Electron in atoms

In the early twentieth century, scientists accepted the idea that an atom consisted of a massive, positively charged nucleus surrounded by negatively charged electrons. Further explanation of the atom s electron arrangement came from research involving light and its interaction with matter. 

Electromagnetic waves, along with water waves and sound waves, exhibit certain common characteristics. All waves consist of a series of crests and troughs that travel away from their source at a velocity that is determined by the nature of the wave and the material through which the wave passes. The rate of vibration of a wave is called its frequency and is defined as the number of waves that pass a given point per second. Wave frequency is expressed in hertz (Hz) one hertz equals one wave per second (s ). 

The frequency and velocity of a wave determine its wavelength, the distance between equivalent points on a continuous wave. For waves of a given velocity, a wave with a higher frequency has a shorter wavelength. For electromagnetic waves, this inverse relation is expressed mathematically by the following equation. 

In this equation, c equals 3.00 X 10 m/s, the velocity of electromagnetic waves in a vacuum A, equals the wavelength in meters and V is the frequency of the waves in hertz. 

A helium-neon laser emits fight with a wavelength of 633 nm. 

The main purpose of this book is the discussion of bonding in several important classes of molecules. Before starting this discussion, we shall review briefly the pertinent details of atomic structure. Since in our opinion the modern theories of atomic structure began with the ideas of Niels Bohr, we start with the Bohr theory of the hydrogen atom. 

Bohr pictured the electron in a hydrogen atom moving in a circular orbit about the proton (see Fig. 1-1). Note that in Fig. 1-1, me represents the mass of the electron, m the mass of the nucleus, r the radius of the circular orbit, and v the linear velocity of the electron. 

For a stable orbit, the following condition must be met the centrifugal force exerted by the moving electron must equal the combined forces of attraction between the nucleus and the electron  

There are two attractive forces tending to keep the electron in orbit the electric force of attraction between the proton and the electron, 

Equating (1-1) and (1-2), we have the condition for a stable orbit, which is 

This chapter is devoted to the electronic structure of atoms. 

We examine at first an one-electron atom. A state of the electron is described by quantum numbers. We consider a more complex problem of a multi-electron atom further and turn our attention to theories that describe the many-body problem. 

Hartree and V.A. Fock made an important contribution to the science of systems consisting of a large number of electrons and nuclei. We review the Hartree theory, which gives an approximation method for the determination of the ground-state eigenfunction and the corresponding eigenvalue of a many-body quantum system. 

Finally, we will reintroduce the atomic structures of chemical elements. 

Although a detailed discussion of the placement of electrons in atoms determines how the atoms behave chemically and, therefore, the chemical properties of each element, it is beyond the scope of this chapter to discuss electronic strnctnre in detail. Several key points pertaining to this subject are mentioned here. 

Electrons in atoms are present in orbitals in which the electrons have different energies, orientations in space, and average distances from the nnclens. Each orbital may contain a maximum of two electrons. The placement of electrons in their orbitals determines the chemical behavior of an atom in this respect, the outermost orbitals and the electrons contained in them are the most important. These outer electrons are the ones beyond those of the immediately preceding noble gas in the periodic table. They are of particular importance because they become involved in the sharing and transfer of electrons through which chemical bonding occurs that results in the formation of huge numbers of different substances from only a few elements. 

Much of environmental chemistry and water chemistry are concerned with electrons in atoms. In the atmosphere, the absorption of electromagnetic radiation, primarily ultraviolet radiation, promotes electrons to higher energy levels, forming reactive excited species and reactive free radicals with unpaired electrons. These phenomena can result in photochemical reactions such as the formation of stratospheric ozone, which is an essential filter for solar ultraviolet radiation. Atomic absorption and emission methods of elemental analysis, important in the study of pollutants, involve transitions of electrons between energy levels. 

Lewis symbol of carbon Lewis symbol of argon FIGURE 19.4 Lewis symbols of carbon and argon. 

The quantized nature of energy transitions is related to the energy states of electrons in atoms and molecules. 

Use a spreadsheet to calculate the wavelengths of the lines In the Balmer, Lyman and Paschen series. Plot them against the value of m. 

Experimental evidence to support theories - emission spectra provide evidence for the existence of energy levels 

Johann Balmer was a German mathematics teacher who measured the distances between the lines in the emission spectrum of atomic hydrogen. In 1885 he produced an empirical relationship relating all the emission lines of the atomic hydrogen spectrum. The wavelength of the lines is given by the following relationship  

In this relationship, m is an integer greater than 2, with each value of m representing a different spectral line. Balmer was able to predict the wavelength of some spectral lines that were in the near ultraviolet range. The success of Balmer s equation was strengthened when other spectral series of emission lines were discovered in the ultraviolet (Lyman series) and in the infrared (Paschen series). The lines in their series could be determined by modified Balmer equations  

In Section 1.5, it was noted that electrons form a cloud of negative charge around the nucleus of an atom. The energy levels, orientations in space, and behavior of electrons vary with the numbm of them contained in an atom. In a gen al sense, the arrangements of electrons in atoms are described by electron configuration, a term discussed in some detail later in this chapter. 

