Chapter 7, Problem 47GQ

### 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

# Which of the following is not an allowable set of quantum numbers? Explain your answer briefly. For those sets that are valid, identify an element in which an outermost valence electron could have that set of quantum numbers.

Interpretation Introduction

Interpretation:

The allowable set of quantum numbers and an element in which an outermost valence electron could have that set of quantum numbers have to be identified and explained

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

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

Reason for the correct option:

• Option a):
• The principle quantum number: n = 2
• Azimuthal quantum number: l = 0, indicates the s-orbital.
• Magnetic quantum number: ml = 0, indicates orientation of s-orbitals in space of an orbital of an given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell.

For,â€‰(2l+1)=â€‰2(0)+1â€‰=â€‰1 The calculation results in the one sub-shell orbital.

• Spin quantum number: ms = -1/2, indicates the orientation of intrinsic angular momentum of an electron in an atom as (-1/2)and(+1/2). It describes the quantum state of an electron.

ms=â€‰âˆ’1/2 Indicates the electron is located as down spin.

That is,

â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰2s1principleâ€‰quantumâ€‰numberâ€‰:â€‰â€‰â€‰2Azimuthalâ€‰quantumâ€‰number:â€‰smagneticâ€‰quantumâ€‰number:â€‰oneâ€‰sub-shellâ€‰isâ€‰present.Spinâ€‰quantumâ€‰number:â€‰down-spin,(â†“â€Šâ€Š)â€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š

The orbital box diagram of the given information is;â†“â€Šâ€Šâ€Šâ€Šâ€Šâ€‰2s1, the innermost orbital 1s2 is understood and the element that Lithium and Beryllium as the both contain outer most valence electron in 2s-orbital.

Hence, the valid option is a.

• Option c:
• The principle quantum number: n = 2
• Azimuthal quantum number: l = 1, indicates the p-orbital.
• Magnetic quantum number: ml = -1, indicates orientation of s-orbitals in space of an orbital of an given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell.

For,â€‰(2l+1)=â€‰2(âˆ’1)+1â€‰=â€‰âˆ’1 The calculation results in the one of the three sub-shell orbitals.

• Spin quantum number: ms = -1/2, indicates the orientation of intrinsic angular momentum of an electron in an atom as (-1/2)and(+1/2). It describes the quantum state of an electron.

ms=â€‰âˆ’1/2 Indicates the electron is located as down spin.

That is,

â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰2p1principleâ€‰quantumâ€‰numberâ€‰:â€‰â€‰â€‰2Azimuthalâ€‰quantumâ€‰number:â€‰pmagneticâ€‰quantumâ€‰number:â€‰oneâ€‰ofâ€‰theâ€‰threeâ€‰sub-shellâ€‰isâ€‰present.Spinâ€‰quantumâ€‰number:â€‰down-spin,(â†“â€Šâ€Š)â€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š

The orbital box diagram of the given information is;

2p1â€‰â€‰â€‰â†“â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰(âˆ’1)â€‰(0)â€‰(+1)â€‰orientationâ€‰ofâ€‰pâˆ’orbitalâ€‰, the innermost orbital 1s2 2s2is understood and the element that Boron through Neon as that series contain outer most valence electron in 2p-orbital

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