14.+Quantum+Theory

=﻿ Quantum Theory = =﻿ ﻿~About Quantum Theory~ = =﻿* Quantum theory??? ummmmm..... Do you know what quantum theory is?.....why we need quantum theory? Everybody wants to know about quantum theory. Quantum theory evolved as a new branch of theoretical physics during the first few decades of the 20th century in an endeavour to understand the fundamental properties of matter. Quantum theory is about nature of matter. =

=~Key Concepts: = =﻿>In the quantum- mechancial model of the atom, the atom's energy has only specific, quantized values. = =>In the quantum- mechanical model of the atom, only the probability of finding the electron in a specific region can be determined. = =>In the hydrogen atom, the most probable distance of the electron from the nucleus is the same as the electron's orbital radius in the Bohr Model. = =>Quantum mechanics is extremely successful in calculating the properties of atoms, molecules and solids. = =>Lasers produce light that is directional, powerful, monochromatic, and coherent. Each property gives the laser useful applications. = = = =﻿~Vocabulary: = =>Quantum Model: A model that predicts only the probability that an electron is in a particular region. = =>Electron Cloud: The region in which there is a high probability of finding an electron. = =>Quantum Mechanics: The study of the properties of matter, using it wave properties. = =>Coherent Light: Light whose waves are in step, with coinciding maxima and minima. = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">>Incoherent Light: Light whose waves are out of step, with their maxima and minima not coinciding. = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">>Stimulated Emission: The process that occurs when an excited atom is struck by a photon having energy equal to the energy difference between the excited state and the ground state the atom drops to the ground state and emits a photon with energy equal to the energy difference between the two states. = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">>Laser: A device that procedures powerful, coherent, directional, monochromatic light that can be used to excite other atoms; the acronym stands for light amplification by stimulated emission of radiation. = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">﻿~Biography:"Who Discovered Quantum Theory" = == =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">Max Planck discovered Quantum theory. = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">"In the year nineteen hundred, in the course of purely theoretical (mathematical) investigation, Max Planck made a very remarkable discovery: the law of = <span style="background-color: transparent; color: #0066cc; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: underline; vertical-align: auto;"><span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-decoration: underline;">[|radiation] =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">of bodies as a function of temperature could not be derived solely from the Laws of Maxwellian electrodynamics. To arrive at results consistent with the relevant experiments, radiation of a given frequency f had to be treated as though it consisted of energy atoms (photons) of the individual energy hf, where h is Planck&apos;s universal constant."-Albert Einstein = = = <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;"><span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">Max Karl Ernst Ludwig Planck was born in Kiel, Germany, on April 23, 1858, the son of Julius Wilhelm and Emma Planck. Planck studied at the Universities of Munich and Berlin, where his teachers included Kirchhoff and Helmholtz, and received his doctorate of philosophy at Munich in 1879. He was a private tutor in Munich from 1880 to 1885. He then was an Associate Professor of Theoretical Physics at Kiel until 1889. That same year he became professor at Berlin University. He was the professor there until he retired in the year of 1926. He died at Göttingen on October 4, 1947. = = = = = = = = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">﻿~Equations: Problem Solvers =

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">1. Hydrogen has a red emission line at 656.3 nm, what is the energy and frequency of a photon of this light? Note: Planck’s constant = 6.626 x 10–34 J·s, speed of light = 2.998 x 108 m/s ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;"> = c  ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">Ephoton = h = hc   = (2.998 x 108 m/s) 656.3 nm 10–9 m 1 nm ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">Ephoton = (6.626 x 10–34 J·s) (2.998 x 108 m/s) 656.3 nm 10–9 m 1 nm ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;"> = 4.568032912 x 1014 s–1 ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">Ephoton = 3.02677861 x 10–19 J ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">4.568 x 1014 s–1 or Hz ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 24px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; vertical-align: auto;">Answer (E): ___ 3.027 x 10^-9 J__ ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 24px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; vertical-align: auto;">Answer (): _4.568 x 10^-10m **

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">2. What is the de Broglie wavelength for an electron moving at 2.42 x 106 m/s? ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">Note: me = 9.109 x 10–31 kg ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;"> = h mu  = ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">6.626 x 10–34 J·s (9.109 x 10–31 kg) (2.42 x 106 m/s) ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; text-align: left; text-decoration: none; vertical-align: auto;">= 3.00583657 x 10–10 m many orders of magnitude larger than the diameter of an electron **

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16px; text-align: left; text-decoration: none; vertical-align: auto;">**<span style="background-color: #ffffff; color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%; vertical-align: auto;"> Answer: ___ 3.01 x 10–10 m ** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 3px; text-align: left; text-decoration: none; vertical-align: auto;">6 = =

= = = = = = = = = = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">~Review Questions: = <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">1. Who discovered Quantum Theory? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">2. What is the difference between quantum mechanics and quantum model? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">3. Does quantum theory deals with atoms, matter of nature, and energy? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">4. In the quantum- mechanical model of the atom, the atom's energy only has? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">5. In the hydrogen atom the most probable distance of the electron from the nucleus is the??? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">6. Quantum mechanics is extremely successful in? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">7. What model is used in quantum theory? <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">8. What is the difference between incoherent light and coherent light? == = = = = = = = = = = = = = = = = = = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 200%;">﻿ = = = =<span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">﻿ = <span style="color: #ff007b; font-family: 'Comic Sans MS',cursive; font-size: 130%;">
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