Chapter 7, Problem 16PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Using an orbital box diagram and noble gas notation, show the electron configuration of titanium. Give one possible set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.

Interpretation Introduction

Interpretation:

The electronic configuration and quantum number of titanium (Ti) has to be derived given the statements.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons (e-) of an given molecule or respective atoms in atomic or molecular orbitals. We consider the electronic configuration of neon atom is 1s22s22p6, the electronic configurations describes each electrons as moving independently orbitals, an average filed created ay all other orbitals.

Quantum numbers: These terms are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

Explanation
1. 1. The Titanium (Ti) is the fourth period position in periodic table, it has four electrons with corresponding outer most orbital shells (n=4). Hence the (18) electrons are assigned to (Argon) and remaining electrons is assigned to (3d, 4s) electron shells.
2. 2. So this element is precedes by the noble gas argon, the electron configuration is Â [Ar]3d104s2. The electronic configuration notations are shown below.

Â Â Atomicâ€‰numberâ€‰ofâ€‰Titaniumâ€‰(Ti)â€‰â€‰â€‰â€‰=22â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰CompleteÂ (spdf)â€‰notationâ€‰ofâ€‰(Ti)â€‰â€‰â€‰â€‰=â€‰1s22s22p63s23p63d24s2â€‰â€‰â€‰OrbitalÂ fillingÂ methodâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â†‘â†“â€‰â€‰â†‘â†“â€‰â€‰â†‘â†“â†‘â†“â†‘â†“â€‰â€‰â†‘â†“â€‰â€‰â†‘â†“â†‘â†“â†‘â†“â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰1s2â€‰â€‰â€‰â€‰â€‰â€‰2s2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰2p6â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰3s2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰3p6â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â†‘â†‘â€‰â€‰â€‰â€‰â†‘â†“â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰3d2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰4s2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰spdfâ€‰withÂ nobleÂ gasÂ notationâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=Â [Ar]3d24s2â€‰â€‰â€‰â€‰â€‰[âˆµâ€‰Atomicâ€‰numberâ€‰ofâ€‰Argon=18]Orbitalâ€‰boxâ€‰notationÂ Â Â Â Â Â Â â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=Â [Ar]â€‰â†‘â†‘â€‰â€‰â€‰â€‰â†‘â†“â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰3d2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰4s2â€‰â€‰â€‰â€‰â€‰â€‰

Assigning for quantum number method: The possible sets of titanium (Ti) quantum number for (3d) electrons methods are given below,

Let us consider the (3d) orbitals in Titanium atom

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