To put it simply. We group our EM waves into groups such as X-rays, microwaves, visible light etc. I was wondering, if the properties of say, x-rays, slowly change into the properties of say, gamma rays, or as soon as the wavelength is larger than 10 picometers it's properties become that of an x-ray. If it's the former, how do we calulate the standards for identifying a wave.
Answer
The EM waves form a continuous spectrum, thus your first description of a gradual change in wave behaviour is correct. However, because of this; there is also no precise way of determining exactly at which frequency a category of EM wave starts or finishes at.
In fact, sometimes the classification of waves can be so hand wavy that the typical description of an EM wave: $$c=f\lambda$$ is treated as a secondary determinant for which category an EM wave belongs to! One such example of this is with X rays and $\gamma$ rays. Their frequencies overlap one another at approximately $10^{18}\:\mathrm{Hz}$ so it is difficult to quantitatively differentiate higher frequency X rays and lower frequency $\gamma$ rays. Instead, we let the origin of the waves decide, $\gamma$ rays are emitted from the nucleus of the atom while X rays are emitted from outside the nucleus; by excited electrons.
To conclude, the EM spectrum can in no way be easily divided into discrete categories and as such there is always some overlap between adjacent categories of wave.
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