The intensity of gamma rays passing through a material as a function of thickness, x is given by where n is the number of atoms per cm³ and $\sigma$ is the absorption cross section. It is observed that the intensity of gamma rays of a particular energy is reduced by half when they passed through 1 cm of lead. What is the thickness of lead needed to reduce the intensity to a quarter? A) 1.0 cm B) 1.5 cm C) 2.0 cm D) 3.0 cm E) 4.0 cm

Question

Quizplus · Accepted Answer

If the intensity is reduced by half when passing through 1 cm of lead, then we can write:

0.5I0 = I0e^(-nF1x)

where I0 is the initial intensity, n is the number of atoms per cm^3 and F1 is the absorption cross section.

Then solving for x, we get:

x = ln(0.5)/(-nF1)

Now we can use this equation again to find the thickness of lead needed to reduce the intensity to a quarter:

0.25I0 = I0e^(-nF1x2)

where x2 is the thickness we want to find.

Then solving for x2, we get:

x2 = ln(0.25)/(-nF1)

Now we can calculate x2/x1:

x2/x1 = ln(0.25)/ln(0.5) = 2

So the thickness of lead needed to reduce the intensity to a quarter is twice the thickness needed to reduce it to half, which is 1 cm. Therefore, the answer is 2.0 cm, which is choice C).

The Intensity of Gamma Rays Passing Through a Material as a Function