A particle is in a state with angular momentum z-component đť‘šâ„Ź and square total angular momentum đť‘™(đť‘™ + 1)â„Ź 2 . (a) show that = = 0. (b) show that = = (đť‘™(đť‘™ + 1)â„Ź 2 â’ đť‘š2â„Ź 2 )/2 . (c) find 〈đťżđť‘Ąđťżđť‘¦ + đťżđť‘¦đťżđť‘Ą 〉/2.
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Using the relation,
v2f=m2−m1m1+m2v2i+2m1m1+m2v1iAccording to question,v2i=0m1=m (suppose)m2=119mNow,v2f=0+2mm+m19v1i=2m19m+1m19v1i=m10 m19v1iv2f=19 10v1ior v2fv1i=19 10Percentage of energy transferred=1/2 m2v2f21/2 m1v1i2×100=1/191×19×1910×10×100=19100×100=0.19 %
in
v2f=m2−m1m1+m2v2i+2m1m1+m2v1iAccording to question,v2i=0m1=m (suppose)m2=119mNow,v2f=0+2mm+m19v1i=2m19m+1m19v1i=m10 m19v1iv2f=19 10v1ior v2fv1i=19 10Percentage of energy transferred=1/2 m2v2f21/2 m1v1i2×100=1/191×19×1910×10×100=19100×100=0.19 %
in
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