Edexcel iGCSE Physics -7.12 - 7.13 Half-Life, and Calculations- Study Notes- New Syllabus
Edexcel iGCSE Physics -7.12 – 7.13 Half-Life, and Calculations- Study Notes- New syllabus
Edexcel iGCSE Physics -7.12 – 7.13 Half-Life, and Calculations- Study Notes -Edexcel iGCSE Physics – per latest Syllabus.
Key Concepts:
update
Half-life of a Radioactive Isotope
The activity of a radioactive source decreases with time. A key quantity used to describe how quickly this happens is the half-life.
Half-life – Definition
Definition: The half-life of a radioactive isotope is the time taken for the activity of a source, or the number of undecayed nuclei, to decrease to half of its original value.
Key idea: Half-life describes the rate of radioactive decay.
Important Features of Half-life
- Half-life is a fixed property of a radioactive isotope.
- It is not affected by temperature, pressure, or chemical state.
- Each isotope has its own characteristic half-life.
Key point: Half-life is the same for an isotope no matter how much of the substance is present.
Half-life and Activity
- After one half-life, activity becomes half.
- After two half-lives, activity becomes one quarter.
- After three half-lives, activity becomes one eighth.
Important: The decrease happens gradually, not suddenly.
Different Isotopes Have Different Half-lives
- Some isotopes decay very quickly (short half-life).
- Some isotopes decay very slowly (long half-life).
- This depends on how stable the nucleus is.
Key idea: More unstable nuclei generally have shorter half-lives.
Why Half-life Is Useful
- Helps predict how activity changes with time.
- Used to choose isotopes for medical and industrial uses.
- Allows comparison of different radioactive sources.
Example
A radioactive isotope has a half-life of 6 hours. Explain what this means and state the fraction of the original activity remaining after 18 hours.
▶️ Answer / Explanation
Meaning of half-life:
- The activity halves every 6 hours.
After 18 hours:
- 18 hours = 3 half-lives.
- After 1 half-life → \( \mathrm{\dfrac{1}{2}} \)
- After 2 half-lives → \( \mathrm{\dfrac{1}{4}} \)
- After 3 half-lives → \( \mathrm{\dfrac{1}{8}} \)
Fraction remaining = \( \mathrm{\dfrac{1}{8}} \).
Example
Two radioactive isotopes have half-lives of 2 days and 20 years respectively. Explain which isotope is more unstable and why.
▶️ Answer / Explanation
- The isotope with a half-life of 2 days decays more quickly.
- This means its nuclei are less stable.
- A shorter half-life indicates greater instability.
- The isotope with a 20-year half-life is more stable.
Using Half-life to Calculate Radioactive Activity
The concept of half-life can be used to calculate how the activity of a radioactive source changes with time. These calculations can be carried out using numerical methods and decay graphs.
Key Idea
Statement: During each half-life, the activity of a radioactive source decreases to half of its previous value.
Important: This applies equally to activity and to the number of undecayed nuclei.
Simple Half-life Calculations
If the half-life is known:
- After 1 half-life → activity = \( \mathrm{\dfrac{1}{2}} \)
- After 2 half-lives → activity = \( \mathrm{\dfrac{1}{4}} \)
- After 3 half-lives → activity = \( \mathrm{\dfrac{1}{8}} \)
General rule:
Activity halves repeatedly at equal time intervals.
Using Half-life Step-by-Step (Exam Method)
- Identify the half-life.
- Calculate how many half-lives have passed.
- Halve the activity for each half-life.
- State the final activity with units (Bq).
Graphical Method for Determining Half-life
A decay graph shows how activity changes with time.
- Activity is plotted on the vertical axis.
- Time is plotted on the horizontal axis.
- The curve slopes downward smoothly.
How to find half-life from a graph:
- Choose an activity value.
- Find half of this value.
- Read the time taken to reach this value.
- This time is the half-life.
Using a Decay Graph to Find Activity
- Locate the given time on the time axis.
- Move up to the decay curve.
- Read across to the activity axis.
- State the activity in becquerels.
Key idea: Graphs allow half-life to be found even when it is not given directly.
Example
A radioactive source has an initial activity of 1600 Bq. Its half-life is 4 hours. Calculate the activity after 12 hours.
▶️ Answer / Explanation
Number of half-lives:
\( \mathrm{\dfrac{12}{4} = 3\ half\text{-}lives} \)
Activity after each half-life:
- After 1 → 800 Bq
- After 2 → 400 Bq
- After 3 → 200 Bq
Final activity: 200 Bq
Example
The graph of activity against time for a radioactive source is shown. The activity falls from 800 Bq to 200 Bq in 10 minutes. Determine the half-life of the source.
▶️ Answer / Explanation
- 800 Bq to 400 Bq → 1 half-life
- 400 Bq to 200 Bq → 2 half-lives
- Total time = 10 minutes
- Time for 1 half-life = \( \mathrm{\dfrac{10}{2} = 5\ min} \)
Half-life = 5 minutes