# soltn6 - 5-1 = k L ='2(ro5 p nru 1.tlxl0 kg = rys le x1s-fm...

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\ 5-1 k L = .!':. :'2#+(ro5 rys) le x 1s-f m p nru 1.tlxl0-' kg' -h h ^=7=p1-r*". . *"*l1lu ffi From Problem S2, a 50 keV electron has ,l = 5.36 x l0-3 nm. A 50 keV proon has K =50keY <<Zncz --1g77 MeV so we use p = (zttl()V2: hE (zXS383 }t"VX50 k"Vtv' lZ0eVnm 1.28x 10{ nm t10 As I = zqo = 40.62 9) nm = 0.105 8 nm the mergy of the electron b nonrelativistig so we can 116€ p=I **x=!' . " - z^' K=ln= G'6?x10-aJ sl' -- -=2r5xr0-rs J=l34ev 2mt z(9.tt x t0rr tg[r.oss x to-10 m)' This b about ten times as large as the ground-otate energy of hydrogen, which is 13.6 eV. t15 For a free, non-relativistic electron t =4 = L *the wavenumber and angular Z Zm. frequency of the etectron s de Broglie wave are given by p = it and E = io, eub6titutinS the3e t€sults tiv€8 the disper8io,,,=ladon o, = # * r, = # = # = t = ^' (a) Lr\$p=11srfitu=y,6p-t P2 (Ad' h2 2m, 2m, Zm;z ,, kez h2 kc2 E=-------.=--- Zm.r' r o) (c) To minimize E take # = - #. 5 = o =, = 4= = whr radius = ao. Ttren

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## This note was uploaded on 04/12/2009 for the course PHYSICS 7C taught by Professor Lin during the Fall '08 term at Berkeley.

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soltn6 - 5-1 = k L ='2(ro5 p nru 1.tlxl0 kg = rys le x1s-fm...

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