Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
••• Occasionally, some radioactive nuclei eject a particle other than an alpha or beta particle. In particular, it has been found that several nuclei, including 223Ra, can emit a 14C nucleus, although this mode is very rare (of order 1 of these decays for every 109 alpha decays). (a) What is the offspring nucleus when 223Ra emits a 14C nucleus, and what is the energy released? (b) Assuming that 14C emission is analogous to alpha decay, one can calculate its probability by the methods of Section 17.10. Explain why the probability P(14C) for escape of a 14C nucleus can be obtained from Eq. (17.72) simply by replacing 2Z by 6Z and taking m to be the mass of 14C. (c) Calculate P(14C), and find the ratio P(14C)/P(α) for the parent 223Ra. [Caution: Z is the charge of the offspring. The answers are quite sensitive to the value of the nuclear radius R; to be definite, take R = 7.5 fm in both calculations.]
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.