Introduction: The photoelectric attenuation coefficient of substances is known to depend upon the energy E of the photon and the effective atomic number of substances (Zeff) as (Zeffx/Ey).Â No definitive values about these indices x, y are given in the literature. The index x is said to lie between, 3.0 and 4.0, while for â€˜yâ€™ different values have been assigned, between 3.0 and 4.0. Methodology: We followed a methodology to find both the exponent y explicitly, from a formula which does not contain x. Through this way, the risk of one parameter leading to an estimation error for the other is automatically eliminated. With the value of y being unmistakably established, we determined the exponent x for different elements. Results: It was found from the NIST data that â€˜yâ€™ = 3.0669 for most substances with low atomic number but no single value can be assigned for the exponent â€˜xâ€™.Conclusions: These results help us to perform model calculations for the attenuation coefficients of different substances. They can also provide important inputs for the diagnostic purposes in the DECT method.