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One half the $\gamma$ rays from 99 $\mathrm{m}$ Tc are absorbed by a 0.170 -mm-thick lead shielding. Half of the $\gamma$ rays that pass through the first layer of lead are absorbed in a second layer of equal thickness. What thickness of lead will absorb all but one in 1000 of these $\gamma$ rays?
1.69 $\mathrm{mm}$
Physics 103
Chapter 32
Medical Applications of Nuclear Physics
Nuclear Physics
University of Michigan - Ann Arbor
Simon Fraser University
Hope College
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in this question. Half the gamma rays from a source are absorbed by a layer of lead off thickness. 0.17 millimeters and half of these gamma rays are absorbed by another layer of the same thickness. In the situation. Lower case D will represent the thickness of one layer 10.17 millimeters. An uppercase the can represent the total thickness, though that will absorb all but one in 1000 gamma rays. And this is what we're looking for so we can set up an equation that represents the situation. 1/2 to the power of X is equal to one in 1000. We can rewrite this as two to the power of X is equal to 1000. Using the power's off. Ellen, we can rewrite this equation as ex ln of two is equal to ln of 1000 by inputting ln into these equations, we can move the X from the exponents pap position to the coefficient position, and that's what we would do to one side we do to the other side. So we add Ellen to two and Ellen to 1000. This way we can isolate X and have X equal tow Alan of 1000 over Ellen Off too, which gives us a numerical value of 9.966 We can use the equation uppercase d equals two x times Lower case T to find the total thickness that we need to absorb all but one in 1000 gamma rays. Knowing X is 9.9 66 And knowing that d he is 0.17 millimeters, we confined that upper case D has a value of 1.69 millimeters.
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