In this paper, we show that Theorem 2.1  (resp. Theorem 2.2 ) is a consequence of Corollary 2.1  ( resp. Corollary 2.2 ).
naturally occurring in building materials may significantly contribute to the
annual doses to the public. For instance, familiar building materials such as
the concrete and gypsum board have been reported to produce a dose of about
0.04 mSv per year for a typical person (NCRP 1987c). External as well as internal
exposures are two pathways of radiation dose imparted to human beings from the
building materials. As information on the radioactivity of such materials is
lacking, the study of gypsum materials used in Egypt was carried out in order
to estimate the annual dose to the Egyptian population due to natural radionuclides
in building materials. During the study, 18 samples of commonly used gypsum raw
materials were collected and measured. The activity concentrations were
determined by gamma ray spectrometry. Their mean values were in the ranges of 499.29
± 11.53 Bq·kg-1 for 40K, 91.97 ± 2.61 Bq·kg-1 for 226Ra, 37.62 ± 1.67 Bq·kg-1 for 238U and 42.27 ± 2.22 Bq·kg-1 for 232Th.
The activity indexed Iγ for 18, different gypsum samples varied from 0.31 ± 0.03
to 2.3 ± 0.19 and the radium equivalent activity (Raeq), from 38.81 ±
1.68 to 324.7 ± 9.42. These values are lower than the limit of 370 Bq·kg-1 adopted by the Organization for Economic Cooperation and Development (OECD).
The average indoor annual effective gamma dose rate (DE) in (mSv/y) for the
people, caused by the building materials of dwellings, was assessed for most
commonly gypsum materials. It was estimated to be in the range from 0.10 ± 0.003
mSv/y to 0.74 ± 0.08 mSv/y. The internal and external hazard indices (Hin,
Hex) and the absorbed dose rate in air D in each sample were evaluated
to assess the radiation hazard for people living in dwelling made of the
studied materials. The absorbed dose rate of indoor air in samples G1, G2, G11,
G17 and G18 is less than the international recommended value which is 55 nGyh-1.
While the absorbed dose rate for samples G3, G4, G5, G6, G7, G8, G9, G10, G12,
G13, G14, G15 and G16 is higher than 55 nGyh-1, these samples are
not acceptable for use as building materials.