I am wondering if the arcane spell failure chance on armor affects activated magical items such as wands, rods, and other items. I was not able to find a clarification on this in the book.
You won't find anything that says activating a magic item doesn't mandate Arcane Spell Failure chances (but see below). The game usually explains what happens not what doesn't happen. It saves negation for really confusing stuff. Here's Arcane Spell Failure Chance:
The short of it is that the somatic components usually required by a spell aren't required by a magic item, but that goes unsaid because making the magic go with a spell is different from making the magic go with a magic item.
Most Magic Items Are Unaffected by Arcane Spell Failure Chances...
Here's Activating a Magic Item
That's it. No Arcane Spell Failure chance. Seriously, the description of how to activate magic items is really long, but none of those mention Arcane Spell Failure either. If it goes unmentioned, often you needn't worry about it.
...But Scrolls Are an Exception
There's one very easily missed sentence in the actual description of Scrolls that says
That means other spell-completion items don't usually look for arcane spell failure chances (unless their descriptions say so, of course), but scrolls do. So while the wizard could perch on his tower in full plate firing lightning bolts from his wand, he'd struggle mightily to do the same with a pile of scrolls.