m = mass of neutron
M = mass of nucleus = 11.3 m
vi = initial velocity of neutron before collision = ?
Vi = initial velocity of nucleus before collision = 0 m/s
vf = final velocity of neutron after collision
Vf = final velocity of nucleus after collision
using conservation of momentum
mvi+MVi=mvf+MVf(m)vi+(11.3m)(0)=mvf+(11.3m)Vfvi=vf+(11.3)Vfvi−vf=(11.3)Vfeq−1
using conservation of kinetic energy
mvi2+MVi2=mvf2+MVf2(m)vi2+(11.3m)(0)2=mvf2+(11.3m)Vf2vi2=vf2+(11.3)Vf2vi2−vf2=(11.3)Vf2(vi−vf)(vi+vf)=(11.3)Vf2(13.7)Vf(vi+vf)=(11.3)Vf2vi+vf=Vfeq−2
adding eq-1 and eq-2
(vi−vf)+(vi−vf)=(11.3)Vf+Vf2vi=12.3Vfvi=6.15Vf
fraction of energy transferred is given as
fraction=(0.5)mvi2(0.5)MVf2fraction=mvi2MVf2fraction=m(6.15Vf)2(11.3m)Vf2fraction=(6.15)211.3=0.298≈0.3
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