Chapter 2, Problem 2A.8E

(a)

Interpretation Introduction

Interpretation:

The ground-state electronic configuration of isoelectronic ${\text{Ti}}^{2+}$, ${\text{V}}^{3+}$ and $\text{Ca}$ ion has to be written and difference if any has to be explained.

Concept Introduction:

The fundamental principles that are followed to write an electronic configuration include three rules as follows:

Electron in a $s$ orbital is relatively low in energy than a ${\text{p}}_{\text{x}}$ electron because the $s$ orbital is in nearer vicinity of nucleus than ${\text{p}}_{\text{x}}$ orbital. This is basis of Aufbau rule that suggests electrons occupy orbitals in order so that lowest energy orbital gets filled first. For instance the order is illustrated as follows:

Hund’s rule suggests electrons are not allowed to be paired up until each degenerate set of orbital has got at least one electron.

Pauli Exclusion Principle states two electrons within the same orbital cannot possess same set for four possible quantum numbers. Quantum-mechanical equivalent for this state means that two electrons are not allowed to have the same space simultaneously. Since one electron may certain discrete same set of n, l and m values, however, the fourth spin quantum number should be different. This provides a unique address to every electron. Since the possible magnitudes of spin can be either +1/2 or -1/2 thus at maximum two electrons can occupy any given orbital.

(b)

Interpretation Introduction

Interpretation:

Number of unpaired electrons in $\text{Ca}$, ${\text{V}}^{3+}$ and ${\text{Ti}}^{2+}$ has to be given.

Concept Introduction:

Refer to part (a).

(c)

Interpretation Introduction

Interpretation:

Neutral atom that has the same electron configuration as ${\text{Ti}}^{3+}$ has to be given.

Concept Introduction:

Refer to part (a).