Calculating Radioactive Decay (OCR GCSE Physics A (Gateway)) : Revision Note

Calculating Radioactive Decay

Higher Tier Only

  • To calculate the half-life of a sample, the procedure is:

    • Measure the initial activity, A0, of the sample

    • Determine the half-life of this original activity

    • Measure how the activity changes with time

  • The time taken for the activity to decrease to half its original value is the half-life

  • Half-life can be shown clearly on a graph

Half-life Graph, downloadable IGCSE & GCSE Physics revision notes

The diagram shows how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed

  • The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life

  • It is the same length of time as it would take to decrease from 50 % activity to 25 % activity

  • The half-life is constant for a particular isotope

Worked Example

The radioisotope technetium is used extensively in medicine. The graph below shows how the activity of a sample varies with time.

Worked Example - Half Life Curve, downloadable AS & A Level Physics revision notes

Determine the half-life of this material.

Answer:

Step 1: Draw lines on the graph to determine the time it takes for technetium to drop to half of its original activity

Worked Example - Half Life Curve Ans a, downloadable AS & A Level Physics revision notes

Step 2: Read the half-life from the graph

  • In the diagram above the initial activity, A0, is 8 × 107 Bq

  • The time taken to decrease to 4 × 107 Bq, or ½ A0, is 6 hours

  • The time taken to decrease to 2 × 107 Bq is 6 more hours

  • The time taken to decrease to 1 × 107 Bq is 6 more hours

  • Therefore, the half-life of this isotope is 6 hours

Worked Example

A particular radioactive sample contains 2 million un-decayed atoms. After a year, there is only 500 000 atoms left un-decayed.

What is the half-life of this material?

Answer:

Step 1: Calculate how many times the number of un-decayed atoms has halved

  • There were 2 000 000 atoms to start with

  • 1 000 000 atoms would remain after 1 half-life

  • 500 000 atoms would remain after 2 half-lives

  • Therefore, the sample has undergone 2 half-lives

Step 2: Divide the time period by the number of half-lives

  • The time period is a year

  • The number of half-lives is 2

2 space 000 space 000 space rightwards arrow from 6 space months to 1 space half space life of space 1 space 000 space 000 space rightwards arrow from 1 space year to 2 space half space lives of space 500 space 000

  • So two half-lives is 1 year, and one half-life is 6 months

  • Therefore, the half-life of the sample is 6 months

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