## 3 Measurement Tests
### Test Results and Analysis
As can be seen from the half-lives of the individual nuclides in Table 1, the half-lives of \({}^{210}\)Po and \({}^{210}\)Bi are 138 days and 5 days, respectively, which are very short and will not exist stably in the tin sphere for a long time. While the half-life of \({}^{210}\)Pb is 22.2 years, which is longer and can exist in the sample relatively stably. Therefore, it can be concluded that \({}^{210}\)Pb undergoes successive \(\beta\)-decays to form \({}^{210}\)Bi and \({}^{210}\)Po in turn, while \({}^{210}\)Po is the source of \(\alpha\)-particles obtained from the test. From the \(\alpha\)-particle emissivity in Table 3, it can be seen that as the content of the Pb element in the tin sphere decreases, its \(\alpha\)-particle emissivity undergoes a more obvious decrease, which is also supported by the positive correlation between the \(\alpha\)-particle emissivity and the content of lead. Figure 4 shows the energy spectrum of the \(\alpha\)-particles emitted and the Gaussian function to fit the curve by the SAC305 tin sphere with an emissivity of 3.76 \(\pm\) 0.2 \(\alpha\)/(cm\({}^{2}\cdot\)h). Due to the relatively low emissivity, the test time was adjusted to 200 h, and the obtained energy spectrum is shown in Figure 4. As can be seen from the figure, the \(\alpha\)-particle counts increased significantly in the energy range from 5 MeV to 5.3 MeV, and the peak position  
Figure 3: The \(\alpha\)-particle emission energy spectrum of thick-film material containing \({}^{232}\)Th [5]. of the Gaussian function fitted curve is at 5.1 MeV. The internal radionuclide types were analyzed, and the radionuclides whose decay-produced \(\alpha\)-particle energies were in the range of 5 MeV\(\sim\)5.3 MeV were \({}^{210}\)Po (5.304 MeV) and \({}^{228}\)Th (5.423 MeV (73.4% probability), 5.340 MeV (26% probability)). For \({}^{228}\)Th, previously analyzed as having at least four peaks in its emission energy spectrum with some of the peaks corresponding to energies greater than 6 MeV, there is obviously no such feature shown in Figure 4, so \({}^{228}\)Th is not an internal radionuclide. Therefore, the internal radionuclide of the SAC305 tin sphere is the same as that of Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere and Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin sphere, all of which are \({}^{210}\)Po. The presence of traces of \({}^{210}\)Pb nuclides in SAC305 tin sphere leads to the production of \({}^{210}\)Po. Figures 5-7 show the \(\alpha\)-particle emission energy spectra and emissivity-time histograms for Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin spheres, Sn\({}_{63\%}\)Pb\({}_{37\%}\) tin spheres, and low-\(\alpha\) SAC305 tin spheres, respectively. As can be seen from the emissivity-time histograms, emissivity eventually stabilizes, so the ultra-low emissivity data are completely reliable. And, as can be obtained from the energy spectra, the energy spectra of the three types of tin spheres exhibit a discrete distribution. Since the emissivities of the low \(\alpha\) tin sphere were all \(\leq\)0.002 \(\alpha\)/(cm\({}^{2}\)-h), a low number of collected \(\alpha\)-particles result. The emissivity of the purified and treated low \(\alpha\) tin sphere was reduced by 3 to 4 orders of magnitude. Figure 4: The \(\alpha\)-particle energy spectrum of the SAC305 tin sphere emission. Figure 5: The low \(\alpha\)\(\alpha\)-particle energy spectrum of the Sn\({}_{10\%}\)Pb\({}_{90\%}\) tin sphere emission and emissivity-time histograms.