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The atomic numbers on the periodic table represent the number of protons in an atom's nucleus and determine the element's identity. The order of appearance of elements on the periodic table is based on the increasing atomic numbers. However, there are instances where the order of appearance does not strictly follow the increasing atomic numbers. This occurs because the periodic table is organized to group elements with similar chemical and physical properties together, rather than strictly adhering to the numerical order.

The periodic table is arranged in a way that emphasizes the underlying patterns and trends in the properties of elements. As a result, elements with similar properties are grouped together in the same column, forming families or groups. This arrangement helps to highlight the similarities and trends in the behavior of elements within a group.

In some cases, the periodic table arranges elements out of strict numerical order to maintain the grouping of elements with similar properties. This is particularly evident in the transition metals, where elements are placed based on their electron configurations and the filling of electron orbitals. As a result, certain elements with higher atomic numbers may be placed before elements with lower atomic numbers to maintain the overall structure of the periodic table.

The goal of organizing elements in this way is to provide a visual representation of the periodic trends and to facilitate the understanding of the periodicity of properties. It allows scientists to quickly locate elements with similar characteristics and predict the behavior of unknown elements based on their position in the table.

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