Chapter 11: Problem 6

Why is the situation of equal numbers of spin up and spin down electrons referred to as all the electrons being "paired"?

Short Answer

Expert verified

The situation of having equal numbers of spin up and spin down electrons in an atomic or molecular orbital is referred to as all the electrons being 'paired' because, in compliance with the Pauli Exclusion Principle, these electrons can match up/'pair' with each other, each pair having one electron with 'spin up' and the other with 'spin down'.

Step by step solution

Definition of Electron Spin

The electron is a fundamental particle that possesses an intrinsic quantum mechanical property known as spin. This property can take two forms, commonly known as 'spin up' (\(\uparrow\)) and 'spin down' (\(\downarrow\)).

Understanding Electron Pairing

Electron pairing refers to the state where two electrons in an atomic or molecular orbital, one with spin up and the other with spin down, pair up. This occurs as a result of the Pauli Exclusion Principle.

Implication of the Pauli Exclusion Principle

The Pauli Exclusion Principle, a fundamental principle in quantum mechanics, states that no two electrons in an atom can have the same four quantum numbers. Since electrons in an atomic or molecular orbital have the same three quantum numbers (n, l, m), they must have opposite spins to satisfy the Pauli Exclusion Principle.

Reason for Referring as 'Paired'

In a situation with an equal number of spin-up and spin-down electrons, all the electrons can be paired within their respective orbitals, each with one electron of 'spin up' and 'spin down'. This ensures compliance with the Pauli Exclusion Principle, so it's referred to as all the electrons being 'paired'.

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Why is the situation of equal numbers of spin up and spin down electrons referred to as all the electrons being "paired"?

Short Answer

Step by step solution

Definition of Electron Spin

Understanding Electron Pairing

Implication of the Pauli Exclusion Principle

Reason for Referring as 'Paired'

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