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← JEE Advanced 2015 · Paper 2
PhysicsMultiple correct+4 / -2Question 16 of 60

JEE Advanced 2015 · Paper 2, Physics question 16

A fission reaction is given by 92236U→54140Xe+3894Sr+x+y^{236}_{92}\mathrm U\to{}^{140}_{54}\mathrm{Xe}+{}^{94}_{38}\mathrm{Sr}+x+y, where xx and yy are two particles. Considering 92236U^{236}_{92}\mathrm U to be at rest, the kinetic energies of the products are denoted by KXeK_{Xe}, KSrK_{Sr}, KxK_x (2 MeV) and KyK_y (2 MeV), respectively. Let the binding energies per nucleon of 92236U^{236}_{92}\mathrm U, 54140Xe^{140}_{54}\mathrm{Xe} and 3894Sr^{94}_{38}\mathrm{Sr} be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option(s) is(are)

Choose one or more options
Answer and worked solution

Official answer: A

Conservation laws.

  • Charge: 92=54+3892=54+38, so x and y are neutral.
  • Nucleon number: 236=140+94+2236=140+94+2.

So x and y are two neutrons.

Energy released.
Q=140(8.5)+94(8.5)−236(7.5)=1989−1770=219 MeV.Q=140(8.5)+94(8.5)-236(7.5)=1989-1770=219\text{ MeV}.
The neutrons take 4 MeV, leaving 215 MeV for Xe and Sr.

Sharing. Their momenta are (nearly) equal and opposite, so K∝1/mK\propto1/m:
KSr=215⋅140234≈129 MeV,KXe≈86 MeV.K_{Sr}=215\cdot\frac{140}{234}\approx129\text{ MeV},\qquad K_{Xe}\approx86\text{ MeV}.

(A)