Energy states of atoms

The allowed energy states of atoms and molecules are described by quantum numbers. 

As already evident from the previous section, symmetry properties of a molecule are of utmost importance in understanding its chemical and physical behaviour in general, and spectroscopy and photochemistry in particular. The selection rules which govern the transition between the energy states of atoms and molecules can be established from considerations of the behaviour of atoms or molecules under certain symmetry operations. For each type of symmetry, there is a group of operations and, therefore, they can be treated by group theory, a branch of mathematics. 

The energy states of atoms are expressed in terms of four quantum numbers j it, the principal quantum number /, the azimuthal quantum number m, the magnetic quantum number and mt or s, the spin quantum number. According to Pauli s exclusion principle, no two electrons can have the same values for all the four quantum numbers. 

The energy states of atoms are purely electronic (atoms have of course no rotational or vibrational states) and these are obtained in a simple picture by fitting the available electrons in the available orbitals. In the ground state all... 

Summary 1. The energy states of atoms are expressed in terms of four quantum numbers ... 

In spite of the shortcomings of Bohr s model, the legacy of Bohr s atom is pervasive. We still talk of energy states of atoms. Our basic understanding of atomic and molecular spectra rests upon Bohr s idea of quantum transitions between energy states. And it was the success of Bohr s hydrogen model that affirmed the need to develop a new physics for atoms. 

The second class of hydrogen-like atoms is called Rydberg atoms. A Rydberg atom is an ordinary atom in which one electron has been elevated to a very high quantum state. The energy states of atoms are identified with the quantum number n, called the principal quantum number. The ground state, or lowest state, is the n = state, which is where atoms spend most of their time. The first excited state is the n = 2 energy state, the second excited state is = 3, and so on. 

Every atom emits characteristic X-rays with discrete energies that identify the atom like fingerprints. For every atom, the, the X-rays are identified according to the final state of the electron transition that produced them. Historically, the energy states of atomic electrons are characterized by the letters K,L,M,N,etc. The K state or K orbit or K shell is the lowest energy state, also called the ground state. The X-rays that are emitted as a result of electronic transitions to the K state, from any other initial state, are called K X-rays (Fig. 3.1). Transitions to the L state give rise to L X-rays and so on. K and Kp X-rays indicate transitions from L to K and M to K states, respectively. 

EHEJIES Wavelike properties of electrons help relate atomic emission spectra, energy states of atoms, and atomic orbitals. 

This article examines the basic theory of energy states of atoms, the quantitative analysis by atomic absorption, and the main components of the atomic absorption spectrometer. 

The second process by which the excited atom can regain stability is by transfer of an electron from one of the outer orbitals to fill the vacancy. The energy difference between the initial and final states of the transferred electron may be given off in the form of an X-ray photon. Since all emitted X-ray photons have energies proportional to the differences in the energy states of atomic electrons, the lines from a given element are characteristic of that element. The relationship between the wavelength of a characteristic X-ray photon and the atomic number Z of the element was first established by Moseley. Moseley s law is written ... 

Fig. 2.8. Schematic electronic energy states of atoms (a), small molecules (b), large molecules (c), and condensed phases (d) either solid or liquid. The electronic density of states (e) corresponds to the level structure shown in (d).

The thermo-chemical or the initial (neutral, un-ionized specimen with n elec-trons)-final (radiation beam ionized specimen with n — 1 electrons) states relaxation dominates the CLS [6, 7]. The energy required for removing a core electron from a surface atom is different from the energy required for a bulk atom. The surface atom is assumed as a Z -F 1 impurity sitting on the substrate metal of Z atomic number. The energy states of atoms at a flat surface or at a curved surface are expected to increase/decrease while the initial states of atoms in the bulk decreases/increase when the particle size is reduced. This mostly adopted mechanism creates the positive, negative, or mixed surface shift in theoretical calculations. 

Solution. In light atoms, a Russell-Saunders type of electron interaction usually take place. In Section 7.6 the method is described in detail. The atomic energy state, in this case, is characterized by a set of quantum numbers the total orbital quantum number L, total spin quantum number S and total internal quantum number J. Thus quantum number Jcan accept values from7 = L + Sup toL - IL — 5 I, changing on unit. A certain energy state of atom (spin-orbital interaction) corresponds to each value J, i.e., an energy sublevel appears. The number of sublevels or number of possible mutual orientations of vectors andL at is defined by the ratio 25 + 1 referred as multiplicity. At L < 5 the number of sublevels is defined by another ratio 2L + 1 (see Section 7.6.3). 

---