On Saturday morning John walked for 2 hours and then ran for 30 minu.pdf

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On Saturday morning John walked for 2 hours and then ran for 30 minutes. Is he ran twice as fast as he walked and he covered 12 miles altogether, how fast did he walk Solution Let w = John\'s speed walking r = John\'s speed running Since distance = speed * time, then: 2w + (0.5)r = 12 r = 2w Substituting 2w for r, we get 2w + (0.5)(2w)=12 3w = 12 w=4 r = 2(4) r = 8 Therefore, John walks at 4mph and runs at 8mph.

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Compare and contrast the ideas that led to the Bohr model of the atom to the ideas that led to the quantum mecchanical theory that gave rise to the hydrogen atom wave functions. Solution The difficulty with the planetary picture provided before the Bohr model is that it is inconsistent with a well established fact of classical electrodynamics which says that an accelerated electric charge must continually radiate energy. If electrons actually followed such a trajectory, all atoms would act as source of radiation. The radiated energy would come from the kinetic energy of the orbiting electron; as this energy gets radiated away, As a result the electron would quickly fall into the nucleus. According to classical physics, no atom based on this model could exist for more than a brief fraction of a second. In contrary The Bohr model is a mixture of classical physics and quantum physics. The main postulated of Bohr\'s orbit are as follows: 1.) The electron in the atom moves in a circular orbit centred on its nucleus. Its motion in the orbit is governed by the Coulomb electric force between the negatively charged electron and the positively charged proton.The radius of orbit can be given as [r = nh/(2*pi*m*v), where n is principal quantum number.Emission spectrum of hydrogen is nicely explained by Bohr model. However, one serious difficulty with the Bohr model was that it was unable to explain the spectrum of any atom more complicated than hydrogen. 2.) An electron in a Bohr orbit does not continuously radiate electromagnetic radiation. Its energy is therefore constant. The orbit is referred to as a stationary orbit. 3.) Electromagnetic radiation isonlyemitted when the electron changes from one orbit to another of a lower total energy. (The electron is said to undergo atransition.) In such a case, the energy lost, E, is emitted asonequantum of radiation of frequencyfas given by thePlanck–Einstein formula: E = hf Although the Bohr model hypothesis for the quantization of angular momentum can be justified in terms of electron wave ideas, the Bohr model remains profoundly unsatisfactory as a wave model for the atom and also was not able to answer that why it doesn\'t fall into the nucleus. The main failures of Bohr\'s model are: - a mixture of classical and quantum ideas (electrons move classically on orbits, but their possible energy states are quantified) - postulates that on the allowed orbits electrons do not radiate (conflict with Maxwell’s theory) - could not account for the maximal electron numbers on one shell - could not explain splitting of the spectral lines in magnetic fields - it is a non-relativistic theory although the speed of the electrons is close to c In the Quantum Mechanical Model, the electron is treated mathematically as a wave. The electron has properties of both particles and waves. The advantage of Quantum Mechanical model over Bohr model is that it was successful to give explaination of the fact that electron does not fall in.

Compare and contrast the ideas that led to the Bohr model of the ato.pdf

On Saturday morning John walked for 2 hours and then ran for 30 minu.pdf

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On Saturday morning John walked for 2 hours and then ran for 30 minu.pdf