s3 - a W v 01.l 4 a it c i 1 y i i 7.1 4 s{Lilla:3 1i PHYS...

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Unformatted text preview: a W v. 01 .l 4 .. a it c i 1 y i i 7. .1 4. s {Lilla :3 1i PHYS 260 Problem Set 3 No(2)_t/T where T is the half—life and is equal to 2 x 10‘8 seconds. I ) 1 l 1. Charged 7r mesons (pions) are produced in high—energy collisions between protons and neutrons. NW) They decay in their own rest frame according to the law ,7) W , a. 1L. a _,_m m m , z m m m“ , (ii. u; z 1 I i ;.., V ‘Ir L .i i miller: _ a W N a. a, 1 ‘:::Wmfl a l Ill 9 A burst of pions is produced at the target of an accelerator, and it is observed that two—thirds of them survive at a distance of 30 m from the target. What is the energy of the pions? (Express .w. a at I 7 r . WV, 7 . v .7 .nflfflwfir ,A .. ._,7 WV 7 r i_i JVANILWWV .. ._r ..V__..., _A_ ,nf. i, 7. .__._il‘___ (awn? , )- r l l l l l ' l ‘ l l 1 1V. , (WWW i_,.1r .._.l l 1' l i l l t . I v ' ‘ ‘ ‘ tin—h? 4 l i a i I i i 7 7 1 I ' 9 * l l ' ' 1 + + 7 z ' < A. v I M, ‘l . . rfij‘p _+I_ , ,1. .. 1r 7 i, ,g., ,,,,;L,,,‘,J x r , T r g-7 in 1 a 2. A particle of mass M0 is at rest in the laboratory when it decays into three identical particles, . a ‘ each of rest mass m0. Two of the particles (labeled 1 and 2) have velocities and directions as shown ‘ l ' ' ” in the figure. a (a) Calculate the direction and the speed of particle 3. l \1 f) (b) Find the ratio Mo/mo. F 1"“ i""“ '*“""‘V”‘“""” l 1 “l I.._ ___.“ . l : a i l l y ‘ l l ‘ l i l v.7 l l l T T l I l _j l: 2 j . “m 1]. >T 0 P6. in l Ail E} 4‘9“ , eenai? WAVHA— _—~.—_— I . i l i l E i-— « ;— y — z a . - i D I; i = b ' I r i ‘ l i ; 1 i i - I ‘ l T : . - c I 3 I _ l v I l i 1 l l | x..____.. ‘T l l l L? (T l 7 rYl 1 : l M -r ‘y a ; AL” r—WX fl -“”—*; '—->‘rm*i‘~‘i—~ (a) what are the energies of the *y rays if the decay process causes them to be emitted in opposite directions along the pion’s original line of motion? (b) what angle is formed between the two 'y rays if they are emitted at equal angles to the 3. The neutral 7r meson (no) decays into two 7 rays (and nothing else). If a 71'0 (whose rest mass is direction of the pion’s motion? 135 M eV/ 02 is moving with a kinetic energy of 1 GeV: i . , V i i l , V i. . , _ . _ m i , n m , ,. r ,, , fl 1 a}. i l i r r. . ,. i y ,- , i,f...|..Lrlx u ; A W . r W. _. M , W W .7 a , r _, r, .: ,, n , ,. ,. _, _, ., , , , , w _, , , , a , .élinii fl .lL: 5!. [lit . Iliri ‘ _ l. i 4; l a z : r. i _, _ H ,. n t, ,_ i i. . , .23 < Li i L i i... y. . ,n i : .W .. i: , fl . , 7. . . . H, v , , , .. W 3 ,, i V l i i pr . .iL Iiirllw 1.LI i, ,n . H ,. _ Ll; mm: ,, lilwmignfiznt l .lwiiiwimikl‘rlim ,V M n W _ t m l | ‘. Ti 1 T. , _ w a ‘ :Imll .u," writ iwlll,.ri/.I..M_Sllwr liar 1 ll! mil r", . M J _ n ,. :1! l“ a H m _ , ...|O \L if l _. fill. j; a? a, 26 S- w 1 . {rfif‘T’fj +5.; : _ 7 Ti « .l x H _ .7 _ ll llilvf ii In x l 1 fl ALI! 1.! ll , _ n if: l. 1 m7 :,r n ., W _, , .. , , i . J *r T L [ 7% l I if E .r 1,111+! A, LizuLtzlLll b T191: r; x i 4. _ , ‘ V , :fm ! | ‘> 7» ;,_, 4,. __ ._,‘._.‘__.-_‘ .J,‘ ,_ 1 1 I, l l I 7L I l A, 1 1 l ,7 .. L,_. ,_, ._ F ....r _.- _,_ y 4 ‘ ‘ 1% x ' ‘ r x L, l l I J. t 1 ‘ L I ii» _ -Mjé "f M E?! M 1 “A” w 49;: * .FWL I «Ag. __ f I”? L” h g 4:9. ,L \ ,,,V TH... I { ,,..L ,, 1- V n, H. i I i; I 5 I 1 l | L 5 r , L ...
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