CHEMISTRY CHAPTER 4. ARRANGEMENT
OF ELECTRONS IN ATOMS
SECTION 1. THE DEVELOPMENT OF A
NEW ATOMIC MODEL
Properties of Light
Light is just one part of the electromagnetic spectrum , which extends from gamma rays ( γ) to radio waves.

Electromagnetic Spectrum

• Wavelength ( λ, Greek letter lambda) is the distance between corresponding points on adjacent waves. So it is measured in meters.
• Frequency ( ν, Greek letter nu) is defined as the number of waves that pass a given point in a specific time, usually one second. It is measured in s -1 , or 1/s.

Frequency and wavelength are related: c = λν where c is the speed of light (in m/s), λ is the wavelength (in m), and ν is the frequency (in s
−1
).
Since c is a constant, λ is
____________ proportional to ν.

Frequency and wavelength are related: c = λν where c is the speed of light (in m/s), λ is the wavelength (in m), and ν is the frequency (in s
−1
).
Since c is a constant, λ is inversely proportional to ν.

Wavelength and Frequency

The Photoelectric Effect
The photoelectric effect refers to the emission of electrons from a metal when light shines on the metal.
The Particle Description of Light
A quantum of energy is the minimum quantity of energy that can be lost or gained by an atom.

Photoelectric Effect

Photoelectric Effect
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Quantization of Energy
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• German physicist Max Planck proposed the following relationship between a quantum of energy and the frequency of radiation:
E = h ν
• E is the energy, in joules, of a quantum of radiation
• ν is the frequency, in s
−1
, of the radiation
• h is a fundamental physical constant now known as Planck’s constant
• h = 6.626 × 10 −34 J• s.

• A photon is a particle of electromagnetic radiation having zero mass and carrying a quantum of energy.
• The energy of a particular photon depends on the frequency of the radiation.
E photon
= hν

Energy of a Photon
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Line-Emission Spectrum
• It was found that each kind of atom, when heated or exposed to electric current, gave off only certain wavelengths of light.
• This means that only certain energies of radiation are produced.

• The set of wavelengths of emitted light are the line-emission spectrum.
• These come from electrons moving from higher energy states
( excited states ) to lower energy states.
• The lowest, most stable state is the ground state .

Hydrogen’s Line-Emission Spectrum

Absorption and Emission
Spectra
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Bohr Model of the Hydrogen Atom
• Niels Bohr proposed a hydrogen-atom model that linked the atom’s electron to photon emission.
• According to the model, the electron can circle the nucleus only in allowed paths, or orbits.
• The energy of the electron is higher when the electron is in orbits that are successively farther from the nucleus.

Bohr Model of the Atom
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• When an electron falls to a lower energy level, a photon is emitted, and the process is called emission.
• Energy must be added to an atom in order to move an electron from a lower energy level to a higher energy level.
This process is called absorption.

Photon Emission and Absorption

• The Bohr model can explain the spectra of hydrogen atoms, but cannot explain the spectra of more complicated atoms.
• A better model was needed.

Comparing Models of the Atom
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SECTION 2. THE QUANTUM MODEL
OF THE ATOM
Electrons as Waves
• French scientist Louis de Broglie suggested that electrons be considered waves confined to the space around an atomic nucleus.
• Since electrons have specific energies, the waves must have specific energies
(described by the equation E = h ν ).

wikipedia
Louis de
Broglie
Nobel Prize in
Physics, 1929

De Broglie and the Wave-
Particle Nature of Electrons
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The Heisenberg Uncertainty Principle
• The Heisenberg uncertainty principle (proposed by German physicist Werner Heisenberg) states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

A policeman stops Heisenberg for speeding. “Do you know how fast you were going?”

http://mathematicianspictures.com/Physics_Mugs_p01.htm

The Schrödinger Wave Equation
• In 1926, Austrian physicist Erwin
Schrödinger developed an equation that treated electrons in atoms as waves and described their positions.
• We can only know the probability of finding an electron in a given place.

• Together with the Heisenberg uncertainty principle, the
Schrödinger wave equation laid the foundation for modern quantum theory.
• Quantum theory describes mathematically the wave properties of electrons and other very small particles.

• Electrons do not travel around the nucleus in neat orbits, as in the Bohr model. Instead, they exist in certain regions called orbitals.
• An orbital is a three-dimensional region around the nucleus that indicates the probable location of an electron.

Electron Cloud
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Atomic Orbitals and Quantum
Numbers
• Orbitals are designated by q uantum numbers.
• Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals.

1. The principal quantum number, symbolized by n, indicates the main energy level occupied by the electron.
• The lower the number, the lower the energy of the electrons and the closer they are to the nucleus.
• For each value of n , there are n 2 orbitals.

• Each orbital can hold a maximum of 2 electrons.
• So the energy level can hold a maximum of ____ electrons.
How many electrons can fit in: n = 1?
n = 3?

• Each orbital can hold a maximum of 2 electrons.
• So the energy level can hold a maximum of 2n 2 electrons.
How many electrons can fit in: n = 1? n = 3?
2n 2 = 2∙1 2 = 2 2n 2 = 2∙3 2 = 18

2.
The angular momentum quantum number, symbolized by l, indicates the shape of the orbital.
• These are most commonly referred to by the letters in the table, and are known as sublevels.
l
0
1
2
3 letter s p d f

Shapes of s, p, and d Orbitals

• Each main energy level ( n ) can hold n different values of l : n possible values of l
1 0 (s)
2 0, 1 (s, p)
3 0, 1, 2 (s, p, d)
4 0, 1, 2, 3 (s, p, d, f)

3. The magnetic quantum number, symbolized by m, indicates the orientation of an orbital around the nucleus.
Number of possible orientations (values of magnetic quantum number, m ): l
0 (s)
1 (p)
2 (d)
3 (f) number
1
3
5
7 description spherical along x, y, and z axes see Fig. 15

Orientations of p orbitals ntu.ac.uk

Orientations of d orbitals chem.ufl.edu

4. The spin quantum number has only two possible values —(+1/2 , −1/2)— which indicate the two fundamental spin states of an electron in an orbital.
• For electrons in the same orbital (same values of n , l , and m ), the spins must be opposite.
• So each orbital can hold only two electrons .

