Use count rate measured in counts/s or counts/minute

5.2.1 Detection of Radioactivity – Count Rate

Learning Objective

Students must be able to:

• Define count rate and use the units counts / second (cps) or counts / minute (cpm),
• Measure a count rate with a detector **connected to a counting device** (counter or digital display),
• Subtract the background count rate to obtain a corrected value,
• Apply detector efficiency to estimate the activity of a source, and
• Recognise the factors that influence the measured rate and the main safety precautions.

1. What is Count Rate?

The count rate is the number of ionising events recorded by a detector per unit time.

\[ R=\frac{N}{t} \] where N = number of counts and t = elapsed time (s or min).

2. Units and Quick Conversion

Count rate is expressed either as:

• counts / second (cps) or
• counts / minute (cpm)

Because 1 minute = 60 seconds:

\[ 1\;\text{cpm}= \frac{1}{60}\;\text{cps},\qquad 1\;\text{cps}= 60\;\text{cpm} \]

Conversion table – counts / second (cps) and counts / minute (cpm)

cpm	cps
30	0.5
120	2.0
300	5.0
600	10.0

3. Background Radiation

Even in a sealed laboratory a small “background” count is present, caused by natural sources such as:

• Cosmic rays (high‑energy particles from space),
• Radon gas and its decay products,
• Uranium, thorium and potassium in rocks, walls and building materials.

Before measuring any source, record the background count rate (R_b) over the same time interval you will use for the source. This value is later subtracted from the raw count rate.

4. Typical Detectors Used in IGCSE

• Geiger‑Müller (GM) tube – most common in school labs.
• Scintillation detector – useful for fast particles.
• Ionisation chamber – rarely available at school but mentioned in the syllabus.

**Important:** The detector must be electrically connected to a counting device (digital counter or computer interface) so that each ionising event is displayed as a count.

5. Measuring Count Rate – Step‑by‑Step Procedure

1. Set the detector to the required mode (cps or cpm) and switch the counter on.
2. Record a background measurement:
   • Place no source (or a sealed “blank” source) at the measurement position.
   • Start the timer and count for a chosen interval t (e.g., 60 s).
   • Calculate the background rate R_b = N_b/t.
3. Place the radioactive source at a fixed, known distance from the detector.
4. Start the timer, count for the same interval t, and note the total counts N.
5. Calculate the raw count rate R_raw = N/t.
6. Corrected count rate (background subtraction):
   Key formula:  \(R = R_{\text{raw}} - R_{b}\)
7. If required, convert between cps and cpm using the table above.

6. Factors That Influence the Measured Rate

• Source strength (activity, A) – more decays → higher R.
• Distance (r) – follows the inverse‑square law: \(R \propto \dfrac{1}{r^{2}}\).
• Shielding / absorber material – reduces the number of particles reaching the detector.
• Detector efficiency (ε) – only a fraction of the emitted particles are recorded: \[ R = \varepsilon A \qquad\Longrightarrow\qquad A = \frac{R}{\varepsilon} \]

7. Safety Reminder (AO3 – practical skills)

• Always keep sealed sources in their labelled containers when not in use.
• Handle sources with tweezers or forceps; never touch them with bare hands.
• Maintain a minimum safe distance (usually ≥ 5 cm) unless the experiment specifically requires a closer approach.
• Use appropriate shielding (e.g., lead or acrylic) when measuring high‑activity sources.
• Follow your school’s radiation‑safety policy and wear any required personal protective equipment (gloves, lab coat, safety glasses).

8. Sample Calculations

8.1 Simple count‑rate conversion

A GM tube records 450 counts in 2 minutes.

1. Raw count rate (cpm): \[ \text{cpm}= \frac{450\;\text{counts}}{2\;\text{min}} = 225\;\text{cpm} \]
2. Convert to cps: \[ \text{cps}= \frac{225\;\text{cpm}}{60}=3.75\;\text{cps} \]

8.2 Subtracting background and estimating activity

Measurements:

• Background: 30 counts in 60 s → R_b = 0.5 cps (30 cpm).
• Source + background: 480 counts in 60 s → R_raw = 8.0 cps (480 cpm).

Net count rate:

\[ R = R_{\text{raw}} - R_{b}=8.0\;\text{cps}-0.5\;\text{cps}=7.5\;\text{cps} \]

If the detector efficiency for the radiation type is ε = 0.25, the activity of the source is

\[ A = \frac{R}{\varepsilon}= \frac{7.5\;\text{cps}}{0.25}=30\;\text{cps} \]

In cpm this is 30 cps × 60 = 1800 cpm.

9. Common Sources of Error (and how to minimise them)

• Background fluctuations – always record and subtract a background value.
• Statistical (Poisson) variation – the standard deviation σ ≈ √N; increase counting time to reduce the relative error.
• Timing errors – use a digital timer or the counter’s built‑in clock; start and stop simultaneously.
• Geometry changes – keep the source‑detector distance fixed; mark the position on the bench.
• Dead‑time of the detector – at very high rates the detector may miss counts; stay below the recommended maximum count rate for the instrument.

10. Suggested Practical Activity (AO3)

Objective: Verify the inverse‑square law and practise background subtraction.

1. Measure the background count rate for 60 s and record R_b.
2. Select three sealed sources (e.g., ⁶⁰Co, ⁹⁰Sr, and a low‑activity “natural” source).
3. Place each source at distances of 5 cm, 10 cm and 15 cm from the GM‑tube window.
4. For each distance, count for 60 s, record the total counts, calculate the net rate R = R_raw – R_b, and convert to cps.
5. Tabulate the data and plot R (cps) against 1/r². The points should lie on a straight line through the origin, confirming the inverse‑square relationship.