When gamma rays are incident on matter, the intensity of the gamma rays passing

Question

When gamma rays are incident on matter, the intensity of the gamma rays passing through the material varies with depth x as

I(x) = I0e??x,

where I0 is the intensity of the radiation at the surface of the material (at

x = 0)

and ? is the linear absorption coefficient. For 0.401-MeV gamma rays in lead, the linear absorption coefficient is 1.57 cm?1.

(a) Determine the "half-thickness" for lead, that is, the thickness of lead that would absorb half the incident gamma rays.
cm

(b) What thickness reduces the radiation by a factor of 102?
cm

Explanation / Answer

The relation between intensity of the rays and thickness is

I = I_0 e ^- ux

when I = I_0/2

I_0/2=I_0 e ^- ux

-ux = ln ( 1/2)

-( 1.57 cm^-1) x = ln ( 1/2)

x = 0.44 cm

-----------------------------------------------------------------------

(b)

I = I_0/ 10 ^2

= I_0/100

10 ^-2 I_0 = I_0 e ^- ux

-( 1.57 cm^-1) x = ln ( 0.01)

x = 2.93 cm

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