The Advanced Molybdenum-based Rare process Experiment in its second phase (AMoRE-II) will search for neutrinoless double-beta (0{ u}b{eta}b{eta}) decay of 100Mo in 200 kg of molybdate crystals. To achieve the zero-background level in the energy range of the double-beta decay Q-value of 100Mo, the radioactive contamination levels in AMoRE crystals should be low. 100EnrMoO3 powder, which is enriched in the 100Mo isotope, is used to grow the AMoRE crystals. A shielded array of fourteen high-purity germanium detectors with 70% relative efficiency each was used for the measurement of background activities in a sample of 9.6-kg powder. The detector system named CAGe located at the Yangyang underground laboratory was designed for measuring low levels of radioactivity from natural radioisotopes or cosmogenic nuclides such as 228Ac, 228Th, 226Ra, 88Y, and 40K. The activities of 228Ac and 228Th in the powder sample were 0.88 pm 0.12 mBq/kg and 0.669 pm 0.087 mBq/kg, respectively. The activity of 226Ra was measured to be 1.50 pm 0.23 mBq/kg. The activity of 88Y was 0.101 pm 0.016 mBq/kg. The activity of 40K was found as 36.0 pm 4.1 mBq/kg.
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