3/20/2024 0 Comments Bohr's atom modelIn which h is Planck's constant, m is the mass of the electron, v is the orbital velocity, and n can have only the integer values 1, 2, 3, etc. The radius of one of these allowed Bohr orbits is given by Specifically, Bohr postulated that the angular momentum of the electron, mvr (the mass and angular velocity of the electron and in an orbit of radius \(r\)) is restricted to values that are integral multiples of \(h/2\pi\). Bohr suggested that the planetary model could be saved if one new assumption were made: certain "special states of motion" of the electron, corresponding to different orbital radii, would not result in radiation, and could therefore persist indefinitely without the electron falling into the nucleus. Niels Bohr was a brilliant Danish physicist who came to dominate the world of atomic and nuclear physics during the first half of the twentieth century. According to classical physics, no atom based on this model could exist for more than a brief fraction of a second. The electron would quickly fall into the nucleus, following a trajectory that became known as the "death spiral of the electron". Moreover, the radiated energy would come from the kinetic energy of the orbiting electron as this energy gets radiated away, there is less centrifugal force to oppose the attractive force due to the nucleus. If electrons actually followed such a trajectory, all atoms would act is miniature broadcasting stations. The difficulty with this picture is that it is inconsistent with a well established fact of classical electrodynamics which says that whenever an electric charge undergoes a change in velocity or direction (that is, acceleration, which must happen if the electron circles around the nucleus), it must continually radiate energy. If this balance were not present, the electron would either fall into the nucleus, or it would be flung out of the atom. ![]() The planetary model of the atom assumed that the electrostatic attraction between the central nucleus and the electron is exactly balanced by the centrifugal force created by the revolution of the electron in its orbit. ![]() This led him to suggest the planetary model of the atom, in which the electrons revolve in orbits around the nuclear "sun".Įven though the planetary model has long since been discredited, it seems to have found a permanent place in popular depictions of the atom, and certain aspects of it remain useful in describing and classifying atomic structure and behavior. Ernest Rutherford, a New Zealander who started out as Thompson's student at Cambridge, distrusted this "plum pudding" model (as he called it) and soon put it to rest Rutherford's famous alpha-ray bombardment experiment (carried out, in 1909, by his students Hans Geiger and Ernest Marsden) showed that nearly all the mass of the atom is concentrated in an extremely small (and thus extremely dense) body called the nucleus. The demonstration by Thompson in 1867 that all atoms contain units of negative electric charge led to the first science-based model of the atom which envisaged the electrons being spread out uniformly throughout the spherical volume of the atom. We will therefore present the theory in a semi-qualitative manner, emphasizing its results and their applications, rather than its derivation. In order to develop and present this theory in a comprehensive way, we would require a number of mathematical tools that lie beyond the scope of this course. The modern theory of the atom makes full use of the wave-particle duality of matter. Our goal in this unit is to help you understand how the arrangement of the periodic table of the elements must follow as a necessary consequence of the fundamental laws of the quantum behavior of matter.
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