Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

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.

••• (a) Substitute the binding-energy formula (16.30) into the relation

to obtain the semiempirical mass formula. [To simplify matters, take A to be odd, so that the pairing term in (16.30) is zero.] (b) Among any set of isobars, the nucleus with lowest mass is the most stable. To identify this nucleus, first write your mass formula in terms of the variables A and Z (that is, replace N, wherever it appears, by A − Z). With A fixed, differentiate m with respect to Z. The minimum mass is determined by the condition ∂m/∂Z = 0. Show that this leads to a relation of the form

where α and β are related to the coefficients (16.31) as follows:

(c) For A = 37, 115, 185, find the values of Z that give the most stable nuclei and compare with the observed values from Appendix D.