LEARNING OBJECTIVE:
1.11.13  Calculate shielding thickness or exposure rates for gamma/xray radiation using the equations. 
SHIELDING CALCULATIONS
The simplest method for determining the effectiveness of the shielding material is using the concepts of halfvalue layers (HVL) and tenthvalue layers (TVL).
One halfvalue layer is defined as the amount of shielding material required to reduce the radiation intensity to onehalf of the unshielded value.
The symbol m is known as the linear attenuation coefficient and is obtained from standard tables for various shielding materials.
One tenthvalue layer is defined as the amount of shielding material required to reduce the radiation intensity to onetenth of the unshielded value.
Both of these concepts are dependent on the energy of the photon radiation and a chart can be constructed to show the HVL and TVL values for photon energies.
Table 2. HalfValue Layers
Photon Energy (keV) 
HVL (cm) 

Lead (11.35 g/cm^{3}) 
Iron (7.86 g/cm^{3}) 
Concrete (2.4 g/cm^{3}) 
Water (1.0 g/cm^{3}) 

500  0.38  1.0  3.3  7.2 
1000  0.86  1.5  4.5  9.8 
1500  1.2  1.8  5.6  12.0 
2000  1.3  2.1  6.4  14.0 
3000  1.5  2.4  7.9  17.5 
The basic calculational approach to photon shielding is to determine the existing exposure rate, decide on the desired exposure rate after shielding and then calculate how many HVL or TVL will be needed. The basic equation for using the HVL concept is:
where:
The basic equation for using the TVL concept is:
where:
Sample Problem 1.1113
Calculate the shielded
exposure rate from a 500 mR/hr Cs137 source with 5 cm of lead shielding. The HVL for
Cs137 and lead is 0.65 cm.

Sample Problem 1.1114
Calculate the shielded
exposure rate from a 7.4 R/hr Cs137 source with 4 cm of lead shielding. The HVL for
Cs137 and lead is 0.65 cm.

Sample Problem 1.1115
Calculate the #TVL and the
thickness of lead required to reduce the exposure rate from a 7.5R/hr Co60 source to less
than 100 mR/hr. One TVL for Co60 and lead is 4.0 cm.

Sample Problem 1.1116
Calculate the #TVL and the
thickness of lead required to reduce the exposure rate from a 450 mR/hr Co60 source to
less than 5 mR/hr. One TVL for Co60 and lead is 4.0 cm.

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REFERENCES:
1. ANL8826 (1988) "Operational Health Physics Training"; Moe, Harold; Argonne National Laboratory, Chicago
2. "Basic Radiation Protection Technology"; Gollnick, Daniel; Pacific Radiation Press; 1983
3. "Radiological Health Handbook"; Bureau of Radiological Health; U. S. Department of Health, Education, and Welfare; Washington, D.C.; 1970.