How can I relate the energy of a gamma particle to electromagnetic radiation power? I have a distinct feeling that dimensional analysis says these two (let's pick 1 MeV and +30dBm) can not be directly compared. What is the missing link between the two? I know one is energy and one is power.
I suppose I'll have to get the energy of +30dBm radiated by an ideal +3dBm antenna at a distance of 2cm impacting an area of $10\times10\,mm$.
$1.6\times10^{-13}$ joules for the 1MeV gamma [unknown] for the radio wave (for reference it will be in the low GHz frequency)
 A: dBm is a way of expressing an energy value relative to 1mW. Specifically $x=10 \log_{10}(\frac{W_1}{1mW})$. Given the values in the question the radio energy emitted is +33dBm, or $10^{3.3} mW$. At a distance of 2cm from the radiation point you can calculate intensity using the calculable area of a sphere 2cm radius centred on the antenna. You can then calculate energy associated with the $100mm^2$ patch on that sphere and compare that value directly to 1MeV. 
A: You are right, these are two completely different and independent things.
dBm is a logarithmic measure for power of a beam (in Watt). 
1MeV is a measure for frequency (photon energy), which is of course independent from power.
The photon energy does not change when the beam is attenuated, amplified, radiated or whatsoever (at least with any linear operation). 
Graphically is the number of photons that changes by attenuation. 
EDIT: I guess for you application you can just ignore the photon energy. Probably you only need the 30 dBm number, which is just 1W.
