# Design of a Low-Resolution Gamma-ray Spectrometer for Monitoring Radioactive Levels of Wastewater
## 3 Results
### Calculation of MDA of \({}^{18}\)F in Water  
Figure 2b shows the background count rates measured for one hour in a 14 L water tank containing tap water, and the counts in the full energy peak of \({}^{18}\)F were 186 counts. Using Equation (4), the _LD_ for the one-hour measurement was calculated as 6.62 \(\times\) 10\({}^{1}\) counts. Then, this value was transferred to 2.09 \(\times\) 10\({}^{5}\) Bq\(\cdot\)m\({}^{-3}\), the _MDA_ for the same measurement live time, using Equation (3) with an absolute detection efficiency (\(\varepsilon\)) of 511 keV. This efficiency was obtained by dividing the counts at 511 keV in NaI(Tl) by the counts at 511 keV in the gamma spectroscopy system, and it was 4.40 \(\times\) 10\({}^{-5}\). This value was smaller than 1 \(\times\) 10\({}^{7}\) Bq\(\cdot\)m\({}^{-3}\), which is the amount prescribed by law in Korea, where the public is predicted to reach the dose limit owing to the draining of \({}^{18}\)F-containing wastewater into the public environment. Using this system, it was possible to determine whether the specific activity of radioactive wastewater containing \({}^{18}\)F could be measured for one hour.  
The change in _MDA_ at various measurement times and assuming that the background radioactivity was constant is shown in Table 4. When the measurement time was one  
Figure 4: Specific activities measured by HPGe and count rates measured by NaI(Tl): count rates (a), (b) and full energy peaks (c), (d) obtained by experiment and calculation, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**R (cm)**} & \multirow{2}{*}{**H (cm)**} & \multirow{2}{*}{**Volume (\(\ell\))**} & **Calculated** & _ACF_ \\  & & & **(counts\(\cdot\)s\({}^{-1}\))** & **(Bq\(\cdot\)s\(\cdot\)m\({}^{-3}\cdot\)counts\({}^{-1}\))** \\ \hline
12.5 & 29.5 & 14.0 & 2.4783 \(\times\) 10\({}^{4}\) & 4.6415 \(\times\) 10\({}^{10}\) \\ \hline
14.4 & 31.4 & 20.0 & 2.2132 \(\times\) 10\({}^{4}\) & 5.1975 \(\times\) 10\({}^{10}\) \\ \hline
16.0 & 33.0 & 26.0 & 2.1122 \(\times\) 10\({}^{4}\) & 5.4460 \(\times\) 10\({}^{10}\) \\ \hline
17.4 & 34.2 & 32.0 & 2.0775 \(\times\) 10\({}^{4}\) & 5.5370 \(\times\) 10\({}^{10}\) \\ \hline
18.6 & 35.4 & 38.0 & 2.0768 \(\times\) 10\({}^{4}\) & 5.5389 \(\times\) 10\({}^{10}\) \\ \hline
19.7 & 36.5 & 44.0 & 2.0768 \(\times\) 10\({}^{4}\) & 5.5389 \(\times\) 10\({}^{10}\) \\ \hline
20.7 & 37.5 & 50.0 & 2.0768 \(\times\) 10\({}^{4}\) & 5.5389 \(\times\) 10\({}^{10}\) \\ \hline
21.6 & 38.6 & 56.1 & 2.0768 \(\times\) 10\({}^{4}\) & 5.5389 \(\times\) 10\({}^{10}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Activity conversion factors (_ACFs_) for various water tank volumes in Figure 1b.  
hour, the _MDA_ calculated using Equation (3) was 2.09 \(\times\) 10\({}^{5}\) Bq\(\cdot\)m\({}^{-3}\); however, when the measurement time was increased to 24 h, the _MDA_ decreased to 4.12 \(\times\) 10\({}^{4}\) Bq\(\cdot\)m\({}^{-3}\). This means that, by increasing the measurement time from one hour to one day, the measurement ability was improved by five times.