Re: rechargeing standard cells with radio waves

You can get a little bit of power from radio waves, but not much.
Typically, the most power you can pick up will be a few milliwatts (if
you're really close to a big transmitter - microwatts are more likely) -
not enough to charge batteries, but enough to play with a little. There's a
reason why crystal radios have headphones - there's not enough power for
speakers!

There is a discussion about power from crystal radios at
 http://www.midnightscience.com/web_frm.htm
Look for messages headed "power from crystal radio".

A circuit design for extracting power from radio waves can be found at
 http://home.t-online.de/home/gollum/dt.htm
If you're close to a transmitter, you might get enough power to run a
second crystal radio.

Here is a diagram for a crystal radio which will drive a small speaker:
 http://hibp.ecse.rpi.edu/~john/xtal.html

Here are some general pages about crystal radios:
The Crystal Set Society
 http://www.midnightscience.com/
Crystal Radio
 http://home.earthlink.net/~drduggee/xtal.htm
Crystal Radio Circuits
 http://www.techlib.com/electronics/crystal.html
Learn about the Crystal Set
 http://www.antique-radio.org/class/class.html
Building a Simple Crystal Radio
 http://www.scitoys.com/scitoys/scitoys/radio/radio.html

and a general one about radios:
How Things Work: Radio
 http://rabi.phys.virginia.edu/HTW/radio.html

This was fun! I built one of these from a kit when I was 9 or 10 years old,
but hadn't thought about it for a while.