Explanation:

Outer orbital configurations:
a) 3d5 4s1
b) 3d5 4s2
c) 3d2 4s2
d) 3d3 4s2

Understanding oxidation states:
Oxidation state refers to the number of electrons an atom loses, gains, or shares during a chemical reaction to form a compound. It is represented by a Roman numeral following the element symbol. The oxidation state depends on the number of valence electrons an atom has.

Determining oxidation states:
To determine the maximum number of oxidation states an element can exhibit, we need to consider the number of valence electrons.

Valence electrons:
Valence electrons are the electrons present in the outermost energy level of an atom. They are responsible for the chemical properties of an element.

Valence electrons in the given configurations:
a) 3d5 4s1 - This configuration has 1 valence electron.
b) 3d5 4s2 - This configuration has 2 valence electrons.
c) 3d2 4s2 - This configuration has 2 valence electrons.
d) 3d3 4s2 - This configuration has 2 valence electrons.

Analysis:
The element with the highest number of valence electrons has the potential to exhibit the largest number of oxidation states. In this case, option b) with 2 valence electrons has the highest number of valence electrons among the given configurations.

Reasoning:
The element in option b) with the configuration 3d5 4s2 is most likely to exhibit the largest number of oxidation states because it has the highest number of valence electrons, which allows for more possibilities of gaining or losing electrons during chemical reactions.

Conclusion:
Based on the number of valence electrons, the element with the outer orbital configuration 3d5 4s2 (option b) has the potential to exhibit the largest number of oxidation states among the given configurations.