The electrons in an atom are held around the nucleus by the attraction between their negative charges and the positive charges of the protons in the nucleus. Opposite electrical charges attract, and like charges repel. The forces of attraction and repulsion are expressed quantitatively by Coulomb s law  

Coulomb s law explains the attraction between negatively charged electrons and the positively charged nucleus in an atom. However, the law does not explain why electrons move around the nucleus, rather than coming to rest on it. The behavior of electrons in atoms—as well as the numbers, types, and strengths of chemical bonds formed between atoms— is explained by quantum theory, a concept that is discussed in some detail in Sections 3.11-3.16. 

Why are some fireworks red, some white, and others blue The key to understanding the chemical behavior of fireworks, and all matter, lies in understanding how electrons are arranged in atoms of each element. 

Visit the Chemistry Web site at chemistrymc.com to find links about electrons in atoms. 

The colorful display from fireworks is due to changes in the electron configurations of atoms. 

It s your birthday, and there are many wrapped presents for you to open. Much of the fun is trying to figure out what s inside the package before you open it. in trying to determine the structure of the atom, chemists had a simiiar experience. How good are your skiiis of observation and deduction  

Using as many observation methods as you can, and without unwrapping or opening the box, try to figure out what the object inside the box is. 

During the latter part of the nineteenth century, it was realized that many phenomena involving electrons in sohds could not be explained in terms of classical mechanics. What followed was the establishment of a set of principles and laws that govern systems of atomic and subatomic entities that came to be known as quantum mechanics. An understanding of the behavior of electrons in atoms and crystalline solids necessarily involves the discussion of quantum-mechanical concepts. However, a detailed exploration of these principles is beyond the scope of this text, and only a very snperficial and simplified treatment is given. 

One early outgrowth of quantmn mechanics was the simplified Bohr atomic model, in which electrons are assumed to revolve aroimd the atomic nucleus in discrete orbitals, and the position of any particnlar electron is more or less well defined in terms of its orbital. This model of the atom is represented in Figme 2.1. 

the Bohr model represents an early attempt to describe electrons in atoms, in terms of both position (electron orbitals) and energy (quantized energy levels). 

Rgure 2.2 (a) The first three electron energy states for the Bohr hydrogen atom. 

In wave mechanics, every electron in an atom is characterized by four parameters called quantum numbers. The size, shape, and spatial orientation of an electron s probability density (or orbital) are specified by three of these quantum numbers. Furthermore, Bohr energy levels separate into electron subshells, and quantum numbers dictate the number of states within each subshell. Shells are specified by a principal quantum number n, which may take on integral values beginning with unity sometimes these shells are designated by the letters K, L, M, N, O, and so on, which correspond, respectively, to n = 1, 2, 3, 4, 5,. . . , as indicated in Table 2.1. Note also that this quantrrm 

Orange light has a frequency of 4.8 x 1014 s-1. What is the energy of one quantum of orange light  

A radio station emits radiation at a wavelength of 2.90 m. What is the station s frequency in megahertz  

Record the frequency of your favorite radio station. What is the wavelength of the radiation emitted from the station  

Which element has the ground-state electron configuration [Kr]5s24d105p4  

8-2 Prelude to Quantum Theory Qrbitals of the Hydrogen Atom 

8-3 Energy Levels, Spectrum, and Ionization Energy of the Hydrogen 8-8 Electron Spin A Fourth Quantum Number 

8-5 8-6 Wave Mechanics Quantum Theory of the Hydrogen Atom Periodic Table 

This image of two neurons (gray objects) is produced by an electron microscope that relies on the wave properties of electrons discussed in this chapter. 

At the end of the nineteenth century, some observers of the scientific scene believed that it was nearly time to close the books on the field of physics. They thought that with the accumulated knowledge of the previous two or three centuries, the main work left to be done was to apply this body of physics—classical physics—to such fields as chemistry and biology. 

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When the states P1 and P2 are described as linear combinations of CSFs as introduced earlier ( Fi = Zk CiKK), these matrix elements can be expressed in terms of CSF-based matrix elements < K I eri IOl >. The fact that the electric dipole operator is a one-electron operator, in combination with the SC rules, guarantees that only states for which the dominant determinants differ by at most a single spin-orbital (i.e., those which are "singly excited") can be connected via electric dipole transitions through first order (i.e., in a one-photon transition to which the < Fi Ii eri F2 > matrix elements pertain). It is for this reason that light with energy adequate to ionize or excite deep core electrons in atoms or molecules usually causes such ionization or excitation rather than double ionization or excitation of valence-level electrons the latter are two-electron events. 

