Inverse Square Spreading Cuts Count Rate - Nuclear Radiation: Decay, Binding, and Shielding Step by Step

Inverse-square spreading says the same radiation budget covers more area as distance grows. Here the source strength is unchanged, but moving the detector from 2 metres to 4 metres doubles distance, so the ideal count rate is divided by 4. Real count rates also depend on detector area, alignment, background, shielding, source geometry, counting time, and statistical uncertainty.

Doubling distance cuts a training count rate by four. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Inverse-square spreading cuts count rate

Doubling distance from 2 metres to 4 metres divides the count rate by 4.

80\div4=20\ 1/\mathrm{s}

The source strength did not change

The count rate changes because the same radiation budget spreads over more area.

\mathrm{rate}=20\ 1/\mathrm{s}