Suppose you are trying to absorb gamma rays with a material whose linear absorption coefficient is 5.0 cm^-1. The intensity of the source without any material in the way is 6.5 counts/s. What is the intensity after the gamma rays have passed through x=1.5 cm of the material?
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The intensity of gamma rays in a material follows the equation,
I' = Ie^(-ux)
Where I' is the intensity as a function of x, I is the intensity when x = 0, x is the thickness and u is the attenuation coefficient.
I' = 6.5e^(-5*1.5) = 0.0036 counts/s
I' = Ie^(-ux)
Where I' is the intensity as a function of x, I is the intensity when x = 0, x is the thickness and u is the attenuation coefficient.
I' = 6.5e^(-5*1.5) = 0.0036 counts/s
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By the Beer-Lambert law, I(x) = I_0 exp(- kx) where k (usually written with the Greek letter mue) is the linear absorption or attenuation coefficient, x is the amount of thickness, exp(x) the exponential function, and I is the intensity (index 0 denotes initial value). So we have in this particular problem, intensity = (6.5) exp(- (5.0)(1.5)) = 0.0036 or 0.004 counts/s. (Effectively zero up to two significant figures.)