The Bohr Model

The discrete line spectrum of hydrogen shows that only certain energies are possible that is, the electron energy levels are quantized. In contrast, if any energy level were allowed, the emission spectrum would be continuous. 

In 1913, a Danish physicist named Niels Bohr (1885-1962), aware of the experimental results we havejust discussed, developed a quantum model for the hydrogen atom. Bohr proposed that the electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits. He calculated the radii for these allowed orbits by using the theories of classical physics and by making some new assumptions. 

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Aithough we wiii not show the derivation here, the most important equation to come from Bohr s modei is the expression for the energy levels available to the electron in the hydrogen atom  

The negative sign in Equation (7.1) simpiy means that the energy of the eiectron bound to the nucieus is iower than it wouid be if the eiectron were at an infinite distance n = co) from the nucieus, where there is no interaction and the energy is zero  

Although Einstein made use of the assumption that light behaves as a particle, there is no denying the validity of the experiments that show that light behaves as a wave. Actually, light has characteristics of both waves and particles, the so-called particle-wave duality. Whether it behaves as a wave or a particle depends on the type of experiment to which it is being subjected. In the study of atomic and molecular structure, it necessary to use both concepts to explain the results of experiments. 

Following Rutherford s experiments in 1911, Niels Bohr proposed in 1913 a dynamic model of the hydrogen atom that was based on certain assumptions. The first of these assumptions was that there were certain allowed orbits in which the electron could move without radiating electromagnetic energy. Further, these were orbits in which the angular momentum of the electron (which for a rotating object is expressed as mvr) is a multiple of h/2ir (which is also written as fi), 

Bohr also assumed that electromagnetic energy was emitted as the electron moved from a higher orbital (larger n value) to a lower one and absorbed in the reverse process. 

The electrostatic force is given by the coulombic force as e2/r2 while the centrifugal force on the electron is mi /r. Therefore, we can write 

Because the moving electron has only one velocity, the values for v given in Eqs. (1.8) and (1.9) must be equal  

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The energy of the electron in any orbit is negative relative to this reference state. 

A change between two discrete energy levels emits a photon of light. 

From classical physics Bohr knew that a particle in motion tends to move in a straight line and can be made to travel in a circle only by application of a force toward the center of the circle. Thus Bohr reasoned that the tendency of the revolving electron to fly off the atom must be exactly balanced by its attraction for the positively charged nucleus. But classical physics also decreed that a charged particle under acceleration should radiate energy. Since an electron revolving around the nucleus constantly changes its direction, it is 

Angular momentum equals the product of mass, velocity, and orbital radius. 

Niels Bohr at 37 years of age, photographed in 1922 when he received the Nobel Prize for physics. 

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Before proceeding with the Bohr model, let us make three points ... 

The quantum mechanical atom differs from the Bohr model in several ways. In particular, according to quantum mechanics—... 

Use the Bohr model to identify lines in the hydrogen spectrum. 

According to the Bohr model, the radius of a circular orbit is given by the equation... 

In chemistry, perhaps because of the significance in visualizing molecular strac-ture, there has been a focus on how students perceive three-dimensional objects from a two-dimensional representation and how students mentally manipulate rotated, reflected and inverted objects (Stieff, 2007 Tuckey Selvaratnam, 1993). Although these visualization skills are very important in chemistry, it is evident that they are not the only ones needed in school chemistry (Mathewson, 1999). For example, conceptual understanding of nature of different types of chemical bonding, atomic theory in terms of the Democritus particle model and the Bohr model, and... 

The Bohr atom went a long way toward explaining the nature of atoms, but there were problems. Although scientists could calculate the emission spectrum of hydrogen using the Bohr model, the model could not account for the spectra of heavier atoms. The biggest problem with the Bohr atom, however, lay in its lack of a... 

This assumption is the basis of the Bohr model for the hydrogen-like atom. When solved for m, this balancing equation is... 

Note that from the solution of a problem involving three dimensions, three quantum numbers result, unlike the Bohr approach, which specified only one. The quantum number n is essentially equivalent to the n that was assumed in the Bohr model of hydrogen. 

The Bohr model is a determinant model of an atom. It implies that the position of the electron is exactly known at any time in the future, once that position is known at the present. The distance of the electron from the nucleus also is exactly known, as is its energy. And finally, the velocity of the electron in its orbit is exactly known. All of these exactly known quantities—position, distance from nucleus, energy, and velocity—can t, according to the Heisenberg uncertainty principle, be known with great precision simultaneously. 

