It is found that ifa neutron suffersan elasticcollinear collision with deuerium at rest , fractional loss of energyis P_(d) whilefor itssimilarcollisionwith carbon nucleous at rest , fractional loss of energy is P_(c ) are respectively .........

It is found that ifa neutron suffersan elasticcollinear collision with

1.	It is found that ifa neutron suffersan elasticcollinear collision with deuerium at rest , fractional loss of energyis P_(d) whilefor itssimilarcollisionwith carbon nucleous at rest , fractional loss of energy is P_(c ) are respectively .........
Answer» `(.89,.28)` `(-28,.89)` (0,0) `(0,1)` Solution : From law of conservationof momentum `mv_(0) +mv_(1)+2mv_(2)` ` :. V_(0) =v_(1)+2v_(2) ""…..(2)` ` :. V_(1)+2v_(2) =v_(2) -v_(1)` ` :. 2v_(1) =-v_(2)` From EQU . (2) `v_(0)= -2v_(1) -v_(1) =-3v_(1)` ` :. v_(1) = - (v_(0))/3` ` :. v_(2) = (2v_(0))/3 ` Decreasein kinetic ENERGY `P_(d) =(1/2mv_(0)^(2)-1/2mv_(1)^(2))/(1/2mv_(0)^(2))` `=(v_(0)^(2) -(v_(0)^(2))/9)/(v_(0)^(2)) "" [ :. v_(1)=-(v_(0))/3]` `P_(d) =8/9 = 0.8888 APPROX 0.89` Now is econd collision: From law of conservation of momentum `mv_(0) =mv_(1) +mv_(2)` ` :. v_(0) =v_(1) +12v_(2) "".....(3)` For elasticcollisione = 1 `v_(2) -v_(1) = v_(0) ""....(4)` From (3) and (4) `v_(1)+12v_(2)=v_(2)-v_(1)` ` :. 2v_(1) = 011v_(2)` ` :. v_(1)-(11v_(2))/2 and v_(2) = -(2v)/13` ` :. v_(1)= -(11v_(2))/2 and v_(2) = - (2v_(1))/13 ` `Now , 13v_(1) = -11v_(0) +v_(1) and v_(2) = - (11v_(0))/13 + v_(0)` ` :. 2v_(1) =-11v_(0) "" :. v_(2) =(2v_(0))/13 ` ` :. v_(1) = (11v_(0))/13` Decrease in kinetic energy `P_(c) = ((1/2mv_(0)^(2))-1/2m(-(11v_(0))/13)^(2))/(1/2mv_(0)^(2))` `:. (v_(0)^(2)-(121v_(0)^(2))/169)/(v_(0)^(2))=(169-121)/169 =48 /169 = 0.28` ` :. P_(d) = 0.89 ,P_(c ) = 0.28` .