The absorption of gamma rays by a material depends exponentially on the thicknes

Question

The absorption of gamma rays by a material depends exponentially on the thickness of the absorbing material. This means that the number N of gamma rays that survive passage through a thickness x of a certain material, for example, lead, is given by If x is in meters, what are the units of the absorption coefficient X ? {Enter the answer using MapleTA syntax.) If one wishes to use a lead sheet that has an absorption coefficient of 90 m'1 to block 99% of the gamma rays incident on its front surface from passing through its back surface, how thick must the lead be? (The numeric answer must be accurate to better than 0.5%; use MapleTA syntax to express your SI units.) If one is able to get only a 2 mm thick sheet of lead, what percentage of gamma rays would it block? Your numeric answer must be accurate to better than 0.5%.

Explanation / Answer

a)

1/m

b)

0.01 = e^(-90*x)

==> -90*x = Ln(0.01)

==> x = Ln(0.01)/(-90)

==> x = 0.05117

==> x = 0.051 m

c)

survaived gamma rays = N/N0 = e^(-90*x) = e^(-90*0.002) = 0.835 = 83.5%

==> blocked = 100 - 83.5 = 16.5%

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