![]() The statistical-mechanical models are easy to use and are not expensive, only few molecular constants of a diatomic molecule are required to predict the thermal property of the system. The thermodynamic property of a gaseous molecule can be predicted theoretically with the aid of analytical model equation it can also be determined by experimental procedures. The need to obtain analytical (or statistical-mechanical) models for the prediction of thermodynamic properties of gaseous substances have recently attracted much attention from the research community. For instance, expectation values, information theoretic, optical, magnetic, electrical, and thermodynamic properties of substances have been investigated through eigen energy levels and eigenfunctions of wave Eqs 17– 34. The solution of Schrödinger wave equation has been instrumental in retrieving information regarding the quantum mechanical system of interest. Some illustrative examples where the different solution techniques are used to solve the Schrödinger equation can be found in Ref. Quite a number of analytical solution methods have been suggested in the literature, the Nikiforov-Uvarov (NU) method, exact and proper quantization rules, supersymmetric quantum mechanics approach (SUSYQM), asymptotic iteration method (AIM), and the recently introduced Nikiforov-Uvarov functional analysis (NUFA) method are some of the methods. The solution of Schrödinger and other wave equations of quantum mechanics can be obtained analytically or by numerical approach. The Varshni conditions ensure that the potential parameters of an oscillator are expressed in terms of molecular constants such as equilibrium harmonic vibrational frequency ( ω e), rotational-vibrational coupling coefficient ( α e), equilibrium dissociation energy ( D e), anharmonicity constant ( ω e x e), and equilibrium bond length ( r e). A diatomic molecule oscillator is required to satisfy the so-called Varshni conditions. The oscillator is a specialized model potential used to describe interactions in diatomic molecules. The list of potential models includes the Morse potential, Eckart potential, Frost-Musulin potential, Rosen-Morse potential, Tietz potential, Hua potential, and Schiöberg potential amongst others.Ī potential energy function whose potential parameters are formulated in terms of the spectroscopic constants of a diatomic molecule is referred to as oscillator. Numerous versions of potential models have been proposed by chemist and physicist to account for observed atomic and molecular phenomena. One of the problems of this representation is the absence of a universal potential energy function that can model every atomic and molecular interactions. Potential energy function (simply known as potential) is a mathematical model used to describe the interaction of a physical system with its environment. The work could be applicable in the fields of molecular physics, chemical physics, solid-state physics and chemical engineering. The results obtained are in good agreement with available literature data on gaseous molecule. The isobaric heat capacity model yields average absolute deviation of 2.1608%, 1.8601%, and 1.9805%. With the aid of the expression for molar entropy of the system, average absolute deviations obtained for the molecules are 0.1878%, 0.1267%, and 0.0586% from experimental data. ![]() The obtained model equations were used to generate numerical data on bound state energy eigenvalues and, to investigate the thermodynamic properties of the ground states chloroborane (BCl), bromine fluoride (BrF), and bromine chloride (BrCl) molecules. The equations were used to derive statistical-mechanical models for the prediction of molar entropy, enthalpy, Gibbs free energy and constant pressure (isobaric) heat capacity of gaseous substances. Analytical equations for bound state pure vibrational energies and canonical partition function were obtained. ![]() In this work, the reparameterized Scarf II oscillator was employed to describe the internal vibration of diatomic systems. 4Department of Physics, Faculty of Natural Sciences, University of JosJos, Plateau, Nigeria.3Department of Physics, Faculty of Science, University of AbujaAbuja, Nigeria.2Department of Pure and Applied Sciences, Taraba State PolytechnicJalingo, Taraba, Nigeria.1Department of Physics, Faculty of Physical Sciences, Modibbo Adama UniversityYola, Adamawa, Nigeria.The data used to construct this figure were extrapolated from the source linked to here.E. The major peaks are identified by element. The intensity of ions is reported in kilocounts per seconds. Example of an ICP-MS spectrum of a metal coating using laser ablation to vaporize the sample before drawing it into the ICP torch.
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