Final answer:
The periodic law was derived from the observation of recurring similar properties among elements when arranged by atomic mass, which then shifted to atomic number. This led to the development of the modern periodic table where elements are grouped based on their properties, as demonstrated by groups of elements like the halogens exhibiting closely related characteristics.
Step-by-step explanation:
The observations that led to the periodic law were predicated on the identification of patterns in the properties of elements when arranged by increasing atomic mass, which was later refined to atomic number. Early chemists noticed that elements with similar properties occurred at regular intervals, a concept known as periodicity. Dmitri Mendeleev, in particular, played a pivotal role, noting the regular occurrence of properties and organizing elements into a table accordingly, even leaving gaps for then-undiscovered elements, predicting their existence and properties. His work was critical in developing the modern periodic table, where elements are positioned in order of increasing atomic number, and housed in groups and periods where elements in the same group exhibit similar chemical properties.
Examples confirming periodic law include the observation that all halogen elements in group 17 show similar properties, such as being non-metals and forming salts with metals. Additionally, the observation that all metals display metallic characteristics and parallel reactivity patterns supported the formulation of the periodic table. Moreover, advancements like the discovery of radioactivity, while not a direct observation leading to the periodic law, provided further insight into the atomic structure and properties of elements.