Cambridge Syllabus Notes

5.2.1 Detection of Radioactivity

What is Background Radiation? 🔭

Think of background radiation as the ambient noise in a classroom. Even when no one is speaking, you can still hear the hum of the air conditioner or distant traffic. Similarly, our surroundings are filled with low‑level radiation from the Earth, cosmic rays, and even the materials in our own bodies. This “background” must be accounted for when we measure the activity of a radioactive sample.

Measuring Count Rates 📊

A Geiger–Müller counter records the number of ionising events per unit time. The raw count we read from the instrument is called the gross count rate: $$ R_{\text{gross}} = \frac{N_{\text{total}}}{t} $$ where $N_{\text{total}}$ is the total counts recorded in a time $t$ (usually in seconds or minutes).

Correcting for Background 🧪

To isolate the activity of the sample, we subtract the background count rate: $$ R_{\text{corrected}} = R_{\text{gross}} - R_{\text{background}} $$ Why subtraction? Because the background is always present; we want only the counts that come from the sample itself.

Example Calculation 📝

Suppose we record the following data in a 5‑minute experiment:

Measurement	Counts	Time (min)
Sample + Background	1250	5
Background only	250	5

First, calculate the gross and background rates:

Gross rate: $ R_{\text{gross}} = \frac{1250}{5} = 250 \, \text{counts min}^{-1} $
Background rate: $ R_{\text{background}} = \frac{250}{5} = 50 \, \text{counts min}^{-1} $

Then correct: $$ R_{\text{corrected}} = 250 - 50 = 200 \, \text{counts min}^{-1} $$ This is the true activity of the sample, free from background noise.

Exam Tips 🎓

1. Always check the units. Convert minutes to seconds if the question asks for counts per second. Remember: $1 \, \text{min} = 60 \, \text{s}$.

2. Be clear about subtraction. The corrected rate is gross minus background, not the other way round.

3. Use significant figures. Match the precision of the given data. If the background count is reported to the nearest 10, round your corrected rate accordingly.

4. Explain your steps. In written answers, show the formula you used and plug in the numbers. This demonstrates understanding and earns extra marks.

Quick Practice Question 🤔

A Geiger counter records 1800 counts in 10 minutes for a sample. The background counter records 300 counts in the same time. What is the corrected count rate in counts per second?

Answer (show your work):

Gross rate: $ \frac{1800}{10} = 180 \, \text{counts min}^{-1} $
Background rate: $ \frac{300}{10} = 30 \, \text{counts min}^{-1} $
Corrected rate: $ 180 - 30 = 150 \, \text{counts min}^{-1} $
Convert to counts per second: $ \frac{150}{60} = 2.5 \, \text{counts s}^{-1} $

So the corrected count rate is $2.5 \, \text{counts s}^{-1}$.

Use measurements of background radiation to determine a corrected count rate