Quantum Numbers and Orbitals
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Electrons Accommodated in Energy
Levels and Sublevels

SECTION 3. ELECTRON
CONFIGURATIONS
Electron Configurations
• The arrangement of electrons in an atom is known as the atom’s electron configuration.
• The lowest-energy arrangement of the electrons for each element is called the element’s ground-state electron configuration.

Electron Configuration
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Rules Governing Electron Configurations
There are three rules that determine how electrons fill orbitals in the ground-state.
1. (The Aufbau principle ) An electron occupies the lowestenergy orbital that can receive it.

Relative Energies of Orbitals

Note that beginning with n=3, the energies of the main energy levels overlap.
Example – 4s is lower than 3d.
The order of filling is:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, etc. (see Fig. 19 also)

macro.lsu.edu

Aufbau Principle
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2. According to the Pauli exclusion principle, no two electrons in the same atom can have the same set of four quantum numbers.
So there can only be 2 electrons in an orbital, with opposite spins.

Pauli Exclusion Principle
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3. ( Hund’s rule ) If orbitals have equal energy, one electron will go into each before a second electron is added to any of them.
The electrons in the orbitals with only one electron each will have the same spin.

Representing Electron Configurations
Orbital Notation
• An unoccupied orbital is represented by a line, with the orbital’s name written underneath the line.
• An orbital containing one electron is represented as: 

• An orbital containing two electrons is represented as: 
• The lines are labeled with the principal quantum number and sublevel letter. For example, the orbital notation for helium is written as follows:
He

1 s

Orbital Notation
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Electron-Configuration Notation
• A simpler way is just to use a superscript to give the total number of electrons in each sublevel.
• Example: the helium configuration is represented by 1 s 2 .
• The superscript indicates that there are 2 electrons in helium’s 1 s orbital.

Reading Electron-Configuration
Notation
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Sample Problem A
The electron configuration of boron is 1 s 2 2 s 2 2 p 1 .
How many electrons are present in an atom of boron?
What is the atomic number for boron?
Write the orbital notation for boron.

The number of electrons in a boron atom is equal to the sum of the superscripts in its electronconfiguration notation: 2 + 2 + 1 = 5 electrons.
The number of protons equals the number of electrons in a neutral atom. So we know that boron has 5 protons and thus has an atomic number of 5.

To write the orbital notation, first draw the lines representing orbitals.
Next, add arrows showing the electron locations. The first two electrons occupy n = 1 energy level and fill the 1 s orbital.

1 s 2 s
2 p

The next three electrons occupy the n = 2 main energy level. Two of these occupy the lower-energy
2 s orbital. The third occupies a higher-energy p orbital.
  
1 s 2 s
2 p

Elements of the Second Period
• The organization of the periodic table is determined by how the electrons fill the orbitals.
• In the first-period elements, hydrogen and helium, electrons occupy the orbital of the first main energy level.

• According to the Aufbau principle, after the 1 s orbital is filled, the next electron occupies the s sublevel in the 2 nd main energy level.
• In the second period (Li = 3 to Ne
= 10), the 2s and 2p orbitals are filled (8 electrons are added). (see
Table 3)

Writing Electron Configurations

Elements of the Third Period
• After the outer octet in energy level 2 is filled in neon, the next electron enters the s sublevel in the n = 3 main energy level.
• In the third period (Na = 11 to Ar
= 18), the 3s and 3p orbitals are filled (8 electrons added) (Tab. 5)

Elements of the Fourth Period
• K = 19 to Kr = 36: 18 electrons are added (Tab. 5)
• The period begins by filling the 4 s orbital because it is lower in energy than 3d.
• The 3d orbitals are then filled (10 electrons).
• Next in energy are the 4p orbitals
(6 electrons)

Elements of the Fifth Period
• In the 18 elements of the fifth period
(Rb = 37 to Xe = 54), sublevels fill in a similar manner as in elements of the fourth period (Tab. 6).
• Successive electrons are added first to the 5 s orbital, then to the 4 d orbitals, and finally to the 5 p orbitals.

Elements of the Sixth and Seventh
Periods
• In the 32 elements of the sixth period (Cs = 55 to Rn = 86), successive electrons are added to the 6s, 4f, 5d, and 6p orbitals.
• In the elements of the seventh period (Fr = 87 and higher), electrons are added to the 7s, 5f,
6d, and 7p orbitals.

Noble-Gas Notation
• The Group 18 elements (helium, neon, argon, krypton, xenon, and radon) are called the noble gases. Each period ends with a noble gas.
• A noble-gas configuration refers to an outer main energy level occupied, in most cases, by 8 electrons.

The symbol for a noble gas, in brackets, is used to abbreviate that part of the configuration.
Example: Ne = 1s 2 2s 2 2p 6
Al = 1s 2 2s 2 2p 6 3s 2 3p 1
The first part is the same as
Ne, so it is abbreviated:
Al = [Ne]3s 2 3p 1

Orbital Notation for Three Noble Gases

Noble-Gas Notation
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Solvay Conference, Brussels, 1927