p43_003 - 3. The conservation laws of (classical kinetic)...

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3. The conservation laws of (classical kinetic) energy and (linear) momentum determine the outcome of the collision. The results are given in Chapter 10, Eqs. 10-30 and 10-31. The Fnal speed of the α particle is v αf = m α m Au m α + m Au v αi , and that of the recoiling gold nucleus is v Au ,f = 2 m α m α + m Au v αi . (a) Therefore, the kinetic energy of the recoiling nucleus is K Au ,f = 1 2 m Au v 2 Au ,f = 1 2 m Au µ 2 m α m α + m Au 2 v 2 αi = K αi 4 m Au m α ( m α + m Au ) 2 =( 5 . 00 MeV) 4(197 u)(4
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