All About Atoms

In 1913 Bohr proposed his quantized shell model of the atom to explain how electrons can have stable orbits around the nucleus. The motion of the electrons in the Rutherford model was unstable because, according to classical mechanics and electromagnetic theory, any charged particle moving on a curved path emits electromagnetic radiation; thus, the electrons would lose energy and spiral into the nucleus. To remedy the stability problem, Bohr modified the Rutherford model by requiring that the electrons move in orbits of fixed size and energy. The energy of an electron depends on the size of the orbit and is lower for smaller orbits. Radiation can occur only when the electron jumps from one orbit to another. The atom will be completely stable in the state with the smallest orbit, since there is no orbit of lower energy into which the electron can jump.
Bohr's starting point was to realize that classical mechanics by itself could never explain the atom's stability. A stable atom has a certain size so that any equation describing it must contain some fundamental constant or combination of constants with a dimension of length. The classical fundamental constants--namely, the charges and the masses of the electron and the nucleus--cannot be combined to make a length. Bohr noticed, however, that the quantum constant formulated by the German physicist Max Planck (see below) has dimensions which, when combined with the mass and charge of the electron, produce a measure of length. Numerically, the measure is close to the known size of atoms. This encouraged Bohr to use Planck's constant in searching for a theory of the atom.
Planck had introduced his constant in 1900 in a formula explaining the light radiation emitted from heated bodies. According to classical theory, comparable amounts of light energy should be produced at all frequencies. This is not only contrary to observation but also implies the absurd result that the total energy radiated by a heated body should be infinite. Planck postulated that energy can only be emitted or absorbed in discrete amounts, which he called quanta (the Latin word for "how much"). The energy quantum is related to the frequency of the light by a new fundamental constant, h. When a body is heated, its radiant energy in a particular frequency range is, according to classical theory, proportional to the temperature of the body. With Planck's hypothesis, however, the radiation can occur only in quantum amounts of energy. If the radiant energy is less than the quantum of energy, the amount of light in that frequency range will be reduced. Planck's formula correctly describes radiation from heated bodies. Planck's constant has the dimensions of action, which may be expressed as units of energy multiplied by time, units of momentum multiplied by length, or units of angular momentum. For example, Planck's constant can be written as h = 6.6 10-34 joule seconds or 6.6 10-34 kilogram-metre/second-metres.
Using Planck's constant, Bohr obtained an accurate formula for the energy levels of the hydrogen atom . He postulated that the angular momentum of the electron is quantized--i.e., it can have only discrete values. He assumed that otherwise electrons obey the laws of classical mechanics by traveling around the nucleus in circular orbits. Because of the quantization, the electron orbits have fixed sizes and energies. The orbits are labeled by an integer, the quantum number n.
With his model, Bohr explained how electrons could jump from one orbit to another only by emitting or absorbing energy in fixed quanta. For example, if an electron jumps one orbit closer to the nucleus, it must emit energy equal to the difference of the energies of the two orbits. Conversely, when the electron jumps to a larger orbit, it must absorb a quantum of light equal in energy to the difference in orbits.
Bohr's model accounts for the stability of atoms because the electron cannot lose more energy than it has in the smallest orbit, the one with n = 1. The model also explains the Balmer formula for the spectral lines of hydrogen. The frequency of the light is related to its energy by Einstein's formula E = h. The light energy is calculated from the difference in energies between the two orbits. The Balmer formula can be expressed as the difference of two terms, each term giving the energy of an orbit. Bohr's model not only explains the form of the Balmer formula but also accurately gives the value of the constant of proportionality R.
The usefulness of Bohr's theory extends beyond the hydrogen atom. Bohr himself noted that the formula also applies to the singly ionized helium atom, which, like hydrogen, has a single electron. The nucleus of the helium atom has twice the charge of the hydrogen nucleus, however. In Bohr's formula the charge of the electron is raised to the fourth power. Two of those powers stem from the charge on the nucleus; the other two come from the charge on the electron itself. Bohr modified his formula for the hydrogen atom to fit the helium atom by doubling the charge on the nucleus. Moseley applied Bohr's formula with an arbitrary atomic charge Z to explain the K- and L-series X-ray spectra of heavier atoms. The German physicists James Franck and Gustav Hertz confirmed the existence of quantum states in atoms in experiments reported in 1914. They made atoms absorb energy by bombarding them with electrons. The atoms would only absorb discrete amounts of energy from the electron beam. When the energy of an electron was below the threshold for producing an excited state, the atom would not absorb any energy.
Bohr's theory had major drawbacks, however. Except for the spectra of X rays in the K and L series, it could not explain properties of atoms having more than one electron. The binding energy of the helium atom, which has two electrons, was not understood until the development of quantum mechanics. Several features of the spectrum were inexplicable even in the hydrogen atom. High-resolution spectroscopy shows that the individual spectral lines of hydrogen are divided into several closely spaced, fine lines. In a magnetic field the lines split even further. The German physicist Arnold Sommerfeld modified Bohr's theory by quantizing the shapes and orientations of orbits to introduce additional energy levels corresponding to the fine spectral lines. The quantization of the orientation of the angular-momentum vector was confirmed in an experiment in 1922 by other German physicists, Otto Stern and Walter Gerlach. They passed a beam of silver atoms through a nonhomogeneous magnetic field, one that is stronger on one side than on the other. The field deflected the atoms according to the orientation of their magnetic moments. (The magnetic moment of an object such as an atom or a compass needle is the measure of its interaction with a magnetic field. The moment points in some direction and is associated in classical physics with orbital currents and the angular momentum of charges.) In their experiment, Stern and Gerlach found only two deflections, not the continuous distribution of deflections that would have been seen if the magnetic moment had been oriented in any direction. Thus, it was determined that the magnetic moment and the angular momentum of an atom can have only two orientations. The discrete orientations of the orbits explain some of the magnetic field effects--namely, the so-called normal Zeeman effect, which is the splitting of a spectral line into three sublines. These sublines correspond to quantum jumps in which the angular momentum along the magnetic field is increased by one unit. decreased by one unit, or left unchanged.
An additional quantum number was needed to complete the description of electrons in an atom. In 1925 Samuel A. Goudsmit and George E. Uhlenbeck, two graduate students in physics at the University of Leiden, in The Netherlands, added a quantum number to account for the fact that some spectral lines are divided into more sublines than can be explained with the original quantum numbers. Goudsmit and Uhlenbeck postulated that an electron has an internal spinning motion and that the corresponding angular momentum is one-half of the orbital angular momentum quantum. An electron has a magnetic moment, and its energy depends on whether the spin is aligned with or against the magnetic field. Independently, the Austrian-born physicist Wolfgang Pauli also suggested adding a two-valued quantum number for electrons, but for different reasons. He needed this additional quantum number to formulate his exclusion principle, which serves as the atomic basis of the periodic table and the chemical behaviour of the elements. According to the exclusion principle, one electron at most can occupy an orbital, taking into account all the quantum numbers. Pauli was led to this principle by the observation that an alkali in a magnetic field has a number of orbitals in the shell equal to the number of electrons that must be added to make the next noble gas. These numbers are twice the number of orbits available if the angular momentum and its orientation are considered alone.
In spite of these modifications, Bohr's model seemed to be a dead end by the early 1920s. It did not explain most fine spectral lines or the anomalous Zeeman effect, which is a complicated type of spectral line splitting that sometimes involves up to 15 sublines. (Its name notwithstanding, the anomalous Zeeman effect is more common than the aforementioned normal Zeeman effect.) Efforts to generalize the model to multielectron atoms had proved futile, and physicists despaired of ever explaining them.

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