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The periodic law states that when elements are arranged in order of ________ their properties repeat themselves at regular intervals.

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Final answer:

The periodic law states that when elements are arranged in order of increasing atomic number, their properties repeat themselves at regular intervals. This allows for the organization of elements into groups based on their similar properties on the periodic table.

Step-by-step explanation:

The periodic law states that when elements are arranged in order of increasing atomic number, their properties repeat themselves at regular intervals. This important concept is the basis for the modern periodic table, where elements are organized not by their atomic mass as initially thought, but by their atomic number.

This organization allows elements with similar chemical properties to be grouped together in columns, known as groups, and elements with the same number of valence shells to be arranged in rows, called periods. The periodic table is divided into several sections, with elements categorized as metals, metalloids, and nonmetals, as well as main-group elements, transition metals, and inner transition metals.

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