Give the electron configuration and the number of unpaired electrons for (a) \(\mathrm{Cr}^{3+} ;\) (b) \(\mathrm{Ti}^{4+} ;\) (c) \(\mathrm{Co}^{3+} ;\) (d) \(\mathrm{Ta}^{2+}\).

The atomic number is a fundamental property of any element. It represents the number of protons in the nucleus of an atom. For example, in the exercise, Chromium (Cr) has an atomic number of 24. This means it has 24 protons. The atomic number is crucial because it determines the element's identity and its position in the periodic table.
Moreover, knowing the atomic number helps us understand the electron configuration of the neutral atom, which is the next step in determining the configuration of ions.
For Titanium (Ti), the atomic number is 22, indicating 22 protons. Similarly, Cobalt (Co) has an atomic number of 27 and Tantalum (Ta) has 73. Each element's unique atomic number makes it distinctive and defines its chemical behavior.

A neutral atom is one where the number of protons equals the number of electrons. In this state, the electrical charges balance out, making the atom neutral.
Understanding the electron configuration for a neutral atom is essential as it forms the basis for understanding the configurations of ions. For instance, the electron configuration for a neutral Chromium atom is \[ [Ar] 3d^{5} 4s^{1} \]. This arrangement changes once it becomes an ion.
The neutral Titanium atom configuration is \[ [Ar] 3d^{2} 4s^{2} \]. For Cobalt, it’s \[ [Ar] 3d^{7} 4s^{2} \], and for Tantalum, it is \[ [Xe] 4f^{14} 5d^{3} 6s^{2} \]. These initial configurations allow us to systematically remove electrons when forming positively charged ions.

Ions are atoms or molecules that have gained or lost one or more electrons, giving them a net charge. Positive ions (cations) form when an atom loses electrons. The exercise involves converting neutral atoms into their ionic states and adjusting their electron configurations accordingly.
For example, Chromium loses 3 electrons to form \[ Cr^{3+} \], resulting in the electron configuration \[ [Ar] 3d^{3} \].
Titanium forms \[ Ti^{4+} \] by losing 4 electrons, leading to \[ [Ar] 3d^{0} \]. Cobalt loses 3 electrons to form \[ Co^{3+} \], resulting in \[ [Ar] 3d^{6} \]. Finally, Tantalum forms \[Ta^{2+}\] by losing 2 electrons, giving \[ [Xe] 4f^{14} 5d^{3} 6s^{0} \].
Understanding these ion forms is vital for predicting and explaining chemical reactions and properties.

Unpaired electrons are those electrons that occupy an orbital alone, without a paired partner. These electrons play a significant role in the chemical and magnetic properties of an atom or ion.
In the given exercise, determining the number of unpaired electrons helps us understand the behavior of the ions. For instance, \[ Cr^{3+} \] has 3 unpaired electrons in the \[ 3d^{3} \] orbital set.
Similarly, \[ Ti^{4+} \] has no unpaired electrons as its configuration is \[ 3d^{0} \]. The \[ Co^{3+} \] ion has 4 unpaired electrons in the \[ 3d^{6} \] configuration. Lastly, \[ Ta^{2+} \] has 3 unpaired electrons in the \[ 5d^{3} \] orbital.
Recognizing unpaired electrons helps in predicting magnetic properties and reactivity of the elements.