Textbook Problem

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State which of the following orbitals cannot exist according to the quantum theory: 2s, 2d, 3p, 3f, 4f, and 5s. Briefly explain your answers.

Interpretation Introduction

Interpretation: According to quantum theory the orbitals that cannot exist should be identified from the given list of orbitals.

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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$. Each l value indicates subshell.

Explanation of Solution

The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$. Each l value indicates subshell.

When $\text{n}\text{=}2$, the values of l are, $l=\left(n-1\right)=0,1$. Each l value indicates subshell where $0$ and $1$ represents s and p orbitals. Therefore according to quantum theory $2d$ cannot exist