The question asks us to identify the pair of elements that have similar atomic radii. To determine this, we need to understand and consider the periodic trends and the placement of these elements in the periodic table.
Periodic Trends:
Atomic radius generally decreases across a period from left to right, due to an increase in nuclear charge attracting the electrons closer to the nucleus.
The atomic radius generally increases down a group as additional electron shells are added.
Analysis of Options:
Sc and Ni: Scandium (Sc) and Nickel (Ni) are both transition metals, but they are not adjacent in the periodic table and have different electron configurations, leading to different atomic radii.
Ti and Hf: Titanium (Ti) and Hafnium (Hf) are in different periods; while it's true that elements in a group often have similar properties, their atomic radii differ more significantly due to the presence of additional electron shells in Hafnium.
Mo and W: Molybdenum (Mo) and Tungsten (W) are both located in group 6 of the periodic table and are both transition metals. They are known for having similar chemical and physical properties due to being in the same group, which includes having similar atomic radii.
Mn and Re: Manganese (Mn) and Rhenium (Re) are also in the same group, but Re, being in a further period, has a markedly larger atomic radius due to additional electron shells.
Conclusion: The pair that has similar atomic radii is Molybdenum (Mo) and Tungsten (W). This similarity is due to their placement in the same group and close periods on the periodic table, where despite increasing atomic number, the addition of electron shells and effective nuclear charge leads to comparable atomic sizes.