What minimum energy is required to create tracks in a cloud chamber? What is the minimum ionizing radiation required for that? I am currently living in Fukushima prefecture and I was wondering if let`s say a flower from my yard that emits 1 pSv will create visible tracks? My dosimeter only shows Sieverts so I cannot be very specific. I would appreciate any help.
Thank you!
 A: A cloud chamber will show individual cosmic rays and individual alpha and beta particle tracks. 
An alpha particle may have say 5 MeV of energy, which is $8 \times 10^{-13}$ J
The Sv unit is the biological effect of $1$ Joule of radiation on $1$ kg of matter. So a pSv is the biological effect of $1 \times 10^{-12}$ J on $1$ kg....
so my answer to your question is yes - but the Sievert scale is pretty complicated and beware that a cloud chamber won't observe gamma radiation nearly as efficiently as alpha and beta particles because most gammas will pass straight through, whereas every alpha will leave a clear track. As pointed out by dmckee gammas can be observed if they, for example, Compton scatter or produce an electron positron pair.
Finally, I should say that given where you are living I can give no guarantee about this - but if I were living where you are I would probably build myself a cloud chamber as you plan to. I hope this is helpful.
A: This is to be read together with the checked answer. There are easy cloud chambers to be home made, like this one.
It is easy to make, and the reason you should watch it is to realize that in a cloud chamber there will always be muon tracks ionizing the air vapor mix and creating seeds for a track. You will need a type of anti-coincidence to make sure that any tracks you see come from particles of your flowers:
1) in a basement under meters of cement the muons are less
2) mu metal is a good shield for muons, but that means a lab
3) You could get a statistical effect by taking two measurements, flowers in  the cup, flowers off and count the tracks in both cases for the same length of time.
"In the cup" because  a plastic cup could have  a wall of 0.2mm thickness and alpha's would be absorbed there and not enter the chamber. The flower will shrivel from the ice but this will not affect the nuclear properties of its constituents. ( thanks to jaromrax pointing this out in  a comment)
P.S.
I just realized because the alpha range is 3 cm in air, the radiation from the flower will be clearly seen and not confused with most cosmic muons, it should be centered around the flower for 3 cm.
