CH5&amp;6

# CH5&amp;6 - 5-25 To find the energy width of...

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Unformatted text preview: 5-25 To find the energy width of the "-ray use "E"t#h2or "E#h2"t#6.58\$10%16eV&s2( )0.10\$10%9s( )#3.29\$10%6eV. As the intrinsic energy width of ~±3"10#6eVis so much less than the experimental resolution of ±5 eV, the intrinsic width can’t be measured using this method. 5-26 The full width at half-maximum (FWHM) is 110 MeV. So "E=55 MeVand using "Emin"tmin=h2, "tmin=h2"E=6.58#10\$16eV%s2 55#106eV( )&6.0#10\$24s’=lifetime ~2"tmin=1.2#10\$23s5-27 For a single slit with width a, minima are given by sin"=n#awhere n=1, 2, 3,Kand sin"#tan"=xL, x1L="aand x2L=2"a#x2\$x1L="aor "=a#xL=5 Å\$2.1 cm20 cm=0.525 ÅE=p22m=h22m"2=hc( )22mc2"2=1.24\$104eV%Å( )22 5.11\$105eV( )0.525 Å( )2=546 eV5-29 With oneslit open P1= "12or P2= "22. With bothslits open, P="1+"22. At a maximum, the wavefunctions are in phase so Pmax="1+"2( )2. At a minimum, the wavefunctions are out of phase and Pmin=¡1¢ ¡2( )2. Now P1P2="12"22=25or "1"2=5, and PmaxPmin="1+"2( )2"1# "2( )2=5"2+"2( )25"1# "2( )2=6242=3616=2.25. 5-32 (a) f=Eh=1.8( )1.6"10#19J( )6.63"10#34J\$s=4.34"1014Hz(b) "=cf=691 nm(c) "E#h"t=6.63\$10%34J&s2’2\$10%6s( )"E#5.276\$10%29J=3.30\$10%10eV6-2 (a) Normalization requires 1="2#\$\$%dx=A2cos2#L4L4%2&xL’()*+,dx=A22’()*+,1+cos4&xL’()*+,’()*+,#L4L4%dxso A=2L. (b) P="2L8#dx=A2cos2L8#2\$xL%&’()*dx=4L%&’()*12%&’()*1+cos4\$xL%&’()*dx%&’()*L8#=2L%&’()*L8%&’()*+2L%&’()*L4\$%&’()*sin4\$xL%&’()*L8=14+12\$=0.4096-3 (a) Asin2"x#\$%&’()=Asin 5*1010x( )so 2"#\$%&’()=5*1010m+1, "=2#5\$1010=1.26\$10%10m. (b) p=h"=6.626#10\$34Js1.26#10\$10m=5.26#10\$24kg m s(c) K=p22mm=9.11"10#31kgK=5.26"10#24kg m s( )22"9.11"10#31kg( )=1.52"10#17JK=1.52"10#17J1.6"10#19J eV=95 eV6-6 "x( ) =Acoskx+Bsinkx#"#x=\$kAsinkx+kBcoskx#2"#x2=\$k2Acoskx\$k2Bsinkx\$2mh2%&’()*E\$U( )"=\$2mEh2%&’()*Acoskx+Bsinkx( )The Schrödinger equation is satisfied if "2#"x2=\$2mh2%&’()*E\$U( )#or "k2Acoskx+Bsinkx( ) ="2mEh2#\$%&’(Acoskx+Bsinkx( )....
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## This note was uploaded on 04/12/2011 for the course PHYS 2D taught by Professor Hirsch during the Winter '08 term at UCSD.

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CH5&amp;6 - 5-25 To find the energy width of...

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