Define the decay constant.

The decay constant is the probability per second that any one nucleus will decay, in other words the fraction of the undecayed nuclei that decay each second, measured in s⁻¹.

Give the SI unit of the decay constant.

The decay constant is measured in s⁻¹, since it is a fraction of the nuclei present decaying per second.

Calculate the activity of a sample containing 6.0 × 10²⁰ undecayed nuclei of a nuclide whose decay constant is 1.0 × 10⁻⁶ s⁻¹.

The activity is λN = 1.0 × 10⁻⁶ × 6.0 × 10²⁰ = 6.0 × 10¹⁴ Bq.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

Topic overview Physical quantities and SI base units Prefixes and standard form Scalars and vectors Resolving vectors and finding resultants Coplanar forces in equilibrium

Moments and Equilibrium

Topic overview Moment of a force Centre of gravity The principle of moments Determining unknown masses using moments

Linear Motion and Dynamics

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Newton's Laws of Motion

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Linear Momentum and Impulse

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Work, Energy and Power

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Current, Charge and Potential Difference

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Resistance and Resistivity

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Waves

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Quantum Physics

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Wave-Particle Duality

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Astronomy

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Deformation of Solids

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Thermal Physics

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Uniform Circular Motion

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Simple Harmonic Motion

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The Nucleus and Radioactive Decay

Topic overview Alpha-particle scattering and the nuclear atom Nuclear radius and nucleon number The density of nuclear matter Alpha, beta and gamma radiation: nature, penetration and range Nuclear equations and changes in nucleon and proton number The random and exponential nature of radioactive decay Activity, the decay constant and A = −λN Exponential decay calculations with A = A₀e^(−λt)Half-life and measuring it

Nuclear Energy, Fission and Fusion

Topic overview Mass–energy equivalence and E = Δmc² Mass defect and binding energy The binding energy per nucleon curve Inside a fission reactor Nuclear power: social, environmental, security and economic issues The ITER tokamak fusion reactor Plasma confinement: gravitational, inertial and magnetic

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Electric Fields

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Capacitors

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Fundamental Particles

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The Nucleus and Radioactive Decay

Activity, the decay constant and A = −λN

3 things to know
Unit A2 1

Overview

Activity of a radioactive source and decay constant.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the equation relating the rate of change of the number of undecayed nuclei to the number present, and explain its minus sign.

Key term

Define the activity of a radioactive source.

Key term

Define the becquerel.

Questions from this subtopic

Each one with the model answer underneath.

1
Define the activity of a radioactive source.
Model answer
The activity is the number of nuclei that decay per second in the source, measured in becquerels.
2
Define the becquerel.
Model answer
One becquerel is an activity of one decay per second.
3
Define the decay constant.
Model answer
The decay constant is the probability per second that any one nucleus will decay, in other words the fraction of the undecayed nuclei that decay each second, measured in s⁻¹.
4
State the equation relating the rate of change of the number of undecayed nuclei to the number present, and explain its minus sign.
Model answer
A = −λN, where A is the rate of change of the number of undecayed nuclei, λ the decay constant in s⁻¹ and N the number of undecayed nuclei present. The minus sign shows that N is falling with time, and the activity quoted as a count of decays per second has magnitude λN.
5
Give the SI unit of the decay constant.
Model answer
The decay constant is measured in s⁻¹, since it is a fraction of the nuclei present decaying per second.
6
Calculate the activity of a sample containing 6.0 × 10²⁰ undecayed nuclei of a nuclide whose decay constant is 1.0 × 10⁻⁶ s⁻¹.
Model answer
The activity is λN = 1.0 × 10⁻⁶ × 6.0 × 10²⁰ = 6.0 × 10¹⁴ Bq.

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