Elementary Modern Physics
Elementary Modern Physics PHY 215
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Miss Lucienne Hamill
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This 7 page Class Notes was uploaded by Miss Lucienne Hamill on Wednesday October 28, 2015. The Class Notes belongs to PHY 215 at Wake Forest University taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/230736/phy-215-wake-forest-university in Physics 2 at Wake Forest University.
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Date Created: 10/28/15
Chapter 5 edoflmper P1 Tlpler Srl a Whatrs the deBroglle wavelength of a leg rnass at a spe ye s de Broglle wavelength ls to bel ar397 b What shouldbe the speed ofsuch a rnass rfrt cm 7 P2 Tlpler 573 Eleetrons m an eleetron rnreroseope are aeeelerated from rest through a potenual dlfference ofva so therr de Broglle wavelength ls 0 04 nrn Whatrs v 7 Mn 1 Q l e Conslder the functlon gk and rts transfonn fx jdk gage If a lncreases then the wldth of m l rnereases stays the same 4 depends on the value ofkn P3 Tlpl er 5720 A eertarn tunrng fork vrbrates at 880 Hz If the tunrng fork ls tapped frequencles eontalned m the sound pulse that reaehed your ear7 P4 Conslder awave packetforwhlch Ak N 7K s k s K 0 everywhere else M V H m ls upheld Q2 partreulartrrne a Where are we most likely to nd the particle b On which side of the yaXis is it more likely to nd the particle c What is the likelihood that we will nd it at X gt 100 P5 Consider a particle described by a wave function wX where the function is 0 for Xlt0 and X gt 3 and AX for in between 0 and 3 a What is A b What is the probability of nding the particle exactly at X 29 c What is the probability of nding the particle between X 2 and X 3 P6 7 Physicists and biophysicists like to do time resolved spectroscopy Recently attosecond laser pulses actually 650 as have been made What is the limit in time resolution one can achieve when working with 300 nm light Q3 According to the Heisenberg Uncertainty Principle there must always be an uncertainty h in the l momentum of aparticle 2 energy of a particle 3 Lifetime of a particle 4 All of the above 5 None of the above P7 Tipler 532 In order to locate a particle eg an electron to within 5 X 103912 m using electromagnetic waves the wavelength must be at least this small Calculate the momentum and energy of a photon with 7 5 X 103912 m If the particle is an electron with AX 5 X 103912 In what is the corresponding uncertainty in its momentum P8 Use the uncertainty relation to estimate the ground state energy of a harmonic oscillator The energy is given by 20060908 Problem Solutions Problem 1 Tipler 130 The formula for the Doppler effect for approach is Equation 138 1 L 1 f0 ll 1 In this problem the proper wavelength in the frame of the source is k0 650 nm red and we want to find the speed of approach v that will shift it to 7 590 nm green The ratio of these two wavelengths is MAO 590650 so the corresponding frequency ratio is fo 650590 1102 becausef ch We substitute into Eq 1 and get M 2 1 1102 2 M 1102 1214 31 12141 3 2214 0214 3 00967 3 v 290 gtlt107 ms 2 This is the speed at which to approach a red light so that it would appear green It s 648gtlt107 mileshour so you would get a ticket for speeding instead of running a red light Problem 2 Tipler 132 Since the frequency is increased the star must be approaching the Earth We compare the formula in the problem telling how much the frequency is increased f 102f0 with the equation for the Doppler shift for an approaching object Eq 1 above and get 1 102 3 We have to solve this for 5 We could solve it by the method that was used in the previous problem square the equation clear is of fractions rearrange it to solve for l and get an answer But let s observe that the frequency changes by only 2 so i must not be very big Therefore here is an opportunity to use the binomial expansion 1 11 1 11 1 1 1 2 12 4 Notice that on the last step we didn t square out 1 y completely we dropped the 52 term That s because in the binomial expansion step we already dropped small terms of the order of 32 so to be consistent we have to drop the 52 term here also Next we take 20060908solndoc 1 L Eq4uin 39 quot quot 39 again ML 1 quot inEq 3 1 12 T212 1o 5 We compare Eqs 3 and 5 and get 6 002 or v 0025 600x106 ms 6 Doing the calculation exactly Wilhout using me binomial expansion gives 00198 Problem 3 Tipler 140 m Alpha Cemaun is 4 r39y away so me traveler wem L 1 p Scy in 6 or 307W my W v58 34vc 1 Wlt341I31 3141p1 31 1 pl 11 05625 v 03 20060908501ndoc 2 b At yAto 16y and 39y1132 1667 Ar 1ss7sy 10y or 4y olderman me omeru39aveler Ennh 6 8 Alpha Cum 2006090850nd0c 3 Problem 4 Tipler 145 Two events exploslons tn frame 5 A rt 480 rn st 0 B x2 1200 rn eta 1500 rn Here ts the spaeetarne graph vvtth these two events plotteol on tt W1 mm mm mt X tt 4 In frame 539 the events oeeur at the same potnt We draw the stratght ltne between the 39 39 39 0 be 39t ttr ongm The slope ofthls ltne ts slopeAB 2 08 12007480 The ltne x 0 vvhteh ts the st39atrts ts parallel to the ltne AB so has the sarne slope General theory p 29 says the slope ofthe st39atrts ts 10 so 1 0480 208 andthen To callbratequot the t axls vve ean olo the followmg Use the Lorentz transformatt equattonz mew 27 2 revvntten as t y x vve ealeulate the ttrne of event A tn 539 252114037048 480 m263mt and ofeventB 20060908soln doe ct 1141500 m 0481200 m 1053 m Therefore cAt39 1053 m 263 m 1316 m and At39 439 gtlt10 6 s To check since the events are at the same point in 839 AI39 is a proper time interval and is related to At by the time dilation formula 76 M w439x106 s y 114 It checks 20060908solndoc 5
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