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Why can Geiger counters count radiation particles but not measure their energy?

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detector output connected to a measuring circuit — radiation measurement Figure 1: (A) A simple equivalent circuit for the development of a voltage pulse at the output of a detector. R represents the resistance and C the capacitance of the circuit; V(t) is the time (t)-dependent voltage produced. (B) A representative current pulse due to the interaction of a single quantum in the detector. The total charge Q is obtained by integrating the area of the current, i(t), over the collection time, t_c. (C) The resulting voltage pulse that is developed across the circuit of (A) for the case of a long circuit time constant. The amplitude (V_max) of the pulse is equal to the charge Q divided by the capacitance C.

Geiger-Müller counters are designed to detect the presence of radiation rather than measure its energy because of their specific mode of operation. In these devices, the voltage applied across the electrodes is high enough to trigger a self-limiting, uncontrolled spread of avalanches known as a Geiger discharge.1

Because this discharge is self-limiting, the detector produces an output pulse of the same large magnitude regardless of the energy deposited by the incident radiation. Whether a particle creates only a single ion pair or deposits a significant amount of energy to create many ion pairs, the resulting electrical pulse remains essentially the same.12

In contrast, devices like proportional counters or spectroscopy systems are capable of energy measurement because their signal output is proportional to the ionization or energy deposited by the radiation. Because the Geiger-Müller counter's pulse amplitude carries no energy information, the instrument is useful only for pulse-counting systems rather than energy analysis.321