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Olasılıksal Atomik Yarıçap Tanımı: Taban Durumu Hidrojen Benzeri Atomlara Uygulanması

Year 2020, Volume: 10 Issue: 2, 608 - 619, 30.12.2020

Fatih Mehmet Avcu Serkan Alagöz

https://doi.org/10.37094/adyujsci.742590

Abstract

Kimya ve Fizik alanında atomların büyüklüğünü ifade etmek için birkaç atom yarıçapı kavramı önerilmiştir. Bu çalışmada, atomik yarıçap tanımları incelenmiş, olasılık ölçüsüne dayanan ve en dıştaki elektronun hidrojen benzeri bir atomun çekirdeği ile merkezlenmiş küresel bir hacimde olma olasılığını dikkate alan olasılıksal bir atomik yarıçap kavramını sunulmuştur. Bu olasılık ölçüsüne bağlı olarak, temel durum hidrojen atomu için %99 olasılık ile atomik yarıçapı hesaplanmış ve bunun hidrojen benzeri atomik sistemler için yorumlanmıştır.

References

  • [1] Zettili, N., Quantum mechanics: concepts and applications, 2nd ed., 408 pp, Wiley, 2013.
  • [2] Adamson, A.W., Advanced inorganic chemistry. By F.A. Cotton and G. Wilkinson, Inorganic Chemistry, 2 (3), 665–665, 1963.
  • [3] Bragg, W.L., The arrangement of atoms in crystals, Nature, 106 (2675), 725–725, 1921. [4] Wyckoff, R.W.G., On the hypothesis of constant atomic radii, Proceedings of the National Academy of Sciences of the United States of America, 9 (2), 33–38, 1923.
  • [5] Huggins, M.L., Atomic radii I, Physical. Review, 19 (4), 346–353, 1922.
  • [6] Michels, A., De Boer, J., Bijl, A., Remarks concerning molecural interaction and their influence on the polarisability, Physica, 4 (10), 981–994, 1937.
  • [7] Montgomery, H.E., Sen, K.D., Electron density and its derivatives at the nucleus for spherically confined hydrogen atom, International Journal of Quantum Chemistry, 109 (4), 688– 692, 2009.
  • [8] Xu, H., Qu, J., Zhang, M., Yan, Y., Sun, X., Zheng, Y., Qiu, M., Liu L., The linear relationship derived from the deposition potential of Pb–Ln alloy and atomic radius, New Journal of Chemistry, 42 (20), 16533–16541, 2018.
  • [9] Szarek, P., Witkowski, M., Woźniak, A.P., Unconventional look at the diameters of quantum systems: could the characteristic atomic radius be interpreted as a reactivity measure, The Journal of Physical Chemistry C, 123 (18), 11572–11580, 2019.
  • [10] French, S.J., Nature of the chemical bond. second edition, revised (Pauling, Linus), Journal of Chemical Education, 17 (11), 551, 1940.
  • [11] Sommerfeld, A., Welker, H., Künstliche Grenzbedingungen beim Kepler problem, Annalen der Physik, 424 (1–2), 56–65, 1938.
  • [12] Varshni, Y.P., Critical cage radii for a confined hydrogen atom, Journal of Physics B: Atomic, Molecular and Optical Physics, 31 (13), 2849–2856, 1998.
  • [13] Gill, P.M.W., Johnson, B.G., Pople, J.A.A., Standard grid for density functional calculations, Chemical Physics Letters, 209 (5), 506–512, 1993.
  • [14] Gill, P.M.W., Johnson, B.G., Pople, J.A., Two-electron repulsion integrals over gaussian s functions, International Journal of Quantum Chemistry, 40 (6), 1991. [15] Slater, J.C., Atomic shielding constants, Physical Review, 36 (1), 57–64, 1930.
  • [16] Tang, C.L., Fundamentals of quantum mechanics: for solid state electronics and optics, Cambridge University Press, 224 pp, 2005.
  • [17] Griffiths, D.J., Schroeter, D.F., Introduction to quantum mechanics 3rd ed., Cambridge University Press, 495 pp, 2018.
  • [18] Rogers, G.L.A., Visual demonstration of the simple quantum theory of the hydrogen atom, European Journal of Physics, 15 (3), 110–110, 1994.

A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms

Year 2020, Volume: 10 Issue: 2, 608 - 619, 30.12.2020

Fatih Mehmet Avcu Serkan Alagöz

https://doi.org/10.37094/adyujsci.742590

Abstract

Several atomic radius concepts were proposed to express size of atoms in chemistry and physics. This study briefly surveys widely used definitions of atomic radiuses and introduces a probabilistic atomic radius concept that is based on the probability measure, which considers probability of the outermost electron to be in a spherical volume that is centered by nucleus of a hydrogen-like atom. Depending on this probability measure, 99% probabilistic atomic radius is calculated for a ground state hydrogen atom and its interpretation for hydrogen-like atomic systems is discussed.

