Question

A certain x ray exposure requires 1.8 mm Al to reduce the radiation intensity from 250 Gya to 125 Gya. What is the half value layer of this x ray beam? How many additional half value layers would be required to reduce the intensity to approximately 31 Gya?

Answer 1

If original intensity of the radiation is 10 And attenuation coefficient is u Then intensity I after passing a thickness x of the material is 1 = 10e Half value layer is the thickness of the material required to reduced the intensity to half of its original intensity Here intensity is reduced to half or original i.e. from 250 Gya to 125 Gya in 1.8 mm Al therefore half value layer is 1.8 mm Al 1 = 10eux 1 10 =eux 1 In- ux ur = ln2 In2 u= Now when intensity is reduced to 31 Gya after passing a total distance x' then 1 = 10e-4(x') 1 1. = e(x) 31 250 = e- x') 31 -(u) x (x') = In 250 In2 31 x (x') = In 250

31 -X' = In 250 (In2) 31 1 x' = - In Х x 250 (In2) (x') = 3x Thickness required to reduce intensity to 31 Gya is 3 times of HVL (half value layer) therefore additional half value layers required are 2