Calculating Activity (SQA National 5 Physics): Revision Note

Exam code: X857 75

Leander Oates

Written by: Leander Oates

Reviewed by: Caroline Carroll

Updated on

Calculating activity

  • Activity is defined as:

The number of nuclear disintegrations per unit time

  • Activity is measured in becquerels

    • The symbol for becquerels is Bq

    • 1 Becquerel is equal to 1 nucleus in the source decaying in 1 second

  • Objects containing radioactive nuclei are called sources of radiation

  • Sources of radiation decay at different rates which are defined by their activity

  • Activity can be calculated using the following relationship:

A space equals fraction numerator space N over denominator t end fraction

  • Where:

    • A = activity measured in becquerels (Bq)

    • N = number of nuclear disintegrations

    • t = time measured in seconds (s)

How does activity vary with time?

  • The activity of a radioactive source decreases with time

    • This is because each disintegration (decay) event reduces the overall number of radioactive nuclei in the source

  • Radioactive decay is a random process

  • The randomness of radioactive decay can be observed by measuring the count rate of a source using a Geiger-Muller (GM) tube

  • When the count rate is plotted against time, fluctuations can be seen 

  • These fluctuations provide evidence for the randomness of radioactive decay

Graph showing count rate decreasing over time, with an irregular, jagged line decreasing from top left to bottom right, labelled axes 'Count Rate/C' and 'Time/t'.
The decreasing activity of a source can be shown on a graph against time. The fluctuations show the randomness of radioactive decay

The decreasing activity of a source can be shown on a graph against time. The fluctuations show the randomness of radioactive decay

Worked Example

A source of radiation has an activity of 2100 Bq.

Determine the number of nuclear disintegrations in 2 minutes.

Answer:

Step 1: Determine the activity

  • The activity of the source is 2100 Bq

  • This means 2100 nuclei decay every second

Step 2: Determine the time period in seconds

  • The time period is 2 minutes

  • Each minute has 60 seconds

  • The time period in seconds is:

2 × 60 = 120 seconds

Step 3: Write out the relevant relationship

A space equals fraction numerator space N over denominator t end fraction

Step 4: Rearrange to solve for the number of disintegrations

  • Multiply both sides by t

A t space equals fraction numerator space N up diagonal strike t over denominator up diagonal strike t end fraction

N space equals space A t

Step 5: Substitute in the known values to calculate

N space equals space 2100 space cross times space 120

N space equals space 2.52 cross times 10 to the power of 5

Step 6: Round to the appropriate amount of significant figures

  • The least precise input value is 2 s.f.

  • Therefore, the final answer can only be given to the same precision

N space equals space 2.5 cross times 10 to the power of 5 space open parentheses 2 space straight s. straight f. close parentheses

Examiner Tips and Tricks

Do not confuse activity and count rate.

Activity is the rate at which unstable nuclei decay, whereas count rate is the rate at which radioactive emissions are detected.

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Leander Oates

Author: Leander Oates

Expertise: Physics Content Creator

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.

Caroline Carroll

Reviewer: Caroline Carroll

Expertise: Physics & Chemistry Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.