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? (b) The initial kinetic energy of the neutron is 1.60 X 10-13J. Find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision. (The mass of the carbon nucleus is nearly 12.0 times the mass of the neutron.)
(a)
The fraction of the kinetic energy of the neutron which is transferred to the carbon nucleus.
Answer to Problem 9.27P
The fraction of the kinetic energy of the neutron which is transferred to the carbon nucleus is
Explanation of Solution
Given info: The initial kinetic energy of the neutron is
Write the equation of initial kinetic energy of the neutron.
Here,
Write the equation of final kinetic energy of the carbon nucleus.
Here,
Divide equation (2) by equation (1).
Write the equation of conservation of momentum.
Here,
Write the equation of initial momentum.
Here,
Write the equation of final momentum.
Here,
Substitute
Initially the carbon nucleus is at rest due to which the initial velocity of the carbon nucleus
Substitute
When an elastic head on collision occurs between two objects then velocity after the collision is same as the velocity before the collision but in negative directions.
Write the equation for velocity for head on elastic collision.
Substitute
Substitute
Substitute
Conclusion:
Therefore, the fraction of the kinetic energy of the neutron which is transferred to the carbon nucleus is
(b)
The final kinetic energy of the neutron and the final kinetic energy of the carbon nucleus.
Answer to Problem 9.27P
The final kinetic energy of the neutron is
Explanation of Solution
Given info: The initial kinetic energy of the neutron is
The fraction of the kinetic energy of the neutron which is transferred to the carbon nucleus is
The fraction of the kinetic energy which stays with the neutron after it transfers its energy to the carbon nucleus is,
Here,
Substitute
Thus, the fraction of the kinetic energy which stays with the neutron is
Write the equation of final kinetic energy of the neutron.
Here,
Substitute
Thus, the final kinetic energy of the neutron is
The neutron transferred a fraction of its energy to the carbon nucleus.
Write the final kinetic energy of the carbon nucleus when the energy is transferred from neutron.
Substitute
Thus, the final kinetic energy of the carbon nucleus is
Conclusion:
Therefore, the final kinetic energy of the neutron is
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Chapter 9 Solutions
PHYSICS:F/SCI.+.,V.2-STUD.S.M.+STD.GDE.
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