The materials analyzed during this work are nineteen (19) samples of lagoon sand. The equipment used in the field for sample collection includes a Garmin (Etrex) brand GPS to determine geographic coordinates, shovels for manual collection and polythene sample bags. The laboratory equipment used for sample preparation consists of an electronic balance (METTLER TOLEDO brand, Model

XP2001S, SNR) for different mass measurements of the samples. There are also Marinelli beakers (SG 500) for the conditioning of the samples, an oven to dry these samples, a ball mill, and a sieve of 2 millimeters mesh.

The radioactivity of the sand samples is measured using the gamma-ray spectrometer installed at the laboratory of the Radiation Protection Institute (RPI) of the Ghana Atomic Energy Commission (GAEC). The measurement chain includes the measurement chamber, a liquid nitrogen cooling system (77 K), a High Purity Germanium (HPGe) coaxial detector model GX 4020-7500 SL (Canberra) with a resolution of 2 keV at 1332 keV (⁶⁰Co). There is also a high voltage power supply (4000 V) necessary for the collection of the electric charges deposited in the detector. A cylindrical lead shielding 10 cm thick makes the contributions of ambient radiation reduction possible. Moreover, there is a multichannel analyzer (MCA) connected to a computer with an acquisition and processing software (GENIE 2000, Canberra). For the calibration, we used standard multi sources composed of²⁴¹Am, ¹⁰⁹Cd, ¹³⁹Ce, ¹¹³Sn, ¹³⁷Cs, ⁵⁷Co, ⁶⁰Co, and ⁸⁸Y.

The nineteen sand samples are collected from the main suppliers and at the construction sites. Each sample is a combination of five (5) incremental samples taken at random from five points in the sand stock from a depth of approximately 15 cm. Two (2) kilograms of each sample is collected and packaged in contamination-free polyethylene bags, adequately labeled in situ to facilitate their exact identification in the preparation laboratory.

In laboratory, all samples are dried at 105˚C in an oven until all moisture has been removed. A constant dry weight of the samples is obtained after 24 hours. The samples are then crushed and sieved (at 2 mm) in order to get rid of the unwanted fractions. After their reduction to a homogeneous powder, the samples are conditioned in Marinelli type geometry (SG 500), sealed against radon for 30 days before the measurements in order to allow a secular equilibrium. This equilibrium corresponds to at least seven half-lives of ²²²Rn (3.81d) between the radionuclides ²²⁶Ra and ²³²Th and their respective descendants [13].

The radioactivity measurement of the samples was carried out at the laboratory of GAEC. One (1) kilogram dry mass sand samples are measured for 10 hours using a Gamma-ray spectrometer. During the measurement, the HPGe detector mounted on the cryostat is cooled with liquid nitrogen (77 K) in order to decrease the resistivity of the material and reduce the thermal background noise. The detector is also surrounded by a cylindrical lead castle of 10 cm thick to attenuate the background noise in the measured spectrum due to natural ambient radioactivity. Spectra analysis are performed using Genie 2000 (Canberra) software. The spectrum of each sample gives the number of counts recorded per second as a function of the energy of the gamma rays emitted by the radionuclides. Background measurements of the laboratory are also carried out in order to obtain net counts for each sample. Thus, an empty Marinelli beaker is measured to find the background noise generated by the ambient natural radioactivity. This background noise is then subtracted from the activities of each radionuclide in the measured samples.

The energy and the calibration efficiency of the detector are determined using a standard multi-source with energies between 60 and 2000 keV. This makes it possible to take into account the desired radionuclides and reduce the counting losses linked to the coincidence summing and self-absorption effects of gamma rays. The energy and calibration efficiency of the detector, respectively, are used to identify the radionuclides detected in the samples. Thus, we can determine their concentrations [14].

The activity concentrations of radionuclides in the sand samples are calculated using the equation below.

C = N n e t ε ⋅ P ⋅ t c ⋅ m s [15] (1)

where: N n e t , ε , t_c (s), m_s (kg), p (%) are, respectively, the number of net counts below the photoelectric peak for each sample, the detection efficiency for specific gamma energy, the count time, dry mass of the sample and probability of detection.

The ⁴⁰K radioactivity is measured directly from the Gamma-ray emitted at 1460.8 keV (10.7%). The radioactivity of ²²⁶Ra and ²³²Th is measured from their descendants in secular equilibrium by making the average of their respective activities. Thus, the gamma rays of ²¹⁴Pb at 295.2 (19.3%) keV and 351.9 (35.8%) keV, and the gamma rays of ²¹⁴Bi at 609.3 (46.1%) keV and 1764.5 (15.1%) keV are used for the measurement of ²²⁶Ra. The ²³²Th radioactivity is measured using the 911.2 (26.6%) keV line of ²²⁸Ac and the 583.2 (30.5%) keV line of ²⁰⁸Tl.

The minimum detectable activity (MDA) of the measurement system is calculated using the following equation:

MDA = σ B ε γ ⋅ P γ ⋅ t c ⋅ m e [16] (2)

where: σ, B, ε γ , P γ , t_c (s), m_s (kg) are, respectively, the statistical coverage factor (equal to 1.645 at the 95% confidence level), the background noise, the efficiency of the detector (HPGe), the probability of emission of gamma rays, the counting time and the dry mass of the sample.

The calculated MDAs are 0.12 Bq·kg⁻¹ for ²²⁹Ra, 0.11 Bq·kg⁻¹ for ²³²Th, and 0.15 Bq·kg⁻¹ for ⁴⁰K.

The distribution of radionuclides ²²⁶Ra, ²³²Th and ⁴⁰K in terrestrial materials is not uniform. The risk induced by the radioactivity existing in a building material is evaluated by different models among them the equivalent radium (Ra_eq). Ra_eq is defined as the weighted sum of the activities of ²²⁶Ra, ²³²Th, and ⁴⁰K, according to Equation (3).

Ra eq = C Ra + 1 . 43C Th + 0.0 77C K [17]. (3)

where: Ra_eq (Bq·kg⁻¹) represents the equivalent radium number; C_Ra, C_Th and C_K activity concentrations (Bq·kg⁻¹) of ²²⁶Ra, ²³²Th, and ⁴⁰K, respectively.

The constants 1, 1.43 and 0.077 are risk conversion coefficients established on the basis that 370 Bq·kg⁻¹ of ²²⁶Ra, 259 Bq·kg⁻¹ of ²³²Th, and 4810 Bq·kg⁻¹ of ⁴⁰K, respectively, produce the same flow gamma dose. The maximum value of Ra_eq recommended is 370 Bq·kg⁻¹ for safer use of the material [2].