I'd build a house on the island and stay there living the
good life eating the fruit and nuts and seaweed, unless
it had major vulcanism / tsunami risks! :D
Yes, using a lot of lemons and limes might work well with
the copper, though you'd need some other metal to be
the other plate in the galvanic cell, and that might be
a problem.
Actually I just read a good article on the fruit battery
thing:
http://amasci.com/miscon/miscon4.html#lemon
You could make a dry pile instead of a citrus fruit
battery, if you had the right metals to stack:
http://amasci.com/emotor/duluc.html
If I could find some good lodestone then I could try making
a generator with it and a coil of the copper wire, though
I'd have to rectify the AC to feed to the radio.
I don't recall that very good (highly magnetized)
natural lodestones are common, though, so that might
result in quite feeble power output.
http://amasci.com/amateur/coilgen.html
I suppose I could try smoldering some coconut shell or
wood chips in the absence of oxygen to make charcoal
as a conductor to work with the copper in
an electrochemical cell, though I don't recall what voltage
that might provide per cell... and the resistance
would probably be depressingly high... hmmm...
I could make a water drip based electrostatic generator
and use that to charge a battery, but that'd depend on
having a rechargable battery, and it'd be problematic since
the low current and high voltage wouldn't suit a battery
or radio very well..
http://amasci.com/emotor/kelvin.html
One could use a water stream or water fall or wind-mill
or hand-cranking to turn a generator once one had one,
but one would need a good magnet for that to work.
One might be able to find gold naturally to melt down
and beat into more wire or conductive plate, eventually.
Iron ore would be handy and could be smelted from
natural iron ore oxide deposits to make some chunks
that could be magnetized and/or used for
electrochemical cell plates. Though an easier sourse of iron
might be from iron meteorites that might be found.
Ah I know, one could use a gold-panning type technique
or lodestone magnet to help sort out the iron ore
dust from the beach sand since there's often a lot there
that's easily sorted out.
I could enlist the help of Gilligan, Mary Anne, and Ginger
and have them run around in the sand scuffing their
feet to make electrostatic charge and have them deposit
it on a leyden jar capacitor the size of a city block... :)
It is interesting to think that in only 20,000 years or so
people have developed such kinds of technologies to
go from stone age to bronze age to metallurgy / iron age
to technologies of steam power, chemistry, electronics,
etc. with most of that change taking place in just the
last 3000 years.
I wonder in the course of 40 years how well even the
most technically educated of us could progress if we were
left on an island with lots of stone age raw materials,
ample food/water/shelter, temperate weather,
but no real technological materials or references for
construction other than what one could devise oneself.
Even making fire would be challenging for most people,
as would making good stone / wooden tools, weaving
rope, etc. Something like making glass, making a furnace
capable of melting copper/gold/glass could be quite
a project.
Learning to identify and refine/melt/cast the ores of
zinc, copper, maybe iron would be needed to get to a
level of technology even ~3000 years old for
copper/bronze/iron.
I suppose the easiest radio transmitter would be a
morse code keyed spark gap transmitter that wouldn't
need much more than wire, a good dry-pile or
few leyden jars and water generator, though you'd be
pretty lucky or very talented to get it to output enough
of a signal to be useful.