The molecular orbital approach to chemical bonding rests on the notion that, as electrons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. Just as our first task in writing the electron configuration of an atom is to identify the atomic orbitals that aie available to it, so too must we first describe the orbitals available to a molecule. In the moleculai orbital method this is done by representing molec-ulai orbitals as combinations of atomic orbitals, the linear combination of atomic orbitals-molecular orbital (LCAO-MO) method. 

The fourth quantum number is called the spin angular momentum quantum number for historical reasons. In relativistic (four-dimensional) quantum mechanics this quantum number is associated with the property of symmetry of the wave function and it can take on one of two values designated as -t-i and — j, or simply a and All electrons in atoms can be described by means of these four quantum numbers and, as first enumerated by W. Pauli in his Exclusion Principle (1926), each electron in an atom must have a unique set of the four quantum numbers. 

We now know that electrons in atoms can hold only particular energies and that their probable whereabouts are described by Schrodiiiger s wave function. The energies and probable locations depend on integer numbers, or quantum numbers. Quantum numbers describe the energy and geometry of the possible electronic states of an atom. These states, in turn, deteriiiilie the chemical behavior of the elements—that is, how chemical bonds can form. 

Group No. of Electrons in Atom Charge of Ion Formed Examples... 

Scientists in the 1920s, speculating on this problem, became convinced that an entirely new approach was required to treat electrons in atoms and molecules. In 1924 a young French scientist, Louis de Broglie (1892-1987), in his doctoral thesis at the Sorbonne made a revolutionary suggestion. He reasoned that if light could show the behavior of particles (photons) as well as waves, then perhaps an electron, which Bohr had treated as a particle, could behave like a wave. In a few years, de Broglie s postulate was confirmed experimentally. This led to the development of a whole new discipline, first called wave mechanics, more commonly known today as quantum mechanics. 

For many purposes, electron configurations are sufficient to describe the arrangements of electrons in atoms. Sometimes, however, it is useful to go a step further and show how electrons are distributed among orbitals. In such cases, orbital diagrams are used. Each orbital is represented by parentheses (), and electrons are shown by arrows written f or, depending on spin. 

The valence electrons in a molecule are distributed among the available molecular orbitals. The process followed is much like that used with electrons in atoms. In particular, we find the following ... 

Quantum mechanical model, 138-139 Quantum number A number used to describe energy levels available to electrons in atoms there are four such numbers, 140-142,159q electron spin, 141 orbital, 141... 

Brickstock, A., and Pople, J. A., Phil. Mag. 43, 1090, The spatial correlation of electrons in atoms and molecules. II. Two-electron systems in excited states. ... 

Daudel, R., Brion, H., and Odiot, S., J. Chem. Phys. 23, 2080, Localizability of electrons in atoms and molecules—application to the study of the notion of shell and of the nature of chemical bonds." Decomposition of the space of an electronic system into small parts where there is a very large probability of finding one and only one electron of a given spin. Discussion of the positional correlation between only one sort of spin, not that of two sorts of spin. 

As soon as we start this journey into the atom, we encounter an extraordinary feature of our world. When scientists began to understand the composition of atoms in the early twentieth century (Section B), they expected to be able to use classical mechanics, the laws of motion proposed by Newton in the seventeenth century, to describe their structure. After all, classical mechanics had been tremendously successful for describing the motion of visible objects such as balls and planets. However, it soon became clear that classical mechanics fails when applied to electrons in atoms. New laws, which came to be known as quantum mechanics, had to be developed. 

The uncertainty principle has negligible practical consequences for macroscopic objects, but it is of profound importance for subatomic particles such as the electrons in atoms and for a scientific understanding of the nature of the world. 

The wavefunctions of electrons in atoms are called atomic orbitals. The name was chosen to suggest something less definite than an orbit of an electron... 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

Fig. 5. The electron distribution function for a Dirac 2s electron in atoms with the indicated atomic numbers. The vertical broken line shows the position of r for...

Of course, even when the world s fastest laser pulses are available, there is always a feehng that what is really required is pulses that are faster still Laser pulses with durations in the attosecond regime would open up the possibility of observing the motions of electrons in atoms and molecules on their natural time scale and would enable phenomena such as atomic and molecular ionisation (Section 1.2) and the dynamics of electron orbits about nuclei to be captured in real time. 

The energies of electrons in atoms play a central role in determining chemical behavior. Several other properties of electrons also influence the physical and chemical characteristics of atoms and molecules. Some properties are characteristic of all electrons, but others arise only when electrons are bound to atoms or molecules. In this section, we describe the properties possessed by all electrons. 

C07-0116. Energetic free electrons can transfer their energy to bound electrons in atoms. In 1913, James... 

Electrons in atoms heavier than helium, Bohr hypothesized, must go into higher energy shells. Thus, lithium, with an atomic number of 3, has two electrons in the n = 1 energy shell, and the third electron must go into a new energy shell with n = 2. 

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