Energy levels in atoms

Note that the K shell has only one energy level, while the higher shells have sublevels within each shell. If an electron is dislodged from the K shell, an electron from an L or an M shell may replace it. The resulting ion emits radiation with energy E equal to the energy difference between the electronic energy levels, such as 

Therefore, for the X-ray photon released when an L electron in a specific sublevel drops down to fill a vacancy in the K shell, 

The frequency or wavelength for transitions between other sublevels and shells is calculated in the same manner. Transitions are not possible between all available energy levels. 

As in all forms of spectroscopy, transitions are governed by quantum mechanical selection rules. Some transitions are allowed by these rules while others are forbidden. For a brief discussion of the selection rules, the interested student should consult the texts by Jenkins or Bertin listed in the bibliography. 

Siegbahn Line Designation Electron Transition Siegbahn Line Designation Electron Transition 

An atom is composed of a nucleus and electrons. The electrons are arranged in shells around the nucleus with the valence electrons in the outer shell. The different shells correspond to the different principal quantum numbers of the possible quantum states. The principal quantum number, n, can have integral values beginning with 1. The shells are named starting with the shell closest to the nucleus, which is called the K shell. The K shell is the lowest in energy and corresponds to the quantum level with n=. The shells moving out from the nucleus are named the L shell, M shell, and so on alphabetically. The letters used for the two lowest shells are historical K is from the German word 

A fourth process can also occur, as shown in Fig. 8.1 (d). Instead of emitting an X-ray photon, the energy released knocks an electron out of the M shell. This electron is called an Auger electron. This Auger process is the basis for a sensitive surface analysis technique. Auger electron spectroscopy and the related method of X-ray photoelectron spectroscopy, based on the measurement of the emitted electron shown in Fig. 8.1(b), are discussed in Chapter 14. 

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The content of The Forces Between Molecules, by Maurice Rigby, E. Brian Smith, William A. Wakeham and Geoffrey C. Maitland, Oxford University Press, Oxford, 1986, is more explicitly about interactions than formal bonds. Again, it will be a fairly austere and mathematical read. In the Oxford Primer series, try Energy Levels in Atoms and Molecules by W. G. Richards and P. R. Scott, Oxford University Press, Oxford, 1994. It s easier than the two books above, and again helps provide some of the background material to the subject. It is still mathematically based. 

Useful books from the Oxford University Press primer series include Foundations of Spectroscopy, by Simon Duckett and Bruce Gilbert, OUP, Oxford, 2000 Introduction to Organic Spectroscopy, by Laurence M. Harwood and Timothy D. W. Claridge, OUP, Oxford, 1997 and Energy Levels in Atoms and Molecules, by W. G. Richards OUP, Oxford, 1996. Each, particularly the last, represents a clear and lucid introduction. 

Explain briefly the phenomenon of light absorption in terms of the energy associated with light and in terms of electrons and the energy levels in atoms and molecules. 

Understand the concept of the quantised nature of light and matter and be able to draw simple diagrams showing quantised energy levels in atoms and molecules. 

Thinking Critically How can the existence of spectra help to prove that energy levels in atoms exist ... 

Each line in an atomic emission spectrum corresponds to the energy given out when an excited electron moves to a state of lower energy. This can either be to a lower excited state or back to the ground state. Atomic emission spectra provide good evidence for discrete (quantised) energy levels in atoms. 

Atomic emission spectroscopy is one of the oldest instrumental techniques used for chemical analysis. It is used to study the transitions between electronic energy levels in atoms or ions. These energy differences are usually in the visible region (400-700 nm) of the electromagnetic spectrum, but if the energy difference is larger, then the transitions may lie in the ultraviolet region. 

You will already know from your studies that the energy levels of atoms and molecules are quantized, i.e. there are discrete energy levels in atoms and molecules (Figure 1.1). 

Fig. 3 Scheme of the calculation of energy levels in atoms, ions and unimetal complexes. The weak-field path (a) + (b) + (c). The strong-field path (b) + (a) + (c). The multiplet path (a) + (c) + (b). The crystal-field multiplets represent an appropriate basis for involvement of the Zeeman perturbation in the magnetic field... 

Energy levels in atoms (left) and molecules (right) The latter have vibronic levels and rotational sub-levels. The S (and T) levels are spin-singlet S = 0 (and spin-triplet S= 1) states. 

W.G. Richards and P.R. Scott, Energy Levels in Atoms and Molecules, Oxford University Press, 1994. 

Figure 6.6. After figures 2.2, 2.4, 2.5, 2.9 and 2.10 of W.G. Richards and PR. Scott, Energy Levels in Atoms and Molecules, Oxford University Press, Oxford, 1994.

Ionization energies can be measured directly to provide evidence for the ordering of the energy levels in atoms. Figure 2.5 shows the variation in first ionization energy with position of atoms in the periodic table. 

To use the Bohr theory of energy levels in atoms to explain light emission and absorption by gaseous atoms 4.6 To understand the spatial orientation of the most common orbitals and the uncertain nature of locating the electron... 

Bohr postulated circular orbits for the electrons in an atom and developed a mathematical model to represent the energies of the orbits, as well as then-distances from the atom s nucleus. His model worked very well for the hydrogen atom. It could be used to calculate the energy of the emitted and absorbed light, as well as the radius of the atom. However, the intensity of the various wavelengths of fight involved was not explained well. Moreover, no other atom was explained well at all. Bohr s theory has since been replaced by a quantum mechanical model, but it was a milestone because Bohr was the first to postulate energy levels in atoms. 

Bohr s postulate that electrons have distinct energy levels in atoms was a milestone in the understanding of the nature of the atom. 

What is the outermost occupied energy level in atoms of the elements in Period 4 ... 

Use experimental emission and absorption spectra to determine spacings between energy levels in atoms (Section 4.2, Problems 11-16). 

We now accept the fact that electrons occupy only certain energy levels in atoms. In most atoms, some of the energy differences between levels correspond to the energy of visible light. Thus, colors associated with electronic transitions in such elements can be observed by the human eye. 

In the present-day model of the atom, neutrons and protons form a nucleus at the center of the atom. Negatively-charged electrons are distributed in the space around the nucleus. The electrons with the most energy are farthest from the nucleus and occupy the outermost energy level. Recall from Chapter 2 that evidence for the existence of energy levels came from the interpretation of the emission spectra of atoms. It s important to know about energy levels in atoms because it helps explain how atoms form chemical bonds and why they form particular kinds of compounds, for example ionic or covalent compounds. 

Figure 3 Energy levels in atoms and stimulation of transitions by external energy.

This apparent contradiction leads to the conclusion that a metal lattice is, in the normal ranges of temperature, filled with electrons in much the same way as, in the case of the heavier atoms, the inner energy levels are filled with their electrons this is why the cloud electrons are not normally affected by the relatively small energy increments associated with heating. In other words, in the metal lattice there are definite electron energy levels, which are just as fundamental, and from some points of view just as important, as the energy levels in atoms. This important idea will now be discussed in rather more detail. 

We now have evidence that electron energy levels in atoms are quantized. 

What if energy levels in atoms were not quantized What are some differences we would notice ... 

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