Final answer:
The atomic radii of Mn and Cu are almost the same due to their similar electron configuration in the valence shells, with both having a single s electron and being influenced by periodic tablerelated stabilities.
Step-by-step explanation:
The atomic radius of Mn (manganese) and Cu (copper) are almost the same primarily because they both have a similar electron configuration in their valence shells, which consists of a single s electron. The valence shell electron configuration is a significant factor influencing the chemistry of elements. Moreover, electron configurations of elements provide the basis for the organization of the periodic table, where elements in the same column typically have similar properties. However, the specific detail that Mn and Cu have nearly identical atomic radii despite having different atomic numbers is due to their positions in the periodic table where Cu represents an exception with a completely filled 3d subshell and Mn preceding the half-filled subshell.