The half value thickness d1/2 is the thickness of the material at which the intensity of the λ-radiation entering it is reduced by one –half.
The half value thickness( also half value layer) depends on the energy of the γ-photons and the material
The intensity of λ-radiation after passing a material with thickness x:
1.I(x) = I(0) (1/2)x/d1/2
I(0) incident intensity in J s-1 m-2
I(x) intensity after passing the material in J s-1 m-2
Remark : x en d1/2 in cm
2. I(x) = I(0) e– μ x
μ = ln2/d1/2
μ absorption coefficient in cm-1
A gamma ray falls perpendicular on a wall of concrete. Thickness of the wall is 30 cm
The number of photons that is falling on the wall amounts 2.0 x104 .
The energy of the photons is 2.0 MeV
The half value thickness of concrete is 6.6 cm for photons of 2.0 MeV
i How many photons per second are transmitted by the wall ?
ii At what thickness of the wall is the number of the transmitted photons per second 2.0 103
i I(x) = 2.0 x 104 (1/2) 30/6.6 = 8.6 x 102 photons/s
ii 2.0 x 103= 2.0 x 104 (1/2) x/d1/2
0.1= (1/2) x/d1/2
log 0.1 = x/d1/2 log (1/2)
-1 = x/d1/2 (- 0.301)
3.32 = x/d1/2
x = 3.32 d1/2 = 3.3 x 6,6 = 21.9 cm
i μ = ln2/d1/2
μ = 0.693/6.6 = 0.105 cm -1
I(x) = I(0) e– μ x
I(x) = 2.0 x 104 e– 0.105 x 30 =( 2.0 x 104)( 0.043) = 8.6 x 102 photons/s
ii 2.0 x 103 = 2.0 x 104 e– μ x
0.1= e– μ x
ln 0.1 = – μ x
-2.302 = – 0.105 x
x = -2.302/-0.105 = 21.9 cm
Remark : Intensity is proportional to the number of photons per second.