ = ln2/λ, where t½ is the half-life in seconds and λ is the decay constant in s⁻¹, with ln2 = 0.693.
- 3
A nuclide has a decay constant of 2.5 × 10⁻³ s⁻¹. Calculate its half-life.
Model answer
t½ = ln2/λ = 0.693/(2.5 × 10⁻³) = 2.8 × 10² s.
- 4
A nuclide has a half-life of 8.0 days. Calculate its decay constant in s⁻¹.
Model answer
The half-life is 8.0 × 24 × 3600 = 6.91 × 10⁵ s, so λ = ln2/t½ = 0.693/(6.91 × 10⁵) = 1.0 × 10⁻⁶ s⁻¹.
- 5
Why is the half-life of a nuclide the same wherever on the decay curve it is measured?
Model answer
The decay is exponential, so the same constant fraction of what remains decays in every equal interval of time, and the time to halve does not depend on how much is present at the start.
- 6
Describe how the half-life of a source of a few minutes' half-life can be measured.
Model answer
Measure the background count rate with the source absent. Place a Geiger–Müller tube a fixed distance from the source and record the count over successive equal intervals, such as ten seconds. Subtract the background from every reading, plot corrected count rate against time, and read off the time for the rate to halve at several points on the curve, then take the mean.
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