Bohr-Einstein equation

Alilfikan went on to demonstrate tfie pfiotoelectron effect, providing a valuable proof of Albert Einstein s equations. His experiments also aided both Einstein and Bohr in their later research efforts. In 192 3 he was awarded a Nobel Prize in physics for both his work in determining the charge on the electron and exploring the photoelectric effect, see also Bohr, Niels Einstein, Albert Thomson, Joseph John. 

During the 19th century, a number of experimental observations were made which were not consistent with the classical view that matter could interact with energy in a continuous form. Work by Einstein, Planck and Bohr indicated that in many ways electromagnetic radiation could be regarded as a stream of particles (or quanta), for which the energy, E, is given by the Bohr equation, as follows ... 

Einstein s equation for the photoelectric effect) (Bohr s equation for the hydrogen atom)... 

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

When Max Planck wrote his remarkable paper of 1901, and introduced what Stehle (1994) calls his time bomb of an equation, e = / v , it took a number of years before anyone seriously paid attention to the revolutionary concept of the quantisation of energy the response was as sluggish as that, a few years later, whieh greeted X-ray diffraction from crystals. It was not until Einstein, in 1905, used Planck s concepts to interpret the photoelectric effect (the work for which Einstein was actually awarded his Nobel Prize) that physicists began to sit up and take notice. Niels Bohr s thesis of 1911 which introduced the concept of the quantisation of electronic energy levels in the free atom, though in a purely empirical manner, did not consider the behaviour of atoms assembled in solids. 

Werner Heisenberg stated that the exact location of an electron could not be determined. All measuring technigues would necessarily remove the electron from its normal environment. This uncertainty principle meant that only a population probability could be determined. Otherwise coincidence was the determining factor. Einstein did not want to accept this consequence ("God does not play dice"). Finally, Erwin Schrodinger formulated the electron wave function to describe this population space or probability density. This equation, particularly through the work of Max Born, led to the so-called "orbitals". These have a completely different appearance to the clear orbits of Bohr. 

By 1903. llie wave theory of light based oil Maxwell s equations was well established, but certain phenomena would not fit in. It seemed that emission and absorption of hght occur discontinuously. This led Einstein to (lie view that the energy is concentrated in discrete particles. It was a revolutionary idea, very hard to understand, as the successes of the wave theory were undeniable. It seemed that light had to be understood sometimes as waves, sometimes as particles, and physicists had to get used to it, The idea was incorporated into Bohr s theory of the hydrogen atom and forms an essential part of it. 

The mathematical treatment of the Rutherford-Bohr atom was especially productive in Denmark and Germany. It led directly to quantum mechanics, which treated electrons as particles. Electrons, however, like light, were part of electromagnetic radiation, and radiation was generally understood to be a wave phenomenon. In 1924, the French physicist Prince Louis de Broglie (1892-1987), influenced by Einstein s work on the photoelectric effect, showed that electrons had both wave and particle aspects. Wave mechanics, an alternative approach to quantum physics, was soon developed, based on the wave equation formulated in 1926 by the Austrian-born Erwin Schrodinger (1887-1961). Quantum mechanics and wave mechanics turned out to be complementary and both were fruitful for an understanding of valence. 

If you recall from the beginning of this chapter, some of the work that led to the development of the modem atomic theory was done by scientists Max Planck, Albert Einstein, Louis de Broglie, Werner Heisenberg, Niels Bohr, and Erwin Shrodinger. The first work centered around light (electromagnetic radiation), while the later work focused on the wave-like nature of matter. The AP test does not probe too deeply into the theoretical considerations of any of these scientists, but some calculations have popped up on previous tests. Therefore, let s turn our attention to some of the equations associated with these scientists work. 

It is possible to find in the history of science many vivid examples illustrating the relativity of the concept fundamental . For instance, the Planck postulate of energy quantization and the Bohr postulate on the quantization on angular momentum made a revolution in physics and were actually axioms at that time. At present from the formal viewpoint, they are only ordinary consequences of Schroedinger s equation [4], Another vivid example is provided by the four famous Maxwell electrodynamic equations which, as was found later, can be derived from Coulomb s law and Einstein s relativity principle [5]. 

It is commonly accepted that the old quantum theory era spans from the birth of Planck s quantum hypothesis to the formulation of Schrodinger s equation. This section describes the old quantum theory in three parts the failure of classical mechanics, the birth of the quantum theory, and the completion of wave mechanics.5 8) This century obviously began with the birth of quantum theory. Many researchers appeared on the scene of quantum theory at the time, but we remember mostly the contributions of four researchers Max Planck (1901), Albert Einstein (1905), Niels Bohr (1913), and de Broglie (1923). Then Schrodinger proposed the new wave equation to conclude the age of the old quantum theory. Heisenberg established matrix mechanics and formulated the uncertainty principle. 

Most practicing physicists have learned what little they know of the history of this period by reading textbooks written after the quantum revolution. Often texts and teaehers treat the Planck radiation law, the Einstein photoelectric equatiorr, the Bohr atom and the Compton effect in one sequence assuming that this provides an adequate background for understanding E = hv and p = hv/c [de Broglie s equation]. This can leave a student with less than total respect for the physicists who took so long to see the obvious necessity for this form of quantization (p. 95). 

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