Penentuan Tingkat-Tingkat Energi Vibrasi Molekul Hidrogen Pada Keadaan Elektronik Dasar Menggunakan Potensial Morse
Abstract
Pendekatan Born-Oppenheimer diterapkan untuk menghitung tingkat energi vibrasi keadaan dasar molekul hidrogen. Persamaan Schrodinger untuk inti atom diselesaikan dengan menggunakan metode semi-klasik, di mana inti atom diasumsikan bergerak secara klasik dalam sumur potensial dan energi vibrasi ditentukan dengan menerapkan aturan kuantisasi kuantum. Potensial yang digunakan pada penelitian adalah potensial Morse. Dalam penelitian ini, tingkat energi vibrasi dihitung dengan metode numerik, yaitu metode integrasi Simpson dan metode regula falsi. 15 Tingkat energi vibrasi dari molekul H2 diperoleh dan dibandingkan dengan data hasil eksperimen. Perbandingan ini mengindikasikan pendekatan yang digunakan pada penelitian ini memberikan hasil yang sangat akurat pada tingkat energi vibrasi yang relatif rendah (0≤n≤4), dengan kesalahan kurang dari 0,7%, dan untuk 5≤n≤8 dengan kesalahan maksimum 7,3%. Keakuratan menurun ketika tingkat energi vibrasi meningkat. Secara khusus, untuk n = 13 dan n = 14, kesalahan meningkat secara signifikan, menunjukkan gagalnya pendekatan ini untuk tingkat energi vibrasi yang relatif tinggi, khususnya untuk dua tingkat energi ini.
Born-Oppenheimer approximation was applied to calculate vibrational energy levels of ground state of Hydrogen molecule. The Schrodinger equation for the nuclei was solved using a semi-classical method, in which the nuclei are assumed to move classically in a potential well and the vibrational energies are determined by applying the quantum mechanical quantization rules. Potential used in this research was the Morse potential. Here, vibrational energy levels of the molecule were calculated using numerical methods, i.e. Simpson integration method and false position method. 15 Vibrational energy levels of the H2 molecule were obtained and compared to the corresponding results from experiments. The comparison indicated that the approximation used in this research yielded very accurate results for relatively low vibrational levels (0≤n≤4), with errors being less than 0.7% and for 5≤n≤8 with maximum of 7.3% errors. The accuracy decreased as the vibrational levels increased, as expected. In particular, for n=13 and n=14, errors significantly increased, indicating the breakdown of the approximation for relatively high vibrational levels, in particular for these two energy levels.
Keywords: Hydrogen Molecule; Morse Potential; Born-Oppenheimer Approximation; Simpson Method; False Position Method
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DOI: https://doi.org/10.17509/wafi.v5i1.18614
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