Quantum Theory and the Atom

The emission spectrum of an atom indicates that the energy it emits is quantized, meaning that only certain quantities of energy can be given off. Niels Bohr used the relatively simple emission spectrum of the hydrogen atom to propose a new atomic model. 

Bohr s model of the atom, sometimes called the planetary model, was accepted at the time because it explained hydrogen s atomic emission spectrum. However, the model was very limited in that it only worked for hydrogen. 

Electrons occupy the space surrounding the nucleus and can exist in several discrete principal energy levels, each designated by one of the principal quantum numbers ( ) that are the integers 1, 2, 3, 4, and so on. 

Electrons in successively higher principal energy levels have greater energy. 

Because of interactions among electrons, each principal energy level consists of energy sub-levels that have slightly different energy values. 

The dual wave-particle model of light accounted for several previously unexplainable phenomena, but scientists still did not understand the relationships among atomic structure, electrons, and atomic emission spectra. Recall that hydrogens atomic emission spectrum is discontinuous that is, it is made up of only certain frequencies of light. Why are the atomic emission spectra of elements discontinuous rather than continuous Niels Bohr, a Danish physicist working in Rutherford s laboratory in 1913, proposed a quantum model for the hydrogen atom that seemed to answer this question. Bohr s model also correctly predicted the frequencies of the lines in hydrogens atomic emission spectrum. 

Bohr s Atomic Orbit Quantum Number Orbit Radius (nm) Corresponding Atomic Energy Level Relative Ener 

In order to complete his calculations, Bohr assigned a number, n, called a quantum number, to each orbit. He also calculated the radius of each orbit. For the first orbit, the one closest to the nucleus, n = I and the orbit radius is 0.0529 nm for the second orbit, n = 2 and the orbit radius is 0.212 nm and so on. Additional information about Bohr s description of hydrogens allowed orbits and energy levels is given in Table 5.1. 

O Reading Check Explain why different colors of light result from electron behavior in the atom. 

The limits of Bohr s model Bohr s model explained hydrogen s observed spectral lines. However, the model failed to explain the spectrum of any other element. Moreover, Bohr s model did not fully account for the chemical behavior of atoms. In fact, although Bohr s idea of quantized energy levels laid the groundwork for atomic models to come, later experiments demonstrated that the Bohr model was fundamentally incorrect. The movements of electrons in atoms are not completely understood even now however, substantial evidence indicates that electrons do not move around the nucleus in circular orbits. 

You now know that the behavior of light can be explained only by a dual wave-particle model. Although this model was successful in accounting for several previously unexplainable phenomena, an understanding of the relationships among atomic structure, electrons, and atomic emission spectra still remained to be established. 

Bohr atomic orbit Quantum number Orbit radius (nm) Corresponding atomic energy level Relative energy 

Scientists in the mid-1920s, by then convinced that the Bohr atomic model was incorrect, formulated new and innovative explanations of how electrons are arranged in atoms. In 1924, a young French graduate student in physics named Louis de Broglie (1892-1987) proposed an idea that eventually accounted for the fixed energy levels of Bohr s model. 

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Another consequence of the quantum theory of the atomic and nuclear systems is that no two protons, or two neutrons, can have exactly the same wave function. The practical appHcation of this rule is that only a specific number of particles can occupy any particular atomic or nuclear level. This prevents all of the electrons of the atom, or protons and neutrons in the nucleus, from deexciting to the single lowest state. 

It has already been noted that the new quantum theory and the Schrodinger equation were introduced in 1926. This theory led to a solution for the hydrogen atom energy levels which agrees with Bohr theory. It also led to harmonic oscillator energy levels which differ from those of the older quantum mechanics by including a zero-point energy term. The developments of M. Born and J. R. Oppenheimer followed soon thereafter referred to as the Born-Oppenheimer approximation, these developments are the cornerstone of most modern considerations of isotope effects. 

A rational deduction of elemental abundance from solar and stellar spectra had to be based on quantum theory, and the necessary foundation was laid with the Indian physicist Meghnad Saha s theory of 1920. Saha, who as part of his postdoctoral work had stayed with Nernst in Berlin, combined Bohr s quantum theory of atoms with statistical thermodynamics and chemical equilibrium theory. Making an analogy between the thermal dissociation of molecules and the ionization of atoms, he carried the van t Hoff-Nernst theory of reaction-isochores over from the laboratory to the stars. Although his work clearly belonged to astrophysics, and not chemistry, it relied heavily on theoretical methods introduced by and associated with physical chemistry. This influence from physical chemistry, and probably from his stay with Nernst, is clear from his 1920 paper where he described ionization as a sort of chemical reaction, in which we have to substitute ionization for chemical decomposition. [81] The influence was even more evident in a second paper of 1922 where he extended his analysis. [82]... 

At about the same time, Bohr published his trilogy articles in which he introduced the quantum theory of the atom and obtained, by various means, the electronic configurations of many of the elements in the periodic system (Scerri, 1994b). In addition, he solidified the notion that the chemical properties of the elements were due to the orbiting electrons, which corresponds to the atomic charge of each nucleus (Bohr, 1913). Here, then, with the discoveries of Moseley and Bohr, was the solution of the tellurium/iodine inversion question. If the elements were ordered according to atomic... 

Thus, the most common assumption was that a material s properties are governed by quantum theory and that relativistic effects are mostly minor and of only secondary importance. Quantum electrodynamics and string theory offer some possible ways of combining quantum theory and the theory of relativity, but these theories have only very marginally found their way into applied quantum theory, where one seeks, from first principles, to calculate directly the properties of specific systems, i.e. atoms, molecules, solids, etc. The only place where Dirac s relativistic quantum theory is used in such calculations is the description of the existence of the spin quantum number. This quantum number is often assumed to be without a classical analogue (see, however, Dahl 1977), and its only practical consequence is that it allows us to have two electrons in each orbital. 

If, contrary to the order of historical development, we have discussed the quantum theory of the atom before quantum statistics, we have our reasons. In the first place, the failure of- the classical theory displays itself in atomic mechanics—for instance, in the explanation of line spectra or the diffraction of electrons—even more immediately than in the attempts to fit the law of radiation into the frame of classical physics. In the second place, it is an advantage to understand the mechanism of the individual particles and the elementary processes before proceeding to set up a system of statistics based upon the quantum idea. 

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