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# A neutron with mass m makes a head-on, elastic collision

## Problem 93P Chapter 8

University Physics | 13th Edition

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University Physics | 13th Edition

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Problem 93P

A neutron with mass ?m? makes a head-on, elastic collision with a nucleus of mass M?, which is initially at rest. (a) Show that if the neutronâ€™s initial kinetic energy is K?0, the kinetic energy that it loses during the collision is 4?mMK?0/(?M? + ?m?)2. (b) For what value of ?M? does the incident neutron lose the most energy? (c) When ?M has the value calculated in part (b), what is the speed of the neutron after the collision?

Step-by-Step Solution:

Solution 93P Step 1: (a). = 0 1 2 Let us consider m = 1and m = M 2 2 K = neutrons eergy lost = energy gain of nucleus = 1/2 MV 2 Since u = 0 u = v v 2 1 2 1 2 K = 1/2 M(u + V 1 1 2 2 K = 1/2 MV 1 (1 + (m M/m + M)) Since V = (m m /m + m )u ,so 1 1 2 1 2 1 2 2 K = 1/2 Mu (2m 1m + M) K = 1/2 Mu 2 4mM/(m + M) 2 1 * 4mMk /(m 0 M) 2 Where k = 1/2 mu 2 0 1 Step 2: (b).value of M does the incident neutron lose the most energy 2 K = 4mMk /(m 0 M) d(K)/dM = 4mMk (m + 0) 4mMk 2 0 *2(M + m)/(M + m) 4 4mMk (m + M) = mMk 0 0 m + M = 2M M = neutron lost more energy. 1

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