7.8 – 7.9

	Chemistry 8th Edition / Chang
	Student Study Guide

Chapter 7: Quantum Theory and the Electronic Structure of Atoms

Index | 7.1 – 7.2 | 7.3 | 7.4 | 7.5 – 7.7 | 7.8 – 7.9 |

ELECTRON CONFIGURATIONS AND THE AUFBAU PRINCIPLE (7.8–7.9)

STUDY OBJECTIVES

Compare the order of orbital energies in the hydrogen atom to the order in a many-electron atom.
Use the Aufbau principle to write the electron configuration of an element.
Use Hund's rule to construct orbital diagrams for the electron configurations of elements.

The Energies of Orbitals. The way electrons are distributed among the orbitals of an atom is its electronic structure or electron configuration. Each of the principal energy levels (called shells) of an atom can be divided into subshells, which are sets of orbitals. The s subshell has one s orbital, the p subshell has three p orbitals, the d subshell has five d orbitals, and so on. In addition each subshell has an electron capacity based on a maximum of two electrons per orbital. The orbitals available to a shell and the subshell capacities are summarized in Table 7.3.

Table 7.3 Allowed Numbers of Orbitals per Energy Level

Principal
Quantum
Number Orbital Shape
l Orbital
Name Number of
Orbitals
per Subshell Electron Capacity
per Subshell

1 0 1s 1 2

2 0 2s 1 2

2 1 2p 3 6

3 0 3s 1 2

3 1 3p 3 6

3 2 3d 5 10

4 0 4s 1 2

4 1 4p 3 6

4 2 4d 5 10

4 3 4f 7 14

In a hydrogen atom all of the orbitals in a particular energy level (same n value) have the same energy. In a hydrogen atom the electron resides in the 1s orbital because it has the lowest possible energy in that orbital. The ground state electron configuration of H is 1s¹, as shown below.

Atoms of elements other than hyrogen have more than one electron and are called many-electron atoms. In these atoms each principal energy level is split into several energies. These energies correspond to the orbitals of one type having a slightly different energy than orbitals of another type. This splitting is shown in Figure 7.1. The energy of an orbital in a many-electron atom depends on both n and l. For a given value of n, the energy of orbitals increases as l increases. Therefore, for atoms other than hydrogen atoms, the 2p orbital has a higher energy than the 2s orbital.

Figure 7.1 The orbital energies in a many-electron atom. Within a shell the orbital energies increase as the l quantum number increases. The energy of an orbital depends on its n and l values. Here the 4s subshell is shown to be lower than the 3d subshell.

The order of increasing energy for orbitals within a given principal energy level is

s < p < d < f < …

This trend results from the fact that s orbitals have a greater electron density near the nucleus than p orbitals, and p orbitals have greater electron density near the nucleus than d orbitals. In a many-electron atom, the energies of the orbitals increase as follows (Figure 7.1):

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s …

Note also that the higher principal energy levels (n values) have more subshells, and as these split in energy some of these subshells can actually be lower in energy than subshells from a lower principal energy level. Thus the energy of a 4s orbital is very close to the energy of a 3d orbital in a many-electron atom. In potassium and calcium atoms the energy of the 4s orbital is less than the energy of the 3d orbital.

Electron Configurations. To write the electron configuration for the ground state of a many-electron atom, recall that the order in which subshells are occupied is from lowest energy to highest energy. The order shown in Figure 7.1 can easily be remembered by drawing Figure 7.24 of the textbook. The general approach of building up the atoms of the elements by adding a proton to the nucleus and an electron to an orbital is called the Aufbau or building up principle.

Helium has two electrons both of which can occupy the 1s orbital. The electron configuration is: He 1s². A lithium atom has three electrons. According to the Pauli principle, we can place only two electrons in the 1s orbital; the third electron must enter the next higher orbital, the 2s orbital. Its electron configuration is: Li 1s²2s¹. The electron configurations of the second period elements are:

Be 1s²2s²

With Be the 1s and 2s orbitals are filled, and so additional electrons must enter the 2p orbitals. The 2p subshell is being filled over the next six elements.

B 1s²2s²2p¹

C 1s²2s²2p²

N 1s²2s²2p³

O 1s²2s²2p⁴

F 1s²2s²2p⁵

Ne 1s²2s²2p⁶

EXAMPLE Electron Configurations

Which of the following electron configurations would correspond to ground states and which to excited states?

a. 1s²2s²2p¹

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b. 1s²2p¹

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c. 1s¹2s²2p¹3s¹

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It corresponds to a ground state.

