The basic unit of radiation dose used to be the `` rad,'' defined in terms of the energy deposited by ionizing radiation per unit mass of exposed matter ( e.g., flesh or bone):
( g means gram here.) More recently, for some reason this nice mnemonic unit has been officially supplanted by yet another ``personal name SI unit'' (presumably meant to honour some distinguished individual), the ``Gray:''
Early work on radiation hazards was based on X-ray
exposure
[I
can remember sticking my feet into the fluoroscope
at the corner shoe store and looking at my foot bones inside
my new shoes; it was quite popular about 40 years ago]
and the units used were always roentgen
(after the scientist by that name), which are about the
same as rad for X-rays only, and are
virtually unused today. Later it was found that even
the rad was too simple; different types
of radiation ( e.g., neutrons) were found to be more (or less)
destructive than X-rays for different types of tissues,
so an empirical ``fudge factor'' called the
Relative Biological Effectiveness (RBE) was invented
to account for these differences (averaged over all
body parts, of course, which decreased its usefulness).
The RBEs of 
-rays, X-rays
and 
-rays
(fast electrons) are all 1 by definition;
thermal neutrons have an average RBE of 3;
fast neutrons (on average),
protons and 
-rays
(4He nuclei) all have RBEs
of 10; and fast heavy ions have an RBE of 20.
(Actually, the RBE of neutrons varies tremendously
for different tissues and is a complicated function
of the neutron energy because of the energy-dependence
of the neutron capture cross-sections of different elements.
Neutrons are very bad.)
A new unit was then constructed by combining the RBE with the dosage in rads, namely the rem (roentgen equivalent to man), defined by
The ``R'' in the preceding paragraph stands for rem and the ``mR'' for millirem -- one thousandth of a rem.