Provide a detailed mechanistic explanation for the following results.
a. Photochemically initiated bromination of resolved 5-1a, $\alpha_{D}+4.21$, affords 5-2a which retains optical activity, $\alpha_{D}-3.23$, but 5-1b under the same conditions gives racemic 5-2b.
b. The stereoisomerization shown below proceeds efficiently, with no other chemical change occurring at a comparable rate, when the compound is warmed with $N$-bromosuccinimide and a radical chain initiator.
c. There is a substantial difference in the reactivity of the two stereoisomeric compounds shown below toward abstraction of the hydrogen atom at $\mathrm{C}(2)$ by the $t$-butoxy radical.
d. Free radical chain chlorination of enantiomerically resolved 1-chloro-2methylbutane yields six dichloro derivatives, of which four are optically active and two are not. Identify the products that are expected to fall in each group. Indicate the mechanistic significance of the identity of the optically active and inactive compounds.
e. Irradiation of the hydrocarbon $5-\mathbf{A}$ in the presence of di- $t$-butyl peroxide generates a radical that can be identified as the 2-phenylethyl radical by its ESR spectrum. This is the only radical identified, even when the photolysis is carried out at $-173^{\circ} \mathrm{C}$.
f. Among the products from heating 1,6-heptadiene with 1-iodoperfluoropropane in the presence of AIBN are two saturated 1:1 adducts. Both adducts give the same product on dehydroiodination, and it can be shown by spectroscopic means to contain a $=\mathrm{CH}_{2}$ unit. Indicate structures for the two adducts and propose a mechanism for their formation.
g. Photolysis of the iodide 5-B gives not only the expected cyclization product 5-C but also 5-D. During the course of the photolysis halides 5-E and 5-F are also formed.
h. Thermal decomposition of $\mathbf{5 - G}$ gives products $\mathbf{5}-\mathbf{H}$ to $\mathbf{5}-\mathbf{K}$ :