Physics 263: Electromagnetism and Modern Physics

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1 Exam 3 May 12, 2003 Page 1 Physics 263: Electromagnetism and Modern Physics Sections Exam 3 ProfJJ Kelly Instructions: This is a closed book, closed notes exam to be completed in 50 minutes You may use a basic scientific calculator, but no other aids are permitted The final page provides a brief compilation of possibly useful information, including relevant physical constants Work each problem in the space provided If additional space is needed, use the back of the previous page and indicate that you have done so Please write your name on each page, including this one Do not use red ink Choose 4 out of 5 problems Use an X in the table below to indicate which problem to omit If there is no X, we will grade the first four Explain your reasoning and show your work Partial credit will be awarded when the relevant physical principles are applied even if mistakes are made in execution of the steps However, correct guesses without any explanation may be penalized Algebraic answers must have consistent dimensions and numerical answers must have consistent units Honor pledge: please copy and sign "I pledge on my honor that I have not given or received any unauthorized assistance on this examination" Pledge: Signature: Printed name: So /u+,'0115 Student ID number: Se'ction: Problem total Score Physics 263 Prof JJ Kelly

2 Page2 1 A Michelson interferometer contains an evacuated cell of length f in one arm, as shown A beam of monochromatic light with wavelength Aoin vacuum is split by the alf-silvered mirror, such that one beam passes through the cell twice before being recombined with a second beam that traverses a similar path in air If a gas is slowly admitted into the cell, N fringes are observed to move past a fixed point on the observation screen Find an expression for the index ofrefraction of the gas, ngas, at its final pressure Explain your reasoning (25 pts) mirror gas cell 8ource i' ; ' i 1'c half-silvered mirror D observationscreen IV o--rv0 TL- r 1 -ct- 7:L cd( (n-i\ J 1 -== rriv o n= \ -t N o 2 -cl- -jj d# Physics 263 Exam 3 Prof JJ Kelly

3 Page3 2a) Light with wavelength A strikes a diffraction grating with spacing a at an angle q>itom perpendicular Find an expression for the angle e for constructive interference of order m 4 o-j, : (15pts) (),p - 0 e;::: h'1, ()'\ >- '!, e = - -1-' 2b) An American standard television picture (before HDTV) contains approximately 485 horizontal lines of varying intensity Estimate the ratio between minimum viewing distance and vertical picture size for which these lines cannot be resolved by a typical viewer Explain your reasoning [Hint: estimate the pupil diameter and use A -550 nm for visible light] (10 pts) h 0 = hjn --k D-Jl d I"-' 3 '?1 m a-:, dl S' Ḻ - h - ;::> ljer-jd '--r ') - "" /1 t'j'>- w rt-c-,() () fj "'"' L = t-il

4 Page4 3 A negative pion at rest decays to a muon and a muonic antineutrino; the reaction is written as n- Ji- +vji' Compute theand antineutrino kinetic energies in MeV given m1c= 270m", mu mil = 206m" and mv ::::: 0 (25pts) CDI1erlldtI{)rI f enu'";y +-y)1c",,"4/vi; +- )J == ry1trc<' F = P = E,/ c A \ + V7\ tj t1", 11j'1 m< 5 t)j /1 1"- " 2 I D cj =- E L v; /A ( C J --" Co!,s;-4 '-Ie ( '2 -" ()'\TTC - /'-) ;:: 0 - t CoJ "2 "2- E := rn'lt + w\,) "2 C ;;"""rr -) :So5"'1 ;t1it C 2-1ft' fy1ev 7S-lJ Y'1,et:L - KA ;: E - m)c"2=- = 5-' b'l r1-\el'2= 'C)e Me-V E ;:pc-=f/c ;/ v "h t/-::i D tl -d --

