Physics: Principles and Problems
9th Edition
ISBN: 9780078458132
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Textbook solutions
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Section 28.2: The Quantum Model of the Atom
Exercise 16
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Reddest light emitted by gallium aluminium arsenide.
Blue light is emitted by Indium gallium nitride.
Krypton-fluoride excimer, Nitrogen, Gallium arsenide, Neodymium, C arbon dioxide emit beams that are invisible to eyes.
Exercise 17
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Yes, the green light can be used to pump a red laser since green light photons carry more energy than the red light photons. This is the reason why the read light cannot be used to pump a green laser.
Exercise 18
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The major shortcomings of the Bohr model include the fact that it was neglecting the classical electromagnetism completely within the atom and could not explain why it doesn’t hold. Secondly, it was a model that could threat one electron atoms only i.e. hydrogen like atoms which took a lot from its generality.
Exercise 19
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The Bohr model precisely defines the electron’s path and it’s speed at any time but the uncertainty principle tells us that we can not know both. On the other hand, the quantum model represents the electron orbits as a density cloud with electron having a certain probabilities to take particular coordinates and momentum values.
Exercise 20
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The key feature of the substance (gas) that is operating in laser is the existence of the excited state which is stable enough that allows a large population of atoms to be in it for an extended period of time. Then, the energy gap between this excited state and atom’s ground state corresponds to the energy of photons incident on the the substance. Now, after the atom is hit by the incident light instead of absorbing the incident photon a spontaneous emission occurs and two photons of the same wavelength (monochromatic) and of a constant phase shift (coherent) are emitted. These two, in a chain-reaction manner, continue their way through the substance thus releasing more and more photons of the same wavelength and constant phase difference. This process is called a stimulated emission.
Exercise 21
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The principal characteristics of the laser light are:
1) monochromacy
2) coherency
3) high intensity
4) directionality
Exercise 22
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According to Heisenberg uncertainty principle the more precisely the position is known, less precisely is the momentum known, i.e. the kinetic energy of a particle. High uncertainty is plausible only when the value of the observable is high enough. Therefore if we know that the nucleus is 4 orders of magnitude smaller than the atom, we can expect that the uncertainty of the momentum of an electron localized in such a small electron cloud would be 4 orders of magnitude larger. This would lead to the fact that momentum itself is 4 orders of magnitude larger and sequentially, the kinetic energy $Kpropto p^2$ will be 8 orders of magnitude larger. So if we are looking a hydrogen atom the energy of the ground state would have to be $approx 10times 10^7$eV which is much larger from common nuclear energies.
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