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# In each of 1 through 10, classify the origin of the system ISBN: 9781111427412 173

## Solution for problem 10.66 Chapter 10

Advanced Engineering Mathematics | 7th Edition

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Problem 10.66

In each of 1 through 10, classify the origin of the system X= AX for the given coefficient matrix. If software is available, produce a phase portrait.A = 3 5 5 7

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Physics 2080 Chapter 30, 31, 32 April 19, 2016 Amanda Biddlecome 1) Blackbody Radiation -­‐blackbodies in a furnace give off electromagnetic radiation -­‐light going into blackbodies is absorbed -­‐Wien’s Displacement Law: f peak =(5.88X10 s K )T 10 -­‐1 -­‐1 -­‐blackbody radiation is quantized depending on frequency E =nhf *n=0,1,2,3…; energy level *f=frequency *h=Planck’s Constant: EITHER (6.63X10 Js) OR (4.14X10 eVs) ­‐34 -­‐15 -­‐Einstein discovered that light (photons) was quanta of light E=hf *energy of quanta of light 2) Photoelectric Effect -­‐more intense beams of light contain more photons but each photons energy remains the same -­‐occurs when beam of light strikes metal and electrons are ejected and produce an electric current -­‐work function=minimum amount of energy required to eject electrons from a metal K max =E-­‐W o *K max =maximum kinetic energy of electron *E=energy *W =wook function -­‐more intensity=more electrons of same energy -­‐cutoff frequency=frequency required to eject electrons 3) Photons -­‐they travel at the speed of light and have zero rest mass energy p=(hf/c)=(h/wavelength) *p=momentum -­‐momentum increases with increasing energy -­‐Compton Effect=change in wavelength of scattered photon because it strikes a stationary electron Δλ=λ -­‐λ=h/m c(1-­‐cosθ) e -­‐wave-­‐particle duality=de Broglie *waves and particles can act like each other λ=h/p *λ=de Broglie’s wavelength *h=Planck’s constant *p=momentum 4) Heisenberg Uncertainty Principle -­‐you can either measure the momentum or the position accurately, not both -­‐generally not noticed in macroscopic situations

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