   Chapter 7, Problem 48GQ

Chapter
Section
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 1s02s02p03s03p03d04s04p1.  The highest energy of electron which can either be in the  4px,4py,4pz orbital it can be either up or spin down, hence there are  2×3=6 possible sets of quantum numbers. But here, only one electron is present which only get the up-spin and the possibility is  1×3=3 sets of quantum numbers.

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

1. 1. Principle quantum number  n=1,2,....n=
2. 2. Angular quantum number  l=0,1,2,....n2=1
3. 3. Magnetic quantum number   ml={0,1,2...,±l}={0,±1}  so the corresponding formula  ml=2l+1=2(1)+1=3total for (4p)orbital
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  ±12

Finally six possible sets of quantum numbers are show below.

1.(n,l,ml,ms)=(4,1,1,+12)2.(n,l,ml,ms)=(4,1,0,+12)3.(n,l,ml,ms)=(4,1,+1,+12)

Therefore, the three possible sets of quantum number are,

1.4porbital4px4py4pzml10+12

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