Half-lives and the random nature of radioactive decay.pptx

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Half-lives and the random nature of radioactive decay

Atomic structure

Lesson 6 of 10

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Warm-up

Atomic structure

Lesson 6 of 10

Answer each one, then check.

1

What does random mean?

2

What is half of 800?

3

What is activity measured in?

4

What is a count rate?

5

What does exponential decay look like on a graph?

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Warm-up - Answers

Atomic structure

Lesson 6 of 10

1

What does random mean?

Cannot be predicted

2

What is half of 800?

400

3

What is activity measured in?

Becquerel (Bq)

4

What is a count rate?

Number of counts per second

5

What does exponential decay look like on a graph?

A curve that falls quickly then more slowly

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Learning Objectives

Atomic structure

Lesson 6 of 10

1

Define half-life.

2

Explain half-life in terms of the random nature of radioactive decay.

3

Determine the half-life of an isotope from a graph or table.

4

Calculate the net decline as a ratio after a given number of half-lives (Higher tier).

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AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER

Atomic structure

Lesson 6 of 10

HALF-LIFE

The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (or activity) to fall to half its initial level.

Radioactive decay is random: we cannot say when any one nucleus will decay, but for a large number of nuclei the half-life is predictable.

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A Decay Curve

Atomic structure

Lesson 6 of 10

Each half-life the activity halves.

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Number of Half-Lives

Atomic structure

Lesson 6 of 10

Higher tier: net decline as a ratio.

Half-lives

Fraction left

Ratio of final to initial

0

1

1 : 1

1

1/2

1 : 2

2

1/4

1 : 4

3

1/8

1 : 8

4

1/16

1 : 16

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Finding a Half-Life from a Graph

Atomic structure

Lesson 6 of 10

The activity of a sample falls from 800 Bq to 400 Bq in 20 minutes and to 200 Bq after 40 minutes. What is the half-life?

1

800 to 400

Halved in 20 minutes

2

400 to 200

Halved again in the next 20 minutes

ANSWER

The half-life is 20 minutes.

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Activity After Several Half-Lives

Atomic structure

Lesson 6 of 10

A source has an activity of 800 Bq and a half-life of 6 hours. Find its activity after 24 hours.

1

Number of half-lives

24 ÷ 6 = 4

2

Halve four times

800 → 400 → 200 → 100 → 50

ANSWER

50 Bq

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Net Decline as a Ratio (Higher)

Atomic structure

Lesson 6 of 10

Calculate the ratio of the final activity to the initial activity after 3 half-lives.

1

Each half-life

Halve the activity

2

After 3

(½)³ = ⅛

ANSWER

The activity falls to 1/8 of its initial value, a ratio of 1 : 8.

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Random Decay

Atomic structure

Lesson 6 of 10

How to explain it.

One nucleus

It is impossible to predict when a particular nucleus will decay.

Many nuclei

The number decaying in a given time follows a pattern, so half-life is a reliable measure.

Count rate

Count rate is also random, so it varies slightly between measurements.

Background

Correct for background radiation to find the true count rate.

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Key Terms

Atomic structure

Lesson 6 of 10

Half-life

The time for the number of nuclei (or the activity) to halve.

Random

Cannot be predicted for a single nucleus.

Count rate

The number of decays detected each second.

Activity

The rate of decay of a source, in becquerel.

Decay curve

A graph showing how activity falls with time.

Background

The radiation that is always around us.

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Atomic structure

Lesson 6 of 10

YOUR TASK

Halve It

10 minutes

A sample has a count rate of 640 counts per minute. Its half-life is 3 hours. What is the count rate after 12 hours? What is the ratio of final to initial count rate?

1

Work out the number of half-lives.

2

Halve each time.

WHAT A GOOD ANSWER SHOWS

12 ÷ 3 = 4 half-lives: 640 → 320 → 160 → 80 → 40 counts per minute. The ratio is 1 : 16.

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Can I...?

Atomic structure

Lesson 6 of 10

Define half-life.

Explain random decay.

Find half-life from a graph.

Halve repeatedly.

Work out the number of half-lives.

State the ratio after several half-lives.

Explain why decay is random.

Use correct units.

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Summary & Exam Focus

Half-life: time for activity to halve.

Random decay but a predictable half-life for many nuclei.

After n half-lives: fraction (1/2)ⁿ.

Read half-life from a graph.

EXAM FOCUS

A radioactive source has a half-life of 20 minutes and an activity of 800 Bq. Find its activity after 60 minutes. (2 marks)

Three half-lives: halve three times.

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