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A neutron makes a head-on elastic collision with a deuterium nucleus (mass ratio 2) initially at rest, losing a fraction p_d of its kinetic energy. In a similar head-on elastic collision with a carbon nucleus (mass ratio 12) at rest, it loses a fraction p_c of its energy. Expressed as percentages, the values of p_d and p_c respectively are nearest to:

1. (89, 28)
2. (0, 0)
3. (0, 1)
4. (28, 89)

Correct answer: (89, 28)

Solution

Fractional energy transferred = 4mM/(m+M)². For deuterium this gives 8/9 (about 89%) and for carbon 48/169 (about 28%).

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