   # What is the maximum number of s orbitals found in a given electron shell? The maximum number of p orbitals? Of d orbitals? Of f orbitals? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 6, Problem 50GQ
Textbook Problem
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## What is the maximum number of s orbitals found in a given electron shell? The maximum number of p orbitals? Of d orbitals? Of f orbitals?

Interpretation Introduction

Interpretation: The maximum number of orbitals for s, p, d and f orbitals should 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.

The values of l (azimuthal quantum number) when the principal quantum number is n are from 0 to (n1). Each value of l indicates subshell and for l=0,2 and 3 represents s, d and f subshells.

In a subshell there are (2l+1) number of orbital.

### Explanation of Solution

• Each value of l indicates subshell and for s subshells, l=0. In a subshell there are (2l+1) number of orbital. Therefore, there is only ((2×0)+1)=1 orbital for s subshells.
• Each value of l indicates subshell and for p subshells, l=1. In a subshell there are (2l+1) number of orbital. Therefore, there are ((2×1)+1)=3 orbitals for p subshells.
• Each value of l indicates subshell and for d subshells, l=2

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