Composition and thickness affect the intensity of radiation exiting a material.

Question

Composition and thickness affect the intensity of radiation exiting a material. The exit intensity can be calculated by using the formula provided below: I = I_0 e^-mu x I = intensity of radiation along x (watts/m^2) I_0 = initial intensity of x-rays (watts/m^2) mu = linear absorption coefficient of absorber for given radiation (per cm) t = thickness of absorber (cm) Listed below as p, are the linear absorption coefficients per cm for various materials. An unshielded x-ray source produces an emission of 500 watts/m^2 at one foot from will be the emitted radiation when I cm, 2 cm, 3 cm, 4 cm, 5 cm, and 10 cm thick placed one foot from the source? What if the shielding is made of iron? Aluminum? point of material to source is one foot From the results for the lead shield, use linear calculate the lead shield thickness required to reduce the emitted radiation to 70 watts/m^2, then 5 watts/m2.

Explanation / Answer

We know I=Ioexp(-alpha*thickness)

for lead thickness 1 cm and alpha=0.77

  I=Ioexp(-alpha*thickness)=500*exp(-0.77*1)= 231.5065 watt /m2

for lead thickness 2 cm and alpha=0.77

   I=Ioexp(-alpha*thickness)=500*exp(-0.77*2)=107.19 watt/m2

for lead thickness 3 cm and alpha=0.77

   I=Ioexp(-alpha*thickness)=500*exp(-0.77*3)=49.63

for lead thickness 4 cm and alpha=0.77

   I=Ioexp(-alpha*thickness)=500*exp(-0.77*4)=22.97

for lead thickness 5 cm and alpha=0.77

   I=Ioexp(-alpha*thickness)=500*exp(-0.77*5)=10.6399

for lead thickness 10 cm and alpha=0.77

   I=Ioexp(-alpha*thickness)=500*exp(-0.77*10)=0.2264

Similarly for iron, same thickness

intensity will be 500*exp(-0.44*1)= 322.0182, 207.3915, 133.5677, 86.0224 ,55.4016 and 6.1387 for other thickness respectively

find the lead thickness, to reduce to 70 watt/m2

I=Ioexp(-alpha*thickness)

70=500*exp(-0.77*thikness)

=70/500=exp(-0.77*thickness)

=ln(70/500)=-0.77*thickness

=thickness=ln(70/500)/-0.77= 2.5534 cm

To reduce to 5 watt/m2

=thickness=ln(5/500)/-0.77= 5.98 cm

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