One half the γrays from 99 m Tc are absorbed by a 0.170 -mm-thick lead shielding. Half of the γr

step 1 In this question, half the gamma rays from a source are absorbed by a layer of lead of thickness

One half the γrays from 99 m Tc are absorbed by a 0.170...

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?

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Key Concepts

Half-Value Layer

The half-value layer (HVL) is the thickness of a specific material required to reduce the intensity of the radiation by half. It is a practical measure used to describe how effectively a material can shield against ionizing radiation. By applying the concept of the HVL, one can determine how many such layers (or equivalent thickness) are needed to reduce the radiation to a desired level.

Logarithmic Calculations in Shielding

Logarithmic calculations are used to relate the thickness of the shielding material to the fraction of radiation that is transmitted. Since the attenuation follows an exponential decay, taking logarithms allows one to solve for the number of HVLs (or the associated thickness) needed to achieve a specific level of attenuation, such as reducing the radiation to one in a thousand of its initial intensity.

Exponential Attenuation

Exponential attenuation describes how the intensity of gamma radiation decreases as it passes through a material. The decrease in intensity follows an exponential law where a constant fraction of the incident radiation is absorbed for every unit thickness of the absorber. This principle is key in calculating the remaining radiation after passage through shielding material and forms the basis for many radiation protection calculations.

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