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

5.2.1 Detection of Radioactivity

Learning Objective

Students should be able to use the count rate measured in counts / second (cps) or counts / minute (cpm) to analyse radioactive sources and to calculate related quantities.

What is Count Rate?

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

\$\text{Count rate} = \frac{N}{t}\$

where \$N\$ is the number of counts and \$t\$ is the time interval.

Typical Detectors Used in IGCSE

• Geiger‑Müller (GM) tube
• Scintillation detector
• Ionisation chamber (rarely in IGCSE labs)

Measuring Count Rate

1. Set the detector to the required mode (cps or cpm).
2. Place the radioactive source at a fixed distance from the detector.
3. Start the timer and record the total number of counts \$N\$ for a chosen time \$t\$.
4. Calculate the count rate using the formula above.

Conversion Between cps and cpm

Because \$1\ \text{minute}=60\ \text{seconds}\$, the two units are related by:

\$1\ \text{cpm}= \frac{1}{60}\ \text{cps},\qquad 1\ \text{cps}=60\ \text{cpm}\$

The table below shows common conversions.

Factors That Influence Count Rate

• Source strength: More decays → higher count rate.
• Distance from detector: Count rate follows the inverse‑square law: \$\text{Rate}\propto\frac{1}{r^{2}}\$
• Shielding material: Absorbers reduce the number of particles reaching the detector.
• Detector efficiency (\$\varepsilon\$): Only a fraction of emitted particles are recorded. The observed count rate \$R\$ is related to the true activity \$A\$ by \$R = \varepsilon A\$

Sample Calculation

Suppose a GM tube records 450 counts in 2 minutes. Find the count rate in both cpm and cps.

1. Calculate 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}\$

Using Count Rate to Estimate Activity

If the detector efficiency for a particular type of radiation is known (e.g., \$\varepsilon = 0.25\$), the activity \$A\$ of the source can be estimated:

\$A = \frac{R}{\varepsilon}\$

For the previous example, \$A = \dfrac{225\ \text{cpm}}{0.25}=900\ \text{cpm}\$ (or \$15\ \text{cps}\$).

Common Sources of Error

• Background radiation – record a background count rate and subtract it from the measured rate.
• Statistical fluctuations – the count follows a Poisson distribution; the standard deviation is \$\sqrt{N}\$.
• Improper timing – start/stop delays affect \$t\$.
• Changing geometry – moving the source during measurement.

Suggested Practical Activity

Measure the count rate from three different sources (e.g., \$^{60}\$Co, \$^{90}\$Sr, and a natural background sample) at distances of 5 cm, 10 cm and 15 cm. Record the data in a table and plot count rate versus \$1/r^{2}\$ to verify the inverse‑square relationship.