p43_075 - 75. A generalized formation reaction can be...

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75. A generalized formation reaction can be written X + x Y, where X is the target nucleus, x is the incident light particle, and Y is the excited compound nucleus ( 20 Ne). We assume X is initially at rest. Then, conservation of energy yields m X c 2 + m x c 2 + K x = m Y c 2 + K Y + E Y where m X , m x ,and m Y are masses, K x and K Y are kinetic energies, and E Y is the excitation energy of Y. Conservation of momentum yields p x = p Y . Now, K Y = p 2 Y / 2 m Y = p 2 x / 2 m Y =( m x /m Y ) K x ,so m X c 2 + m x c 2 + K x = m Y c 2 +( m x /m Y ) K x + E Y and K x = m Y m Y m x £ ( m Y m X m x ) c 2 + E Y ¤ . (a) Let x represent the alpha particle and X represent the 16 O nucleus. Then, ( m Y m X m x ) c 2 = (19 . 99244 u 15 . 99491 u 4 . 00260 u)(931 . 5MeV / u) = 4 . 722 MeV and K α = 19 . 99244 u 19 . 99244 u 4 . 00260 u ( 4 . 722 MeV + 25 . 0MeV)=25 . 35 MeV . (b) Let
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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