Chapter 44 569 Q44.20 An electron has spin quantum number 1 2 . When a nucleus undergoes beta decay, an electron and antineutrino are ejected. With all nucleons paired, in their ground states the carbon-14, nitrogen-14, nitrogen-12, and carbon-12 nuclei have zero net angular momentum. Angular momentum is conserved in any process in an isolated system and in particular in the beta-decays of carbon-14 and nitrogen-12. Conclusion: the neutrino must have spin quantum number 1 2 , so that its z-component of angular momentum can be just = 2 or − = 2 . A proton and a neutron have spin quantum number 1. For conservation of angular momentum in the beta-decay of a free neutron, an antineutrino must have spin quantum number 1 2 . Q44.21 The alpha particle and the daughter nucleus carry equal amounts of momentum in opposite directions. Since kinetic energy can be written as p m 2 2 , the small-mass alpha particle has much more of the decay energy than the recoiling nucleus. Q44.22
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