Quantum Theory

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Quantum Theory FYI 1/3 of exams reviewed, and normal is around 71%. Perusing: Ch13.1-13.5 No HW this week !

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What is Quantum Theory? Quantum hypothesis is a hypothesis expected to portray material science on an infinitesimal scale ,, for example, on the size of iotas, atoms, electrons, protons, and so on. Established hypotheses: Newton – Mechanical movement of items (F = mama) Maxwell – Light regarded as a wave NEITHER OF THESE THEORIES QUITE WORK FOR ATOMS, MOLECULES, ETC. Quantum (from Merriam-Webster) Any of the little additions or packages into which numerous types of vitality are subdivided. Light is a type of vitality is a quantum of EM vitality

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The Wave – Particle Duality OR

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Light Waves Until around 1900, the traditional wave hypothesis of light depicted most watched marvel. Light waves: Characterized by: Amplitude (A) Frequency ( n ) Wavelength ( l ) Energy of wave an A 2

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And then there was an issue… In the mid 20 th century, a few impacts were watched which couldn't be comprehended utilizing the wave hypothesis of light. Two of the more persuasive perceptions were: 1) The Photo-Electric Effect 2) The Compton Effect I will depict each of these today…

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What in the event that we attempt this ? Fluctuate wavelength, altered plentifulness No Yes, with low KE No Yes, with high KE No Photoelectric Effect (I) "Traditional" Method Increase vitality by expanding abundancy electrons discharged ? electrons transmitted ? No electrons were radiated until the recurrence of the light surpassed a basic recurrence, and soon thereafter electrons were discharged from the surface! (Review: little l  vast n )

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Photoelectric Effect (II) Electrons are pulled in to the (emphatically charged) core by the electrical drive In metals, the peripheral electrons are not firmly bound, and can be effortlessly "freed" from the shackles of its molecule. It just takes adequate vitality… Classically, we increment the vitality of an EM wave by expanding the power (e.g. splendor) Energy an A 2 But this doesn't work ??

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PhotoElectric Effect (III) A substitute view is that light is acting like a molecule The light molecule must have adequate vitality to " free " the electron from the particle. Expanding the Amplitude is essentially expanding the quantity of light particles , however its NOT expanding the vitality of every one !  Increasing the Amplitude does diddly-squat! In any case, if the vitality of these "light molecule" is identified with their recurrence , this would clarify why higher recurrence light can thump the electrons out of their iotas, however low recurrence light can't…

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"Light molecule" Before Collision After Collision Photo-Electric Effect (IV) In this "quantum-mechanical" picture, the vitality of the light molecule (photon) must conquer the coupling vitality of the electron to the core. In the event that the vitality of the photon surpasses the coupling vitality , the electron is discharged with a KE = E photon – E restricting . The vitality of the photon is given by E=h n, where the consistent h = 6.6x10 - 34 [J s] is Planck's steady.

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Photons Quantum hypothesis depicts light as a molecule called a photon According to quantum hypothesis , a photon has a vitality given by E = h n = hc/l h = 6.6x10 - 34 [J s] Planck's consistent , after the researcher Max Planck. The vitality of the light is relative to the recurrence (contrarily corresponding to the wavelength) ! The higher the recurrence (bring down wavelength) the higher the vitality of the photon. 10 photons have a vitality equivalent to ten times a solitary photon. Quantum hypothesis depicts tests to astounding exactness , though the traditional wave portrayal can't .

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The Electromagnetic Spectrum Shortest wavelengths (Most vivacious photons) E = h n = hc/l h = 6.6x10 - 34 [J*sec] (Planck's steady) Longest wavelengths (Least vigorous photons)

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Momentum In material science, there's another amount which we hold pretty much as sacrosanct as vitality, and this is energy . For a question with mass , force is given by: The units are: [kg] [m/s] == [kg m/s] Unlike vitality , which is a scalar , energy is a vector. That is it has both extent & bearing. The bearing is along the heading of the speed vector. The reason it is vital in material science, is, on account of like Energy: TOTAL MOMENTUM IS ALWAYS CONSERVED

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Do photons convey force ? DeBroglie's recommended that the a photon conveys vitality, as well as conveys energy. In any case, p = mv , and photon's have m=0, so by what means would it be able to be that the energy is not zero?? DeBroglie hypothesized that photons convey force, and their energy is: If we substitute: E = hc/l into this condition, we get: Momentum conveyed by a photon with wavelength l

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DeBroglie's Relation DeBroglie connection p = h/l = h/p Photons convey energy !!! E = h c/l Photons additionally convey vitality !!! Both vitality & energy are conversely relative to the wavelength !!!  The most astounding vitality photons are those which have little wavelength (that is the reason gamma beams are so hazardous)

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Incident X-beam wavelength l 1 M A T E R Scattered X-beam wavelength l 2 l 2 > l 1 e Electron comes flying out The Compton Effect In 1924, A. H. Compton played out an investigation where X-beams encroached on matter, and he quantified the scattered radiation. Louis de Broglie Problem: According to the wave picture of light, the episode X-beam ought to surrender some of its vitality to the electron, and develop with a lower vitality ( i.e., the adequacy is lower), yet ought to have l 2 =l 1 . It was found that the scattered X-beam did not have a similar wavelength ?

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Electron at first very still (practically) Scattered X-beam E 2 = h c/l 2 Incident X-beam E 1 = h c/l 1 l 2 > l 1 e Quantum Picture to the Rescue Compton found that on the off chance that you regard the photons as though they were particles of zero mass, with vitality E=hc/l and energy p=h/l  The impact carries on pretty much as though it were 2 billiard balls impacting ! Photon acts like a molecule with vitality & energy as given above!

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Summary of Photons can be dealt with as " bundles of light " which carry on as a molecule. To portray cooperations of light with matter, one for the most part needs to speak to the molecule (quantum) depiction of light. A solitary photon has a vitality given by E = h c/l , where h = Planck's consistent = 6.6x10 - 34 [J s] and, c = speed of light = 3x10 8 [m/s] l = wavelength of the light (in [m]) Photons additionally convey energy . The force is identified with the vitality by: p = E/c = h/l

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So is light a wave or a molecule ? On naturally visible scales, we can treat countless as a wave. At the point when managing subatomic marvel , we are frequently managing a solitary photon , or a couple. For this situation, you can't utilize the wave depiction of light. It doesn't work !