C612+C612→Mg1224Kpr = Kb + Q.Because the kinetic energies «mc2, we can use a non relativistic treatment: K = mv2/2 = p2/2m. The least kinetic energy is required when the product particles move together with the same speed. With the target at rest, for momentum conservation we havepb = ppr = mprv, or Kb = pb2/2mb = (mpr2/2mb)v2 = (mpr/mb)Kpr, or Kpr = (mb/mpr)Kb.When we use this in the kinetic energy equation, we get(mb/mpr)Kb = Kb + Q;[(mb/mpr) – 1]Kb = Q, which gives Kb = – Qmpr/(mpr – mb).69. (a) If we assume a thin target, we find the cross section for backward scattering fromR/R0 = nσx;1.6×10–5 = (5.9×1028 m–3)σ(4.0×10–7 m), which gives σ = 6.8×10–28 m2 = 6.8 bn.
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