   Chapter 6, Problem 30PS

Chapter
Section
Textbook Problem

A possible excited state for the H atom has an electron in a 5d orbital. List all possible sets of quantum numbers n, ℓ, and mℓ for this electron.

Interpretation Introduction

Interpretation: The possible set of quantum number for an excited H atom whose electron is in 5d orbital has to be identified.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

For an orbital ns, the principal quantum number is n

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell

The values of ml when the orbital angular quantum number is l are from l to +l.

Explanation

Principle quantum number is represented by n and for an orbital ns, the principal quantum number is n

Hence, for the orbital 5d, the principal quantum number, n=5

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell. For d subshell, l=2.

The values of ml when the orbital angular quantum number is l are from l to +l.

When l=2, the values of ml are, ml=2,1,0,1,2. Since there are five ml values, five set of quantum numbers are possible.

1. i. n=5, l=2 and ml=2
2. ii

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