Despite the completely uncertain character of the question, the physical methods are mainly non-destructive, while chemical methods require chemical destruction of the probe. Thus, the chemical methods of analysis require some special preparation procedure of the probe. On the other hand, chemical methods of analysis are less sensitive as well as less accurate (as usual). However, physical methods associated with some quite expensive instruments, while chemical methods are usually express, simple and require relatively large amount of probe.
Finally, the problems of those methods are mainly:
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