The above is what I'm seeing on my oscilloscope. It's zener diode noise. Scope's set for 0.5V/div vertically, and 1ms/div horizontally. The oscilloscope has a 20MHz bandwidth, but the noise doesn't really change much at higher speeds. You certainly can't see individual waves at 20MHz.
The trace is about 5 divisions high (this may be difficult to make out on my image). 5 divisions = 2.5V from top bit of green to bottom bit of green as judged by eye. The longer you watch it, the higher some of the peaks can be seen to go. That's the stochastic nature of white noise.
What does this 2.5V represent? It can't be RMS as it's only some bit of green that I can see. It's a kinda peak to peak but one that changes depending on how long you watch it. Is there a rule of thumb to determine a X volts/sqrt(hz) value? Datasheets give noise values for op amps. They must be able to measure it somehow.