Radioactivity and Half Life

Objectives

Lesson outcomes

Describe radioactive decay as random and spontaneous, using count-rate fluctuations as evidence.
Define activity, decay constant, and half-life for a radioactive sample.
Use A = lambda N, lambda = 0.693 / t1/2, and exponential decay relationships in calculations.
Sketch and interpret decay graphs for activity, number of undecayed nuclei, or corrected count rate.

Syllabus

CIE 9702 syllabus points

6 linked

23.2.1 understand that fluctuations in count rate provide evidence for the random nature of radioactive decay
23.2.2 understand that radioactive decay is both spontaneous and random
23.2.3 define activity and decay constant, and recall and use A = λN
23.2.4 define half-life
23.2.5 use λ = 0.693 / t 1 2
23.2.6 understand the exponential nature of radioactive decay, and sketch and use the relationship x = x0e –λt, where x could represent activity, number of undecayed nuclei or received count rate

Definitions

Required definitions

Activity
the rate of decay of nuclei in a radioactive sample.
Decay constant
the probability per unit time that an individual nucleus will decay.
Half-life
the time taken for the number of undecayed nuclei, or the activity, to fall to half its initial value.

Lesson Notes

Student guidance and lesson notes

Overview

This lesson develops radioactive decay from a qualitative idea into a mathematical model. You will connect random count-rate fluctuations to spontaneous nuclear decay, then use activity, decay constant, half-life, and exponential graphs to describe how a sample changes over time.

What You Need to Know

Radioactive decay is spontaneous: it is not triggered by temperature, pressure, chemical state, or other external conditions.
Radioactive decay is random for individual nuclei, so short count-rate measurements fluctuate even when the source and detector are unchanged.
Use activity and decay constant to connect the number of undecayed nuclei to the decay rate.
The relationship A = lambda N links activity to the number of undecayed nuclei.
Use half-life to interpret activity, count-rate, and undecayed-nuclei graphs.
Exponential decay can be modelled with x = x0 e^(-lambda t), where x can represent activity, undecayed nuclei, or corrected count rate.

How to Work Through It

Start by looking at repeated count-rate readings and deciding what they show about randomness.
Define activity, decay constant, and half-life before using them in equations.
Practise converting between half-life and decay constant.
Use decay graphs and exponential equations to find missing times, activities, or numbers of undecayed nuclei.

Check Your Understanding

Why do repeated count-rate readings vary even if the source has not changed?
How are activity and number of undecayed nuclei linked?
If a source has passed through three half-lives, what fraction of its original activity remains?
What must be corrected before using a measured count rate in a decay calculation?

Common Mistakes

Saying decay is unpredictable for a whole sample rather than for individual nuclei.
Treating half-life as the time for all nuclei to decay.
Forgetting that count rate should be corrected for background radiation before analysis.
Mixing up lambda as a probability per unit time with activity as decays per unit time.

Next Steps

Keep the decay equations and graph shapes secure for nuclear physics calculations.
Be ready to link changes in nuclear mass to energy in the next lesson.