Final answer:
Henry Moseley resolved the inaccuracies in Mendeleev's periodic table, which was arranged based on atomic masses, by arranging the elements according to their atomic numbers determined by X-ray spectroscopy. This corrected the placement of elements and upheld the table's periodic law.
Step-by-step explanation:
Henry Moseley solved the problem of the elements that did not fit the pattern according to their properties by determining that the proper organization of the periodic table should be based on atomic number rather than atomic mass. Upon examining x-ray spectra of the elements, Moseley was able to use X-ray spectroscopy to measure atomic numbers. This method established a more accurate factor for the arrangement of elements. His rearrangement according to atomic number resolved the discrepancies observed in Dmitri Mendeleev's initial version of the periodic table where elements were arranged by atomic mass.
Mendeleev, who had organized elements based on similar properties and increasing atomic mass, had to leave gaps in his periodic table for yet undiscovered elements and even switched the order of some elements to maintain the periodicity based on properties. When elements like gallium and germanium were discovered, they closely matched Mendeleev's predictions for eka-aluminum and eka-silicon, giving credibility to his periodic table. However, the final piece of the puzzle was provided by Moseley, who realized that the periodic law was fundamentally based on the atomic number, after the discovery of the atomic nucleus.