LINE SPECTRA AND THE BOHR MODEL

LINE SPECTRA AND THE BOHR MODEL We examine the light that atoms give off when appropriately stimulated (line spectra). Line spectra indicate that electrons exist only at certain energy levels around a nucleus and that energy is... 

Using theories to explain natural phenomena - line spectra and the Bohr model... 

Line Spectra and the Rydberg Equation Bohr Model of the Hydrogen Atom Energy Levels of the Hydrogen Atom Spectral Analysis... 

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. 

Line spectra for multi-electron atoms are more complex than the hydrogen line spectrum, and thus are less easily explained in an explicit fashion at a middle school, high school, or even first year undergraduate level. However, discussions of this topic with respect to the hydrogen atom allow for the instructor to point out many important features of rudimentary quantum mechanics. Among these are the quantized nature of the electrons in atoms, the Bohr model of one-electron atoms, the dual wave-particle nature of light, the... 

The Bohr Model The Bohr model was a first attempt to explain the bright-line spectra of atoms. While it did predict the spectrum of the hydrogen atom, it failed to predict the spectra of other atoms and was consequently replaced by the quantum-mechanical model. 

Analysis of the spectrum of the H atom led to the Bohr model, the first step toward our current model of the atom. From its use by 19 -century chemists as a means of identifying elements and compounds, spectrometry has developed into a major tool of modem chemistry. The terms spectmscopy, spectrophotometry, and spectrometry refer to a large group of instrumental techniques that obtain spectra that correspond to a substance s atontic or molecular eneigy levels. (Elements produce lines, but complex molecules produce spectral peaks.) The two types of spectra most often obtained are emission and absorption spectra ... 

Scientists of the nineteenth century lacked the concepts necessary to explain line spectra. Even in the first decade of the twentieth century, a suitable explanation proved elusive. This changed in 1913 when Niels Bohr, a Danish physicist and student of Rutherford, proposed a new model for the hydrogen atom. This model retained some of the features of Rutherford s model. More importantly, it was able to explain the line spectrum for hydrogen because it incorporated several new ideas about energy. As you can see in Figure 3.8, Bohr s atomic model pictures electrons in orbit around a central nucleus. Unlike Rutherford s model, however, in which electrons may move anywhere within the volume of space around the nucleus, Bohr s model imposes certain restrictions. 

Bohr s Theory. In order to overcome the drawbacks of Rutherford s model and to account for the line spectra of hydrogen, Niel Bohr in 1913 put forward a theory called Bohr s theory. The main postulates of Bohr s theory are as follows ... 

Soon after the nuclear model was proposed, Niels Bohr (1885-1962), a young Danish physicist working in Rutherford s laboratory, suggested a model for the H atom that predicted the existence of line spectra. In his model, Bohr used Planck s and Einstein s ideas about quantized energy and proposed three postulates ... 

In 1913, Bohr proposed a model for the hydrogen atom that appeared to explain the line spectra discussed in Section 6.2. The motion of the electron around the nucleus was considered to be similar to the motion of a planet around the sun, the gravitational attraction that keeps the planet in a circular or an elliptical orbit being replaced by the coulom-bic attraction between the electron and the positively charged nucleus. To account for the line spectra, Bohr postulated that the angular momentum of the electron was restricted to multiple values of fl. This was an arbitrary postulate at the time it was made, but it comes naturally from the quantum mechanical description of a particle moving in a circle, as we have already seen in Section 5.1.3. 

Bohr felt instinctively that Planck s quantized energies were related to the discrete lines of elemental spectra— and to the planetary model of the atom— but he could not find the connection. Thirty years earlier Johann Jakob Balmer, a teacher at a girls secondary school, part-time lecturer at the University of Basel (where, we may note, Paracelsus burned the works of Galen), and mathematics hobbyist had found a numerical relationship between frequencies of the lines in the hydrogen spectrum. The relationship was not obvious because it depended on the reciprocal squares of integers, and this was the very feature that caught Bohr s attention. He later said, As soon as I saw Balmer s formula, the whole thing was immediately clear to me. ... 

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