Friday, March 2, 2007

Valueing Old Barometers

quantum numbers

The description of the hydrogen atom by Bohr was a great success, despite being burdened with a series of ad hoc assumptions, the result of empirical observations. Also marks the beginning of a new way of describing nature.

physics (and science in general) is to describe the nature based on observable and measurable phenomena. Planetary orbits, for example, are described in terms of distance and guidance on a fixed point (the Sun) for each time step: describe what your path. Bohr's description, however, despite considering the atom as a small solar system (with the peculiarity of the quantification of the orbits), do not get these paths. It focuses instead on obtaining the energies that have electrons in their orbits, and how it changes it, because ultimately, is this phenomenon that can be observed and measured experimentally (the later development of quantum mechanics showed that even makes sense to calculate the trajectory of the electron). Thus, the description of an electron in an atom, is not to know its history, but what is your state , the orbit that takes information that is contained in the quantum number n .

Bohr atomic model explains perfectly the absorption and emission lines of a hydrogen atom. However, he had problems for atoms with more electrons. And even new lines were discovered in the hydrogen atom for which there was no solution.

azimuthal number

Arnold Sommerfeld (1868-1951) proposed the inclusion of new quantum numbers. Of planetary motion, which is known as wider orbit is elliptical. Sommerfeld proposed azimuthal quantum number, l , as a measure of how it was elliptical orbit, its eccentricity. Sommerfeld found that the value varying from l l = 0 to the value l = n-1 being l = 0 a perfectly circular orbit. Thus, the number n no longer represents an orbit, without determining the distance from the core, means a layer which can contain from l = 0 to l = n-1 orbits, all the same distance from the nucleus

For example, for first layer ( n = 1), the only possible value of l is 0. That is, the first layer contains a single orbit is circular. layer n = 2 contains the 2 orbits l = 0 (circular), and l = 1 (elliptical) to n = 3, l = 0, l = 1 and l = 2, (3 orbits with varying degrees of eccentricity), and so on.

magnetic Number

Pieter Zeeman (1865-1943) discovered in 1890 the effect that bears his name. Found that in a gas inside a magnetic field, some lines are unfolded, and appeared triplets around a common line. After inclusion of the azimuthal number, Bohr made new calculations by introducing the magnetic quantum number, m .

An electron orbiting a nucleus is an electric current, and as such, produces a magnetic field perpendicular to the plane in which the electron moves. It is a small magnet . By applying an external magnetic field, this magnet oriented, but this orientation is also quantized, so that it can take values \u200b\u200branging from m m =- l, to m = l .


The emergence of more and more lines, and more and more quantum numbers, is but proof of fine structure in the management of the electrons in the atom. Electrons are placed in layers, which differ in a quantity of energy. Within each layer, there is a difference in energy between each orbit, but is much smaller than that between layers, hence were discovered only when it increased the accuracy of the experiments. Moreover, the Zeeman effect reveals the existence of orbits that can be separated in energy by applying a magnetic field, revealing an internal structure of the orbits.



Spin Number

After inclusion of the numbers and azimuthal magnetic , the triplets were explained the Zeeman effect. However, the Zeeman effect also had other collections of lines (doublets), which were not explained by these numbers, called anomalous Zeeman effect .

Wolfgang Pauli (1900-1958) sensed the existence of a fourth quantum number, but was unable to realize the idea. Were instead George Uhlenbeck and Goudsmit Sam who proposed the quantum number spin, s, whose characteristic is not due to the orbit occupied in the atom, but the own rotation of the electron on itself.

The existence of an angular momentum (rotation) intrinsic electron was evidenced by the famous experiment of Stern and Gerlach : an electron beam through a nonuniform magnetic field. The interaction of the magnetic field with angular momentum causes the electrons to deviate from its path. According to classical physics, each electron would have an orientation of angular momentum with respect to the random magnetic field, so that everyone would suffer a distinct deviation, and the beam is open continuously over an area. However, it was observed that the beam is split into two beams clearly defined.

Prueba de la cuantización de Spin, según el experimento de Stern y Gerlach


This result suggests that the intrinsic angular momentum of the electron is quantized, and can only have two possible values \u200b\u200bof s: +1 / 2 and -1 / 2 , most often referred to colloquially spin up or spin down . This makes the value of spin rotation in a very strange phenomenon. The spin is to describe the symmetry of the rotation. Take

ace in the deck. If broken 360 degrees back to its position initial. This is equivalent to a spin s = 1 . If you take a French king in a deck, when rotated 180 degrees (half turn), will be like in its original position. This is an example of spin s = 2.

Spin=1 y Spi =2




The spin s = 1 / 2 means that it is necessary to rotate 720 ° (two laps) to regain the starting position. Rotation is very difficult to imagine. The closest thing is a movement like the following:

1 - Take an electron in the palm
2 - Rotate the hand inward, passing the electron under the arm to complete the turn. Now the electron has a spin, but the arm is in a forced position. The entire assembly electron-arm is not in the same position as at the beginning.
3 - Raise the arm (without pulling the electron), at the height of the head while touring the hand.
4 - The electron and arm are now in the same position as at the beginning, for which the electron has two turns. This would be something like the spin s = 1 / 2


Spin 1/2. Cuidadín con las dislocaciones de codo



With the inclusion of the quantum number completes the description of the possible states of the electrons in atoms. The combination of these four numbers identify the status and power they have, and may explain any emission or absorption line as the transition of an electron from one state to another NLMs n'l'm state's' .

The Bohr-Sommerfeld model can explain the experimental observations. However, based on some assumptions that are not shown, the quantization of varying amounts.

Until now, we can speak of a quantum physics, which simply applies quantization rules of physics and classical mechanics. The emergence of quantum mechanics can deepen the concepts, and give rise to themselves, these rules of quantization, and a series of new effects and implications, without equivalent in the classical world.

Annex


Electronic configuration of atoms

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