The special unit of exposure. There is no derived Sl unit for this quantity, and the interrelationship is given in terms of coulomb per kilogram of air: I R = 2.58 X 10-4 C/kg (exactly). For conversion from Röntgen to Gray the approximate formula used for X-Rays and photons like Gamma-Rays is 1 Rontgen= 0.87 Rad (in air), 1Rontgen = 0.97 Rad (in water) . The latter is recommended for biological materials.
Exposure in air of 1 roentgen (R) = 2.580 x 10-4 C /kg (by definition)
Energy needed for ionization in air (W/e) = 33.97 J/C (Attix 1986, p 31)
Therefore, 1 R (in air) = (2.58 x 10-4)(33.97)J/kg (air)= 87.64 x 10-4 Gy (in air)
Now to convert dose in air to dose in water.
Dose water / Dose air = (men/r) water / (men/r) air
This ratio varies with energy of gamma rays. It has a value of about 1.11 for gamma rays from cobalt60 and Cesium137 (Attix 1986, p 33).
Here, men/r = mass-energy absorption coefficient.
Dose water = Dose air 1.11 (for these gamma rays)
Thus, 1 R (exposure in air), = 87.64 x 10-4 x 1.11 Gy (in water) = 97.3 10 -4 Gy (in water)
= 0.973 rad (in water)
Attix1986 ATTIX, F.H., Introduction to Radiological Physics and Radiation Dosimetry, John Wiley & Sons, New York, 1986
Conversion data kindly prepared by Kishor Mehta (IAEA)
*C=Coulomb of charge.