5 Page5 4 By analyzing the scattering of sunlight, Thomson estimated the classical radius of the electron to be 282 fm where 1 femtometer is 10-15m Suppose that an electron is illuminated by sunlight with an intensity of 500 W/m2and that all light within a disk of this radius is completed absorbed a) How long would it take for the electron to acquire an energy of 1 ev? How does this compare with the observation that photoelectrons are emitted promptly when light of sufficiently short wavelength illuminates a metal, even if the intensity is small? (15 pts) /ie 7,/ _I 10 S' -=- I-rJ 0f4 y t' i:>e L 1 t::= I, tj = r Jf" r - / I'TJr2 -:u --- o-p- "6 -tl LI; 7:L b) How does the photon hypothesis solve this problem? (10 pts) fj{ -fi- ;, 4 J CL -t <>-, J J Ji- ;, ) ;r -rl } ;, } a--i' z;l ()

6 Page 6 5 Positronium consists of an ordinary (negatively charged) electron plus a positron (the positively-charged antiparticle of the electron) orbiting about their center of mass as a bound system similar to an atom Use the Bohr model to deduce the binding energy of positronium Express your final answer in electron volts [Hint: the electron and positron have equal masses In the Bohr model these two particles would be on opposite sides of a diameter through the center of their common circular orbit and the total orbital angular momentum is quantized] (25 pts) ) 2 E :=c ;;2 (mevl) - - ""2 - me-v - r e-?- -( )L ;)y'y\e\j -r -::: n 1:; / 15 t -t- el \ E:= - -=- Ltr ] -0' )2 r - ::---"Z IY\-1<- e I:: [ r r\: \/, I,,/ '- -' E = - L ""'( "- '-)'- " '1 lhtj2 I '"l,j2 - m G Lf e - 1'11 ';:; l:t3= L& e V M tltyf e g =-EI tlt; -tt--t Physics 263 Exam 3 Prof JJ Kelly

7 Page7 Possibly useful information! - Q jdiie=- Eo! - d<l>b jdse=-- dt D = EE = EoE+P - 1 static: E =- 4nEo f E E2 B2 u=+- 2 2fJ-o r dq2 r = (n-1)(---) f RJ R2 1(8) =10 sma ( ) smgle slit:, x =y(x-ut), ux t =y(t--) c2 na a =-sin8 A a 2 tdiib=o IdS - jh!l{ - I -- +eo a:e ) B = fj-h = fj-o (H + M) - fjf Idsxr static: B = - r2 S=ExB/fJ-o =s0 s I f 4n 1(8) = I sm N{3 grating: )( sin {3 J E = ymc2 P=ymv trd (3 =-sin8 A 2 Y = (1- (y) -X (mc2) = E2 - (pc y Ji2 --If/'(x) + V (x)lj/(x) =EIj/(x) 2m

8 Page c =- Eof-lo m c = 29979x1O8 - s Eo = 88542xlO-12 F m f-lo=4nxlo-7 A e = x C me = 91O9xlO-31 kg = 0511MeV / c2 N A =6022x1O23 mole-1 mp =1672 X kg =93827 MeV / c2 f-lb=927xlo-24 { T h =6626 X J S lic =1973eV run f-ln =505xlO-27 { T li =1055xlO-34J s e2 1 4nEolic 137 Dimensions and Sf Units for Basic Electromagnetic Quantities Quantity Unit Abbreviation Conversions Dimensions Charge Coulomb C Q Electric potentia] Volt V lic ML2T2Q-I Electric field Volt/meter Vim NIC MLT-2Q-I Capacitance Farad F CN M -I D2T2Q2 Current Ampere A Cis QT-1 Magnetic field Tesla T N I(A m) MT-1 Q-I Magnetic flux Weber Wb JIA ML2T-1Q-l Inductance Henry H JIAL ML2Q-2 Resistance ohm Q VIA ML2T-1Q-2

. Explain your reasoning and show your work. Partial credit will be awarded when the

. Explain your reasoning and show your work. Partial credit will be awarded when the Name: Page 1 Physics 263: Electromagnetism and Mol1:ernPhysics Sections0101-0105 Final Exam Prof J.J. Kelly Instructions:. This closed book, closed notes exam contains 8 problems to be completed in 2 hours.