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.)

b.The initial kinetic energy of the neutron is 1.70 10-13 J. Find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision
neutron= ?
carbon nucleus=?

Explanation / Answer

let the mass of the neutron be m implies the mass of carbon = 12m since the collision is elastic both conservation of momentum and energy is applied => mv = mv1 +12m v2 and 1/2 mv^2 = 1/2m v1^2 + 1/2(12m)v2^2 => v = v1 + 12 V2 and v^2 = v1 ^2 + 12v2 ^2 => v^2 = (v- 12v2)^2 + 12 V2 ^2 => 156 v2 ^2 = 24 v(v2) => v2 = 1/6.5(v) kinetic energy of carbon nucleus = 1/2(12m)(v/6.5)^2 ratio of kinetic energy transferred = (24/169)(1/2) x100 = 28.4 % if the initial kinetic energy of the neutron = 1.7 x 10^-13 J => kinetic energy final of the carbon nucleus = 0.482 x 10^-13 J and final kinetic energy of the neutron = 1.217 x 10^-13 J

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