A Cs137 source is homogeneously distributed through a right

A Cs-137 source is homogeneously distributed through a right cylindrical bucket of water having diameter = height = 30 cm. What is the approximate absorbed dose rate in Gy per day in water at the center of the bucket if 160 atoms of Cs disintegrate per g s? Use the straight-ahead approximation and the mean radius method of calculating the photon dose. Give the answers for each component of the dose. Attix book chapter 5 question 2

Repeat the question for a mouse-sized cylindrical mass of water 3 cm in diameter by 3 cm long!

Solution

Cs-137 decays in two forms by emitting 1.174 Mev beta or 0.512 Mev beta and 0.662Mev gama photon.

The weighing factor for bothe beat and gama is same afor both beat and gama and is 1.

We can take the total decay energy 1.174 Mev and ignore the decay modes.

per decay the absorbed energy = 1.174 Mev

160 atoms of cs-137decay per g s

mass of the solution = r²h ( density of water = 1gm/cc)

                                        = 3.14*15²*30 = 21205.75 gms

number of CS-137 atoms decay per s

                                   =   21205.75 *160

We approximate 50% of the photon emissions go away from the center and 50% reache the center.

Total energy aborbed /s =   21205.75 *80 * 1.174 Mev

                                               = 21205.75 *80 * 1.174*1.602e-13 J

                                               = 3.19e-7 J/s

mass of the water absorbing the energy = 21205.75/2 gms

                                                                                 = 10.603 Kg

energy abosrbed /kg = 3.19e-7/10.603 J/s

                                           = 0.30 e-7 J/Kg/s

                                           = -0.30e-7 Gy/s

dose absorbed per day = 0.30*24*3600 = 25994 Gy/Day

dose abosrbed by a mouse sized cylinder

mass of the cylinder = 3.14*1.5²*3 = 21.195 gms

dose absorbed by the mouse = 0.0212*25994 = 550.94 Gy