Appendix 1 also shows how the periodic table of the elements (Appendix 5) can be built up from the known rules for filling up the various electron energy levels. The Bohr model shows that electrons can only occupy orbitals whose energy is fixed (quantized), and that each atom is characterized by a particular set of energy levels. These energy levels differ in detail between atoms of... 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

As a final note, closer inspection of the emission lines from Na shows that most emission lines are not, in fact, single lines, but are closely spaced doublets or triplets - for example, the strong yellow line discussed above at 589.3 nm is composed of two separate lines at 589.0 and 589.6 nm. This is termed fine structure, and is not predictable from the Bohr model of the atom. It is addressed in the Bohr-Sommerfield model, and is the result of a quantum mechanical interaction, known as spin-orbit coupling, further discussion of which is not necessary for this volume. 

With the failure of the Bohr model it was found that the properties of an electron in an atom had to be described in wave-mechanical terms (p. 54). Each Bohr model energy level corresponding to... 

How the Bohr model explains the coloured lines in hydrogen s emission spectrum. When an excited electron falls from a higher energy level to a lower energy level (shown by the downward-pointing arrows), it emits a photon with a specific wavelength that corresponds to one of the coloured lines in the spectrum. 

Which of the following did the Bohr model of the atom help explain ... 

One must expect the presence of mixed terms of the form k B in the expansion. The term of lowest order a —2, d = l), contributing oczf to the stopping cross section, would indicate a difference between the Barkas-Andersen correction evaluated from the Born series and the Bohr model, respectively. While such a comparison has not been performed in general terms, a numerical evaluation for the specific case of Li in C revealed a negligible difference [24]. 

The essential point in binary stopping theory is the avoidance of an expansion of T p) in powers of Zi this is achieved by mapping the Bohr model on a binary-collision problem involving a screened interaction potential, following a suggestion by Lindhard [21] but with an additional term that generates exact equivalence in the limit of distant collisions. The theory has been implemented in the PASS code [33] which allows incorporation of several features that were either unknown or of no interest at Bohr s time. 

The Bohr model of the atom took shape in 1913. Niels Bohr (1885-1962), a Danish physicist, started with the classic Rutherford model and applied a new theory of quantum mechanics to develop a new model that is still in use, but with many enhancements. His assumptions are based on several aspects of quantum theory. One assumption is that light is emitted in tiny bunches (packets) of energy call photons (quanta of light energy). 

The illustrations that depict the electron configurations of the atoms of each element are based on the Bohr model of quantum energy shells. 

An atom is composed of a nucleus of protons and neutrons surrounded by an electron cloud. Theoretically, electrons may be found at any distance from the nucleus, although they preferentially rotate around low-energy orbits or levels. Within a single level, various sublevels can be distinguished. [The term level corresponds to electron shell in the Bohr model. The terminological analogy is shell K = level I (n = 1) shell L = level II (n = 2) shell M = level III (n = 3) shell N = level IV ( = 4) and so on.] Electron levels are established according to four quantum numbers ... 

It is instructive to follow the derivation of the London dispersion interaction, for the simplest case of two interacting hydrogen atoms, nsing the Bohr model where the electron is regarded as travelling in well-defined orbits about the nucleus. The orbit of smallest radius, Uq, is the ground state and Bohr calculated that... 

In the Bohr model of the hydrogen atom, an electron travels in a circular orbit about the nucleus at approximately 5 x 10 mlles Per hour How many rev°-lutions per second does the electron make if the radius of the orbit is 2 x 10"9 inches ... 

An estimate of die size of the proton and an understanding of the structure of the hydrogen atom resulted from two major developments in atomic physics the Rudierford scattering experiment (1911) and the Bohr model of die atom (1913). Rutherford showed that the nucleus is vanishingly small compared to the size of an atom. The radius of a proton is on the order of 10-13 centimeter as compared with atomic radii of 10-3 centimeter, Thus, the size of a hydrogen atom is determined by the radius of the electron orbits, but the mass is essentially that of the proton,... 

With the particlelike nature of energy and the wavelike nature of matter now established, let s return to the problem of atomic structure. Several models of atomic structure were proposed in the late nineteenth and early twentieth centuries. A model proposed in 1914 by the Danish physicist Niels Bohr (1885-1962), for example, described the hydrogen atom as a nucleus with an electron circling around it, much as a planet orbits the sun. Furthermore, said Bohr, only certain specific orbits corresponding to certain specific energy levels for the electron are available. The Bohr model was extremely important historically because of its conclusion that electrons have only specific energy levels available to them, but the model fails for atoms with more than one electron. 

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