At present, counting atoms in a one-kilogram sphere made of (28)Si-enriched silicon allows the determination of the Avogadro constant with the 2.0 × 10(-8) relative standard uncertainty required for the realization of the definition of the new kilogram. With the exception of carbon, oxygen, boron, nitrogen, and hydrogen, the claimed uncertainty is based on the postulation that the silicon material used to manufacture the sphere was above a particular level of purity. Two samples of the silicon were measured using instrumental neutron activation analysis to collect experimental data to test the purity assumption. The results obtained in two experiments carried out using different research reactor neutron sources are reported. The analysis confirmed that the silicon material was of sufficient purity by quantifying the ultratrace concentration of 12 elements and determining the detection limits of another 54 elements.