Conclusions / Validity
Paschen's law requires that
- there are already free electrons at the cathode which can be accelerated to trigger impact ionization. Such so-called seed electrons can be created by ionization by cosmic x-ray background.
- the creation of further free electrons is only achieved by impact ionization. Thus Paschen's law is not valid if there are external electron sources. This can for example be a light source creating secondary electrons via the photoelectric effect. This has to be considered in experiments.
- each ionized atom leads to only one free electron. But multiple ionizations occur always in practice.
- free electrons at the cathode surface are created by the impacting ions. The problem is that the number of thereby created electrons strongly depends on the material of the cathode, its surface (roughness, impurities) and the environmental conditions (temperature, humidity etc.). The experimental, reproducible determination of the factor is therefore nearly impossible.
- the electrical field is homogeneous.
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