This is an excited state.

Orbital Diagrams. The above electron configurations tend to hide information about the number of electrons in any one outer orbital. The 2p subshell consists of three 2p orbitals: 2p_x, 2p_y, and 2p_z. Therefore the capacity of the subshell is 6 electrons. If we use an orbital diagram, a choice arises about where to place the electrons. In carbon, for example, are the 2 electrons in the p subshell both in the 2p_x orbital, or are they distributed so that the 2p_x and the 2p_y each have one electron? To make the choice first we need to describe an orbital diagram.

An orbital diagram uses boxes to designate individual orbitals, and groups of boxes to designate subshells.

An arrow pointing up stands for an electron spinning in one direction, and an arrow pointing down ¯ stands for an electron spinning in the opposite direction.

The orbital diagrams for carbon and nitrogen are drawn as follows. Electrons are placed into orbitals according to Hund's rule, which states that electrons entering a subshell containing more than one orbital will have the most stable arrangement when the electrons occupy the orbitals singly, rather than in pairs. Thus carbon has one electron in the 2p_x and one in the 2p_y, rather than two electrons in the 2p_x.

According to Hund's rule, nitrogen atoms have the electrons in the 2p subshell distributed with one each in the 2p_x, 2p_y, and 2p_z.

The orbital diagram indicates the number of unpaired electrons in an atom. The presence, or absence, of unpaired electrons is detected experimentally by the behavior of a element when placed in a magnetic field. Paramagnetism is the property of attraction to a magnetic field. Diamagnetism is the property of repulsion by a magnetic field. The atoms of paramagnetic substances contain unpaired electrons. Those of diamagnetic substance contain only paired electrons. Using the three principles that have been given (Aufbau, Pauli, and Hund's rule) the electron configurations of the ground states of most atoms can be estimated.

EXAMPLE Orbital Diagrams

a. Write the electron configuration for arsenic.
As

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b. Draw its orbital diagram.

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c. Are As atoms diamagnetic or paramagnetic?

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The electron configuration of As is:

As [Ar]4s²3d¹⁰4p³

The orbital diagram for the outer orbitals is:

Noble Gas Core Abbreviations. The electron configurations of the noble gas elements can be used as abbreviations when writing electron configurations. Neon has the configuration Ne 1s²2s²2p⁶. All elements beyond neon have this configuration for the first 10 electrons. We use the symbol [Ne] to represent the configuration of the 10 electrons in neon and call it a neon core. Similarly 18 electrons arranged in the ground state of an argon atom (1s²2s²2p⁶3s²3p⁶) are called an argon core, written [Ar]. [Kr] and [Xe] cores can also be used. In practice we select the noble gas that most nearly precedes the element being considered. Therefore, calcium and strontium could be written in full or abbreviated as follows:

Ca 1s²2s²2p⁶3s²3p⁶4s² or [Ar]4s²

Sr 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s² or [Kr]5s²

EXAMPLE Electron Configurations

Write the electron configuration for a potassium atom using full notation and noble gas core abbreviations.
full notation = K
noble gas core abbreviation = K

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According to the order of orbital energies, the 3d does not fill next. Rather, the 4s orbital is lower in energy than the 3d. The last electron in potassium enters the 4s orbital. The electron configuration of potassium is:

K 1s²2s²2p⁶3s²3p⁶4s¹

or in terms of the argon core abbreviation:

K [Ar]4s¹

OBJECTIVE CHECK

Complete the following questions to check your understanding of the material. Select the check button to see if you answered correctly.

What element has atoms with the electron configuration [Xe]6s²4f¹⁴5d¹⁰6p²?
What third period element has atoms in the ground state with three unpaired electrons?
Write the electron configuration for the following atoms:
Sb
V
Pb
How many unpaired electrons do oxygen atoms have?

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Principal Quantum Number	Orbital Shape l	Orbital Name	Number of Orbitals per Subshell	Electron Capacity per Subshell

1	0	1s	1	2
2	0	2s	1	2
2	1	2p	3	6
3	0	3s	1	2
3	1	3p	3	6
3	2	3d	5	10
4	0	4s	1	2
4	1	4p	3	6
4	2	4d	5	10
4	3	4f	7	14

B	1s²2s²2p¹
C	1s²2s²2p²
N	1s²2s²2p³
O	1s²2s²2p⁴
F	1s²2s²2p⁵
Ne	1s²2s²2p⁶