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A = λN

PHY095 · Quantum & Nuclear Physics · Class 12 + College

Geiger counter counting

Objective: To understand how a Geiger–Müller counter measures activity, using a digital simulation only.

🧰 Apparatus

  • (Digital only) simulated GM tube and counter
  • Stopwatch
  • Results table

📐 Formulas and SI units

A = λN (Bq = counts/s for a perfect counter)
corrected rate = measured − background

💡 Theory

A GM tube contains low-pressure gas. Each ionising particle that enters starts an avalanche of ions, giving one pulse (a click) on the counter. The count rate is proportional to the activity A = λN of the source. Counts are random, so we count for a fixed time and subtract the background count.

🪜 Procedure

  1. Note the background count rate with no source (simulated).
  2. Set λ and N for the simulated source.
  3. Count for 10 s and calculate the count rate.
  4. Repeat three times and average.
  5. Compare with A = λN.

📋 Observations Simulated values

✅ Result and conclusion

10 000 nuclei with λ = 0.01 /s give 100 counts per second (1000 in 10 s) in the simulation.

🔬 In a real lab

Real counters catch only some of the radiation (geometry and efficiency) and miss counts at high rates (dead time).

⚠️ Safety

This experiment is digital only. No radioactive sources are used; the source in the scene is simulated.

❓ Quick check

1. Each click of a GM counter means…

2. Background radiation should be…

3. Doubling N makes the count rate…

🏋️ Practice

Easyλ = 0.002 /s, N = 50 000. A?

Answer: 100 Bq

MediumMeasured 130 /s, background 0.5 /s. Corrected?

Answer: 129.5 /s

ChallengeWhy count for a long time?

Answer: Random counts average out