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

Example

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

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

Resolution 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

Resolution II

i     μ = ln2/d1/2

μ = 0.693/6.6 = 0.105 cm -1

I(x) = I(0) eμ 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. 