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## Homework Statement

Canadian nuclear reactors use heavy water moderators in which elastic collisions occur between the neutrons and deuterons* of mass 2.0 u (see Example 8.11 in Section 8.4).

(a) What is the speed of a neutron, expressed as a fraction of its original speed, after a head-on, elastic collision with a deuteron that is initially at rest?

## Homework Equations

εcni = εcnf + εcdf

pni = pnf + pdf

## The Attempt at a Solution

__0.5u * vni ^ 2 = 0.5u * vnf ^ 2 + 1u * vdf ^ 2__

1u * vni = 1u * vnf + 2u * vdf

2u * vdf = 1u * vni - 1u * vnf

vdf = 0.5 * vni - 0.5 * vnf

__vdf = 0.5 * (vni - vnf)__

0.5u * vni ^ 2 = 0.5u * vnf ^ 2 + 1u * (0.5 * (vni - vnf)) ^ 2

0.5u * vni ^ 2 = 0.5u * vnf ^ 2 + 1u * (0.5 * vni - 0.5 * vnf)) ^ 2

0.5u * vni ^ 2 = 0.5u * vnf ^ 2 + 1u * (0.25 * vni ^ 2 - 0.5 * vni * vnf + 0.25 * vnf ^ 2

vni ^ 2 = vnf ^ 2 + 2 * (0.25 * vni ^ 2 - 0.5 * vni * vnf + 0.25 * vnf ^ 2

vni ^ 2 = vnf ^ 2 + 0.5 * vni ^ 2 - vni * vnf + 0.5 * vnf ^ 2

**0.5 * vni ^ 2 = 1.5 * vnf ^ 2 - vni * vnf**

What can I do with

**"- vni * vnf"**

I think I can handle b) and c), but not without the answer of a), which is, according to the book,

**1/3 vni**.