Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 73

Chapter 6, Problem 73

(d) What object is represented by the half arrows in an orbital diagram? What does the direction of the arrow signify?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

In an orbital diagram, the half arrows represent electrons. Each arrow corresponds to one electron within an orbital.

The direction of the arrow indicates the electron's spin. Electrons have a property called spin, which can be either 'up' or 'down'.

An upward-pointing arrow typically signifies an electron with a spin quantum number of +1/2, while a downward-pointing arrow signifies a spin quantum number of -1/2.

The Pauli Exclusion Principle states that no two electrons in the same atom can have identical sets of quantum numbers. Therefore, in a single orbital, one electron will have an 'up' spin and the other will have a 'down' spin.

Understanding the direction of the arrows helps in determining the electron configuration and the magnetic properties of the atom or molecule.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Orbital Diagrams

Orbital diagrams are visual representations of the electron configuration of an atom. They illustrate the distribution of electrons among the various orbitals, which are regions of space where electrons are likely to be found. Each orbital can hold a maximum of two electrons, and the diagrams help in understanding how electrons fill these orbitals according to the principles of quantum mechanics.

Half Arrows in Orbital Diagrams

In orbital diagrams, half arrows represent individual electrons within the orbitals. Each arrow points either up or down, indicating the spin of the electron, which can be either 'up' (spin +1/2) or 'down' (spin -1/2). This notation is crucial for adhering to the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers.

Direction of the Arrow

The direction of the half arrow in an orbital diagram signifies the spin of the electron. An upward-pointing arrow represents an electron with a positive spin, while a downward-pointing arrow indicates a negative spin. This distinction is important for understanding the behavior of electrons in magnetic fields and their overall contribution to the atom's magnetic properties.

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Textbook Question

(a) What are 'valence electrons'?

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For each element, indicate the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) sodium (b) sulfur.

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Textbook Question

What is the maximum number of electrons that can occupy each of the following subshells? (a) 3s, (b) 2p, (c) 4d, (d) 5s.

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Textbook Question

What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) n = 3, ml = -1; (b) n = 4, l = 2; (c) n = 4, l = 3, ml = -2; (d) n = 5, l = 2, ml = 0.

An experiment called the Stern–Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (c) Would this experiment work for a beam of fluorine (F) atoms?

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