Calculating Radioactive Decay (OCR GCSE Physics A (Gateway))

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

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

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

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

• 1 year divided by 4 (2²) is a quarter of a year or 3 months

• Therefore, the half-life of the sample is 3 months