Final answer:
Comparing atomic radii of transition metals like Fe, Ru, Mn, Tc, Co, Rh, Ru, and Os: Ru and Os have approximately the same atomic radius because they are both in group 8 of different periods but have a similar d-subshell electronic configuration.
Step-by-step explanation:
The atomic radius is a measure of the size of an atom's electron cloud, and it gives us a good indication of the size of an atom. When comparing atomic radii within the same group of the periodic table, the atomic radius increases as you move down the group. This is because additional electron shells are added, which are further from the nucleus.
For the transition metals (groups 3-12), the atomic radii do not change as uniformly. Within a given period, the atomic radii generally decrease from left to right as the effective nuclear charge increases, but across different periods, the similar electron configuration in the d-subshell results in atomic radii that are not drastically different.
Comparing the pairs given: (a) Fe and Ru, (b) Mn and Tc, (c) Co and Rh, (d) Ru and Os, we can deduce that Ru and Os have approximately the same atomic radius because they occupy similar positions in different periods of the transition metals group. In this case, while ruthenium (Ru) is in the second row of the block, osmium (Os) is right below it in the third row, which results in similar atomic radii due to the similar d-subshell electronic configuration.