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.

• One argument against the proton–electron model of the nucleus concerns the total spins of nuclei. The proton, electron, and neutron all have spin , and the total spin of any number of spin-half particles takes the familiar form . If there is just one particle, then of course, . With two particles, the spins can be parallel or antiparallel, giving s = 1 or 0. It can be shown that the general rule is this: For an odd number of particles, the total spin has some half-odd-integer value for . For an even number of particles, the total spin has s equal to some integer . In light of this rule, consider the nucleus 14N. (a) Assuming that 14N is made of 7 protons and 7 neutrons, predict the character of its total spin (integer or half-odd integer). (b) Repeat for the proton–electron model of 14N. (c) The observed total spin of 14N is integer; which model does this support?