A neutron in a nuclear reactor makes an elastic, head-on collision with the nucl

Question

A neutron in a nuclear reactor makes an elastic, head-on collision with the nucleus of a carbon atom initially at rest.
(a) What fraction of the neutron's kinetic energy is transferred to the carbon nucleus? (The mass of the carbon nucleus is about 12.0 times the mass of the neutron.) YOU ALREADY TOLD ME THE ANSWER TO PART A TO BE 0.28 BUT WHAT ABOUT PART B?



(b) The initial kinetic energy of the neutron is 2.50 x 10-13 J. Find its final kinetic energy AND the kinetic energy of the carbon nucleus after the collision. THANK YOU!

Explanation / Answer

a) fraction of kinetic energy transferred=1/2*Mc*V22 /1/2*Mn*V2

Mn*V+0 = Mn*V1 + Mc*V2

V = V1 + 12V2

V2 = V21 + 144V22 + 24*V1*V2

1/2*Mn*V2 + 0 =  1/2Mn*V21 + 1/2 M2*V22

V2 = V21 +12V22

-132V2 = 24V1

V =- (132/24)*V2 + 12 V2

= 6.5 V2

thus energy transferred = 12*V22/6.52*V22

= 0.28

b)The initial kinetic energy of the neutron is 2.50 x 10-13 J.

energy transferred to carbon = 0.28*2.50 x 10-13 J

= 0.7 x 10-13 J

final energy of neutron =  2.50 x 10-13 J - 0.7 x 10-13

= 1.8  x 10-13 J

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