Keywords

Quantum Mechanics Solutions of Wave Equations Atomic Radius Bound states

References

  • [1] Zettili, N., Quantum mechanics: concepts and applications, 2nd ed., 408 pp, Wiley, 2013.
  • [2] Adamson, A.W., Advanced inorganic chemistry. By F.A. Cotton and G. Wilkinson, Inorganic Chemistry, 2 (3), 665–665, 1963.
  • [3] Bragg, W.L., The arrangement of atoms in crystals, Nature, 106 (2675), 725–725, 1921. [4] Wyckoff, R.W.G., On the hypothesis of constant atomic radii, Proceedings of the National Academy of Sciences of the United States of America, 9 (2), 33–38, 1923.
  • [5] Huggins, M.L., Atomic radii I, Physical. Review, 19 (4), 346–353, 1922.
  • [6] Michels, A., De Boer, J., Bijl, A., Remarks concerning molecural interaction and their influence on the polarisability, Physica, 4 (10), 981–994, 1937.
  • [7] Montgomery, H.E., Sen, K.D., Electron density and its derivatives at the nucleus for spherically confined hydrogen atom, International Journal of Quantum Chemistry, 109 (4), 688– 692, 2009.
  • [8] Xu, H., Qu, J., Zhang, M., Yan, Y., Sun, X., Zheng, Y., Qiu, M., Liu L., The linear relationship derived from the deposition potential of Pb–Ln alloy and atomic radius, New Journal of Chemistry, 42 (20), 16533–16541, 2018.
  • [9] Szarek, P., Witkowski, M., Woźniak, A.P., Unconventional look at the diameters of quantum systems: could the characteristic atomic radius be interpreted as a reactivity measure, The Journal of Physical Chemistry C, 123 (18), 11572–11580, 2019.
  • [10] French, S.J., Nature of the chemical bond. second edition, revised (Pauling, Linus), Journal of Chemical Education, 17 (11), 551, 1940.
  • [11] Sommerfeld, A., Welker, H., Künstliche Grenzbedingungen beim Kepler problem, Annalen der Physik, 424 (1–2), 56–65, 1938.
  • [12] Varshni, Y.P., Critical cage radii for a confined hydrogen atom, Journal of Physics B: Atomic, Molecular and Optical Physics, 31 (13), 2849–2856, 1998.
  • [13] Gill, P.M.W., Johnson, B.G., Pople, J.A.A., Standard grid for density functional calculations, Chemical Physics Letters, 209 (5), 506–512, 1993.
  • [14] Gill, P.M.W., Johnson, B.G., Pople, J.A., Two-electron repulsion integrals over gaussian s functions, International Journal of Quantum Chemistry, 40 (6), 1991. [15] Slater, J.C., Atomic shielding constants, Physical Review, 36 (1), 57–64, 1930.
  • [16] Tang, C.L., Fundamentals of quantum mechanics: for solid state electronics and optics, Cambridge University Press, 224 pp, 2005.
  • [17] Griffiths, D.J., Schroeter, D.F., Introduction to quantum mechanics 3rd ed., Cambridge University Press, 495 pp, 2018.
  • [18] Rogers, G.L.A., Visual demonstration of the simple quantum theory of the hydrogen atom, European Journal of Physics, 15 (3), 110–110, 1994.
There are 16 citations in total.

Details

Primary Language English
Subjects Atomic, Molecular and Optical Physics
Journal Section Physics
Authors

Fatih Mehmet Avcu 0000-0002-1973-7745

Serkan Alagöz 0000-0003-2642-8462

Publication Date December 30, 2020
Submission Date May 25, 2020
Acceptance Date December 3, 2020
Published in Issue Year 2020 Volume: 10 Issue: 2

Cite

APA Avcu, F. M., & Alagöz, S. (2020). A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms. Adıyaman University Journal of Science, 10(2), 608-619. https://doi.org/10.37094/adyujsci.742590
AMA Avcu FM, Alagöz S. A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms. ADYU J SCI. December 2020;10(2):608-619. doi:10.37094/adyujsci.742590
Chicago Avcu, Fatih Mehmet, and Serkan Alagöz. “A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms”. Adıyaman University Journal of Science 10, no. 2 (December 2020): 608-19. https://doi.org/10.37094/adyujsci.742590.
EndNote Avcu FM, Alagöz S (December 1, 2020) A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms. Adıyaman University Journal of Science 10 2 608–619.
IEEE F. M. Avcu and S. Alagöz, “A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms”, ADYU J SCI, vol. 10, no. 2, pp. 608–619, 2020, doi: 10.37094/adyujsci.742590.
ISNAD Avcu, Fatih Mehmet - Alagöz, Serkan. “A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms”. Adıyaman University Journal of Science 10/2 (December 2020), 608-619. https://doi.org/10.37094/adyujsci.742590.
JAMA Avcu FM, Alagöz S. A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms. ADYU J SCI. 2020;10:608–619.
MLA Avcu, Fatih Mehmet and Serkan Alagöz. “A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms”. Adıyaman University Journal of Science, vol. 10, no. 2, 2020, pp. 608-19, doi:10.37094/adyujsci.742590.
Vancouver Avcu FM, Alagöz S. A Probabilistic Atomic Radius Definition: Application to Ground State Hydrogen-Like Atoms. ADYU J SCI. 2020;10(2):608-19.
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