The Coulomb energy for different nuclear model with small computing effort and high accuracy is a great challenge in physics as well as in quantum chemistry research. In this work we applied a classical electrodynamics theory and derived a simple procedure and expression for calculating the Coulomb energy for atomic nuclei taking into consideration the finite size of protons. The corresponding results are compared with the direct Coulomb energy obtained from two-parameter Fermi distributions. The formula obtained, which varies directly to the proton number and varies inversely to the cube root of mass number, was applied and calculated numerically the values of Coulomb energy for light, medium and heavy nuclei. To examine the effect of finite size of proton on Coulomb energy, a graph of Coulomb energy as a function of proton number was presented. The results obtained showed that due to the finite size of proton, the values of the previously calculated values of the Coulomb energy are reduced by less than 2%. This is because the protonproton distance increased due to finite size effect of the proton and thus affects the magnitude of the Coulomb energy. This showed that calculation of Coulomb energy by taking into consideration, the finite size of proton leads to agreement with the experimental values. Thus, in studying the nuclear structure, it is very natural to assume the protons to be extended rather than point charges.
A model for energy dissipation is presented which demonstrates energy transfer from a collective degree of freedom, represented by free motion, into intrinsic modes, represented by four coupled oscillators. The quantum mechanical probability amplitude for internal excitation is expressed as a multiple integral of a product of translational and intrinsic wavefunctions and exactly solved analytically. Its numerical values as a function of quantities of physical interest have been calculated, represented graphically and discussed. The results show that the probability distributions are peaked.
The population health risk due to heavy metal exposure has been becoming serious and worldwide environmental issue that has attracted considerable public attention. In this study, the level of heavy metal (Cd, Cr, Fe, As and Pb) in soil samples were determined using Atomic Absorption Spectrophotometer methods (AAS) to assess heavy metals contamination of soil due to mining activities around Gombe, Nigeria. The results obtained showed that the highest concentrations of 96.7271±2.770 mg/kg for Fe were observed in Unguwar Baka I, 25.5355±1.782 mg/kg for Pb were observed in Unguwar Baka I, 21.9673±2.047 mg/kg for Cr were observed in Tumu, 12.9675±1.969 for Cd were observed in Unguwar Baka I and 0.5782±0.025 mg/kg for As were observed in Unguwar Baka. In all the sampling locations, the levels of heavy metals in soil samples measured have the variation pattern in the order: Fe > Cr > Pb > Cd > As. The levels of the Fe, Cr, Pb, Cd, and As are higher than the World Health Organization (WHO) permissible limits in soil. This indicates that their concentration in the soil had the higher capability to pose severe health risk to the community of that area. This information will contribute to awareness of the potential impacts of heavy metals pollutants around the mining area of Gombe state.
The study was carried out to evaluate the quality of soil at the finished landfill located in Cai Dau town, Chau Phu district, An Giang province, Vietnam. Twelve soil samples were collected including 6 samples in the surface layer (0-20 cm) (namely S1-S6), 6 samples in the subsurface layer (60 -80 cm) (namely S1-S6) for the analysis of heavy metals such as Fe, Mn, Cu, Pb, Ni, Cr, Zn. The analytical results showed that all the heavy metals occurred in soil in which Fe was the highest and Ni was the lowest. The concentrations of the heavy metals in the soil surrounding the closed landfill in both layers were in the descending order of Fe> Mn> Zn> Cr> Cu> Pb> Ni. These heavy metals concentrations were within the allowable range of QCVN 03: MT/BTNMT-agricultural land. The occurrence of heavy metals in different layers at the surrounding landfill could potentially result in negative impact on the environments since heavy metals have the capability of accumulation. Therefore, monitoring of the environments around closed landfill should be implemented and the long-term risk of heavy metals should be estimated.
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