Chapter 7, Problem 48GQ

### 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

# A possible excited state for the H atom has an electron in a 4p orbital. List all possible sets of quantum numbers (n, ℓ, mℓ, ms) for this electron.

Interpretation Introduction

Interpretation:

All possible set of quantum numbers for the electron in a 4p-orbital has to be listed.

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

The selected electronic configuration involves the (4s and 4p) orbitals.

In the excited electron configuration of HYDROGEN is â€‰1s02s02p03s03p03d04s04p1â€‰â€‰â€‰. Â The highest energy of electron which can either be in the Â 4px,4py,4pz orbital it can be either up or spin down, hence there are Â 2Ã—3=6 possible sets of quantum numbers. But here, only one electron is present which only get the up-spin and the possibility is Â 1Ã—3=3 sets of quantum numbers.

Let us consider (4p) orbitals in Hydrogen atom.

1. 1. Principle quantum number Â n=1,2,....n=â€‰4Â
2. 2. Angular quantum number Â l=0,1,2,....nâˆ’2â€‰=1Â
3. 3. Magnetic quantum numberÂ  Â ml={0,1,2...,Â±l}={0,â€‰Â±1}Â  so the corresponding formula Â ml=â€‰2l+1=2(1)+1=3â€‰totalÂ forÂ (4p)â€‰orbitalÂ
4. 4. Further we consider the (4p) electron shells, the (n and l ) are fixed and (ml) will as (-1, 0, +1) and spin quantum number can be Â Â±12

Â Â Finally six possible sets of quantum numbers are show below.

â€‚Â 1.(n,l,ml,ms)=â€‰â€‰â€‰(4,â€‰1,â€‰âˆ’1â€‰,+12)â€‰â€‰2.(n,l,ml,ms)=â€‰â€‰â€‰(4,â€‰1,â€‰0â€‰,+12)3.(n,l,ml,ms)=â€‰â€‰â€‰(4,â€‰1,â€‰+1â€‰,+12)â€‰

Therefore, the three possible sets of quantum number are,

â€‚Â 1.â€‰4pâ€‰orbitalâ€‰â†‘â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰4pxâ€‰â€‰â€‰â€‰4pyâ€‰â€‰4pzâ€‰â€‰â€‰mlâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰âˆ’1â€‰â€‰â€‰â€‰â€‰â€‰â€‰0â€‰â€‰â€‰â€‰â€‰â€‰â€‰+12

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