Final answer:
Mendeleev developed the Periodic Table by arranging elements in order of increasing atomic mass on separate note cards, identifying periodic patterns in their properties, and predicting undiscovered elements. His predictions were confirmed as new elements were found, earning global acceptance for his Periodic Table.
Step-by-step explanation:
Dmitri Mendeleev's systematic approach to developing his Periodic Table of elements involved the use of separate note cards for each element, which he then arranged in order of increasing atomic mass. This allowed for the identification of periodic — repeating — patterns in the elements' chemical properties. When the elements were ordered by atomic mass, elements with similar properties emerged at regular intervals, which is why these patterns are termed 'periodic.' Mendeleev also left intentional gaps in his table, predicting the properties and atomic masses of undiscovered elements. As scientists discovered these new elements and found that they matched Mendeleev's predictions, the periodic table was universally accepted and became a fundamental tool in chemistry.
Mendeleev published his periodic table in 1869, before the discovery of atomic numbers, which is why he initially used atomic masses to arrange the elements. Although he had to adjust the order of some elements to maintain proper grouping, his predictions were validated when elements like gallium and germanium were discovered and fit neatly into the table, solidifying his periodic law.