Worked example: A GM tube records 1200 counts in 10 minutes near a source. Estimate the count rate, and explain why moving twice as far away roughly quarters it. Step 1: Rate = 1200/600 s = 2 counts/s = 120 counts/min. Step 2: Radiation spreads over a sphere of area 4πr² — doubling r quadruples the area, so flux (particles per unit area) falls to 1/4: the inverse-square law. Step 3: Expected new rate ≈ 30 counts/min (plus constant background ~20–50/min from cosmic rays and natural radioactivity, which must be subtracted). Step 4: GM limitation: it cannot tell whether the clicks are alpha, beta or gamma — for identification you need a scintillator's energy spectrum. Conclusion: GM counters measure intensity via the inverse-square law — simple, robust, but blind to particle identity.