Potassium is one of the elements responsible for natural radioactivity. It is also a very important mineral for human life. It is found in soil and water, and stored in food like beans, fruit and cacao. Samples of the same kind of food with different provenance allow studying the effect of the soil on the potassium content. The radioactive isotope ⁴⁰K has a natural abundance of 0.012% [1] . In 10.6% of the cases, it decays via a β⁺ decay to a metastable state of ⁴⁰Ar. In the isomeric transition to the ground state, ⁴⁰Ar emits a photon of 1460 keV, which can be identified by different kinds of detectors [2] . Measurements of the potassium content of food samples have been performed using Atomic Absorption Spectrometers [3] , Fluorimeters [4] , Sodium Iodide Based Detectors [5] [6] and High Purity Germanium (HPGe) Detectors [7] - [9] .

HPGe detectors have an excellent energy resolution. Individual gamma lines up to several MeV can be measured with good efficiency, if the detectors are large enough. They are ideally suited to investigate natural radioactivity in food. The purpose of this study is to measure the potassium content of different food samples and to evaluate the possible effects of soil and water. The method used is gamma ray spectroscopy with HPGe detectors.

The energy spectrum shown in Figure 1 was obtained with a potassium chloride (KCl) [10] calibration sample. The peak at 1460 keV, has a FWHM of 2.03 keV, demonstrating the excellent energy resolution of HPGe detectors. All peaks expected from natural radioactivity are suppressed due to a lead shield and the strength of the ⁴⁰K peak. Clearly visible is the 511 keV peak from pair production in the vicinity of the detector.

In Section 2, the experimental setup is described. A complete description of the preparation of the samples of food is found in Section 3. In Section 4, the method to extract the potassium content of the food samples from the spectra is described. The results of the analysis are shown and discussed in Section 5. The paper closes with some conclusions.

The experimental setup is shown in Figure 2. An HPGe Detector produced by Canberra is surrounded by a multilayer shield with a cavity to place the samples.

Tables 2-5 provide an overview of all the food measurements discussed in this paper. The relevant quantities for each measurement are its lifetime and the mass of the sample. The date of the measurement is also given as the samples were purchased shortly before the measurements and variations with production time are probable.

The measurements listed in different tables were done with slightly different setups. A calibration measurement was done for each of these configurations. All samples were weighed to a precision of 0.1 g. The samples were placed in plastic containers. The container and its relative position to the detector were the same for all the measurements in a given configuration to guarantee the same geometrical acceptance.

Figure 5 shows pictures of different samples as used in the measurements. The first phase of the study (see Table 2) focused on fruit and nuts (F_12). In addition, some chocolates (DC_12) were investigated. In the DC_12 subset the % values indicate the cacao content of the dark chocolates as listed by the producer Lindt. Fruit and chocolate samples were cut in small pieces to fill the container as shown in Figure 5. The second and the third phases (see Table 3 and Table 4) focused on chocolate. The DC_13 and DC_14 subsets contain dark chocolates with different nominal cacao content produced by Vivani and Lindt, respectively. Using these samples, together with the DC_12 samples, the connection between the cacao percentage and the potassium content was investigated. The CC_13 and CC_14 subsets contain dark chocolate with the same nominal cacao content (75%) but different places of origin of the cacao. Using these samples, the effect of the place of origin of the cacao on the potassium content was investigated. The chocolate samples listed in Table 3 and Table 4 were chopped in order to obtain a uniform distribution of the chocolate in the container. This was not done in phase one. However, the effect of chopping was measured to be below 5% [13] and was neglected. The fourth phase (see Table 5) focused on legumes (L_14). Those were the samples for which the highest potassium content was expected. The effect of the self-absorption was estimated in a Monte Carlo study to be below 5% for the KCl, i.e. for the highest density of all the samples, and therefore neglected.

The measured potassium content, , for all samples listed in Tables 2-5 are given in Tables 6-9. Also given are expectations, [17] , and statistical () and systematic () uncertainties. The statistical uncertainties dominate. The expected values [17] are reported without uncertainties.

Figure 7 shows the F_12 results on fruit and nuts listed in Table 6. The agreement between the expected and measured values is good for fresh fruit like bananas, kiwis and strawberries. The disagreement observed for processed food points to the influence of the processing techniques. The nuts show a potassium content lower than expected, while the dried fruit shows a higher one. The more dehydrated the fruit, the higher is the relative potassium content. The ratios between expectation and measurement are not uniform but the trends are very clear.

The subset DC_12 of Tables 6-8 list the results for chocolate. Given the cacao content, C (%), of a bar of chocolate of 100 g, the expected potassium content is calculated as:

where is the potassium content of pure cacao. Potassium is assumed to be contained only in

cacao. Figure 8 shows the correlation between the nominal content of cacao and the measured potassium content for samples produced by Lindt (DC_12 and DC_14, purchased in summer 2012 and summer 2014 respectively) and Vivani (DC_13), purchased in autumn 2013. The expected potassium content (Equation (5)) are also shown. Both Lindt chocolates have higher potassium content for higher percentage of cacao. However, the proportionality is not as expected: for lower (higher) nominal cacao content the measured potassium content is lower (higher) than expected. For Vivani chocolates, the potassium content is basically independent of the nominal % of cacao. This behavior could point to inaccurately quoted percentages of cacao or to production techniques influencing the potassium content of the product.

Figure 9 shows a comparison between the expected and the measured potassium content in bars of chocolate produced by Bonnat with cacao coming from different countries. Measurements for each place of origin were performed with two slightly different setups and using two samples of chocolate (75% of cacao) purchased in different years. The results are from autumn 2013 (CC_13 in Table 7) and from summer 2014 (CC_14 in Table 8). The two sets of measurements agree within the uncertainties. However, the measurements show a potassium content significantly lower than expected. This behavior could point either to a cacao content lower than declared or to specific production techniques that might influence the potassium content. No significant variations due to the place of origin are observed.

Table 9 shows the results for legumes. Figure 10 shows the comparison between the expected and the measured potassium content. Both, red lentils and green peas, have a potassium content higher than expected, while the white beans autumn short. However, the white beans still have the highest measured potassium content.

In this paper, a simple and clean method to measure the potassium content of samples of food with germanium detectors was presented. The results verify the high potassium content expected for fruit, nuts, chocolate and legumes. However, the expectations are not always met quantitatively. Especially the expected dependence of the potassium content of chocolate on the listed percentage of cacao could not be confirmed. No dependence on the origin of the samples could be established with statistical significance. The highest measured potassium contents are 1705 mg/100g from dark chocolate with 90% of cacao and 1630 mg/100g from white beans. Eating either 100 g of 90% cacao chocolate or 100 g of white beans provide approximately 50% of the daily recommendation of 3.5 g [18] of potassium.

We thank the entire GeDet group of the Max-Planck-Institute for Physics in Munich for their help and technical support. We would like specially to thank the students A. Burger, M. Duda and M. Schuster who helped carrying out some of the measurements. Part of the material presented in this paper is based upon work supported by the LMU-Mentoring founding program (autumn 2013).

Iris Abt,Lucia Garbini,Oliver Schulz, (2016) Measurement of the Potassium Content of Different Food Samples with High Purity Germanium Detectors. Detection,04,73-85. doi: 10.4236/detection.2016.43010