Mass Spectrometry has been the usual method to determine Ar concentrations in mineral samples for dating them through the40Ar/40K ratio. This technique has been replaced since 1966 by measurement of40Ar/39Ar ratio, after artificial production of39Ar from the39K(n,p)39Ar reaction produced in the fast neutron flux of a nuclear reactor. This method requires the fusion of the sample by incremental heating until reaching a temperature of 1000°C in order to get the total release of both argon isotopes. In principle, it should be possible to determine the40Ar/40K ratio by activation analysis in an easier, non-destructive way, but it presents the following drawbacks: manufacture of argon standards; usual low ratio peak/Compton distribution for both peaks: 1.29 Mev and 1.52 Mev (41Ar and42K respectively), since potassium minerals are usually very rich in sodium, manganese and chlorine; reaction41K(n,p)41Ar induced by fast neutrons present in the thermal flux; and possible contamination of the samples and standards with atmospheric40Ar (99.6% of elementary Ar, whose proportion in the atmosphere at sea level is 0.93%). This paper describes how these problems may be solved, also determining the limits of Ar and K concentration related to Compton distribution, in our experimental conditions.