Among the following series of transition metal ions, the one where all metal ions have same \(3 d\) electronic configuration is: (a) \(\mathrm{Ti}^{2+}, \mathrm{V}^{3+}, \mathrm{Cr}^{4+}, \mathrm{Mn}^{5+}\) (b) \(\mathrm{Ti}^{3+}, \mathrm{V}^{2+}, \mathrm{Cr}^{3+}, \mathrm{Mn}^{4+}\) (c) \(\mathrm{Ti}^{+}, \mathrm{V}^{4+}, \mathrm{Cr}^{6+}, \mathrm{Mn}^{7+}\) (d) \(\mathrm{Ti}^{4+}, \mathrm{V}^{3+}, \mathrm{Cr}^{2+}, \mathrm{Mn}^{3+}\)

D-block elements, often known as transition metals, are a distinctive group in the periodic table that include elements from Groups 3 to 12. These elements are characterized by the filling of their d-orbitals with electrons.

One of the fascinating aspects of d-block elements is their tendency to form colored compounds, display variable oxidation states, and have magnetic properties. This is largely due to the arrangement of electrons in their d-orbitals. Unlike the s-block elements where only one or two outermost s-orbital electrons are present, the number of electrons in the five d-orbitals of transition metals can vary from 1 to 10.

Transition metals typically have a higher density and melting points when compared to s-block elements. Their ability to form various compounds comes from the incomplete filling of the d-orbitals which allows for a diverse range of oxidation states and coordination compounds.

Understanding electron configuration is essential when studying transition metal ions. It denotes the distribution of electrons among the orbitals of an atom. In a neutral atom, electrons are added according to the Aufbau principle, which states that electrons occupy the lowest energy orbital available.

The typical electronic configuration of transition metals consists of electrons in the outermost s-orbital and then in the five d-orbitals. For example, the ground state electronic configuration of titanium (Ti) is 4s23d2. However, when these elements form ions, the electrons from the s-orbital are removed first before the d-electrons. This is because the s-orbitals have a slightly higher energy than the d-orbitals for ions. This step is crucial in understanding the properties of transition metal ions and predicting their behavior in various chemical reactions.

Ionization involves the removal of one or more electrons from an atom to form an ion. The charges on transition metal ions are indicative of their oxidation states, which are linked to the number of electrons removed from the metal atom.

In transition metals, the number of electrons present in the outer s-orbital and d-orbitals can lead to a variety of oxidation states, since these elements can lose different numbers of electrons. For example, manganese (Mn) can exhibit oxidation states from +2 to +7, each of which corresponds to a different arrangement of electrons around the Mn nucleus. The specific oxidation state that a transition metal ion adopts in a compound affects the compound's reactivity, color, and magnetic properties.

When solving problems related to transition metal ions, like in the exercise provided, recognizing different possible ionization states is key. The exercise required identifying the series where all metal ions have the same 3d electronic configuration, thus the oxidation states and the initial electron configuration need to be considered to correctly solve such problems.