Fractional Derivative Models for Energy Levels and Molar Entropy of Diatomic Molecules

Authors

  • Abubakar Ahmed
    a:1:{s:5:"en_US";s:24:"Modibbo Adams University";}
  • E. S. Eyube
  • B. D. Mohammed
  • J. B. Ayuba
  • B. Sabo

Keywords:

Diatomic molecules, Fractional parameters, Thermodynamic functions, Energy eigenvalues

Abstract

This study develops new analytical equations for the energy levels and molar entropy of substances by solving the Schrödinger equation with the Pöschl-Teller potential. While thermodynamics is crucial in fields like agriculture, drug design, and medical research, existing models often use spectroscopic constants but overlook fractional parameters, which limits their accuracy for gaseous diatomic molecules. By integrating fractional parameters alongside spectroscopic constants, this study addresses this limitation and improves precision. The new equations are applied to analyze pure substances, including Br2 (X 1∑g+), Cl2 (X 1∑g+), CO (X 1∑+), and Na2 (X 1∑g+). The mean percentage absolute deviation (MPAD) of the energy levels obtained is 1.4797%, 0.9043%, 0.0898%, and 1.1352%, respectively, compared to Rydberg-Klein-Rees data. For molar entropy, the MPAD values are 0.1381%, 0.1360%, 0.1322%, and 0.6437% relative to data from the National Institute of Standards and Technology (NIST) database. These results indicate a significant improvement in accuracy over existing models and are consistent with the literature on gaseous molecules.

Dimensions

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Published

2024-06-30

How to Cite

Ahmed, A., Eyube, E. S., Mohammed, B. D., Ayuba, J. B., & Sabo, B. (2024). Fractional Derivative Models for Energy Levels and Molar Entropy of Diatomic Molecules. Nigerian Journal of Physics, 33(S), 164-174. https://doi.org/10.62292/njp.v33(s).2024.258

Issue

Vol. 33 No. S (2024): Nigerian Journal of Physics - Vol. 33(S)

Section

Articles
Copyright & Licensing

How to Cite

Ahmed, A., Eyube, E. S., Mohammed, B. D., Ayuba, J. B., & Sabo, B. (2024). Fractional Derivative Models for Energy Levels and Molar Entropy of Diatomic Molecules. Nigerian Journal of Physics, 33(S), 164-174. https://doi.org/10.62292/njp.v33(s).2024.258

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