What is meant by saying that radioactive decay is random?

It is impossible to predict which nucleus will decay next or when a particular nucleus will decay, since each has the same fixed chance of decaying in a given interval.

Define the decay constant.

It is the probability that a given nucleus will decay per unit time, and it has the unit s⁻¹.

Why does a count-rate measurement fluctuate even for a source of essentially constant activity?

Decay is random, so the number of decays in successive equal intervals scatters about a mean value.

OCR A-Level Physics B H557

Planning

Topic overview Choosing apparatus and techniques Identifying and controlling variables Judging whether a method will work

Implementing

Topic overview Using apparatus and techniques correctly Units for measurements Recording and presenting observations

Analysis

Topic overview Processing results and reaching conclusions Significant figures and mathematical processing Graphs, gradients and intercepts

Evaluation

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Creating Models

Topic overview Capacitance and charge storage Energy stored on a capacitor Capacitor discharge and the exponential model The time constant of an RC circuit Charging a capacitor Investigating capacitor charge and discharge Radioactive decay as a random process Activity, decay constant and half-life Determining the half-life of an isotope Iterative numerical models of exponential change Exponential curves on linear and logarithmic scales Simple harmonic motion: the defining relationship Solutions and graphs of simple harmonic motion Modelling oscillations step by step Energy in simple harmonic motion Period of a mass–spring system and a simple pendulum Free and forced vibrations, damping and resonance

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Probing Deep Into Matter

Topic overview Particle accelerators and high-energy beams Scattering and the nuclear atom Paths of scattered particles and closest approach Discrete energy levels in atoms Electron standing waves and the confined electron Quarks, hadrons and leptons Conservation laws and nuclear equations Charged particles in detectors and magnetic fields Relativistic energy and the relativistic factor

Ionising Radiation and Risk

Topic overview The nature of ionising radiations Effects on living tissue and radiation safety Absorbed dose, effective dose and risk Binding energy and nuclear stability The Nuclear Valley and modes of decay Fission, fusion and nuclear power Activity, half-life and the decay constant Investigating absorption and half-life

Creating Models

Radioactive decay as a random process

3 things to know
Components 01, 02 and 03

Overview

Recall questions on the random and spontaneous nature of radioactive decay, why the decay rate is proportional to the nuclei remaining, dN/dt = −λN and the decay constant, fluctuating count rates, demonstrating randomness, why the exponential model works, subtracting background, comparing capacitor discharge with decay, heating a source, and samples of different size.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What is meant by saying that radioactive decay is spontaneous?

Key term

Why is the number of nuclei decaying per second proportional to the number of nuclei remaining?

Key term

What differential relationship models radioactive decay?

Questions from this subtopic

Each one with the model answer underneath.

1
What is meant by saying that radioactive decay is random?
Model answer
It is impossible to predict which nucleus will decay next or when a particular nucleus will decay, since each has the same fixed chance of decaying in a given interval.
2
What is meant by saying that radioactive decay is spontaneous?
Model answer
The decay is unaffected by external conditions such as temperature, pressure or the chemical state of the atom.
3
Why is the number of nuclei decaying per second proportional to the number of nuclei remaining?
Model answer
Each undecayed nucleus has the same fixed probability of decaying in a given short time, so twice as many nuclei produce twice as many decays.
4
What differential relationship models radioactive decay?
Model answer
The rate of change of the number of undecayed nuclei is dN/dt = −λN.
5
Define the decay constant.
Model answer
It is the probability that a given nucleus will decay per unit time, and it has the unit s⁻¹.
6
Why does a count-rate measurement fluctuate even for a source of essentially constant activity?
Model answer
Decay is random, so the number of decays in successive equal intervals scatters about a mean value.

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