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A SIMPLE MATRIX APPROACH TO DETERMINATION OF THE HELIUM ATOM ENERGIES Pingak, Redi Kristian; Kolmate, Rosara; Bernandus, Bernandus
Jurnal Penelitian Fisika dan Aplikasinya (JPFA) Vol 9, No 1 (2019)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jpfa.v9n1.p10-21

Calculation of He atomic energy levels using the first order perturbation theory taught in the Basic Quantum Mechanics course has led to relatively large errors. To improve its accuracy, several methods have been developed but most of them are too complicated to be understood by undergraduate students. The purposes of this study are to apply a simple matrix method in calculating some of the lowest energy levels of He atom (1s2, triplet 1s2s, and singlet 1s2s states) and to reduce errors obtained from calculations using the standard perturbation theory. The convergence of solutions as a function of the number of bases is also examined. The calculation is done analytically for 3 bases and computationally with the number of bases using MATHEMATICA. First, the 2-electron wave function of the Helium atom is written as the multiplication of two He+ ion wave functions, which are then expanded into finite dimension bases. These bases are used to calculate the elements of the Hamiltonian matrix, which are then substituted back to the energy eigenvalue equation to determine the energy values of the system. Based on the calculation results, the error obtained for the He ground state energy using 3 bases is 2.51 %, smaller than the errors of the standard perturbation theory (5.28 %). Despite the fact that the error is still relatively large from the analytical calculations for singlet-triplet 1s2s energy splitting of He atom, this error is successfully reduced significantly as more bases were used in the numerical calculations. In particular, for n = 25, the current calculation error for all states is much smaller than the errors obtained from calculations using standard perturbation theory. In conclusion, the analytical calculations for the energy eigenvalue equation for the 3 lowest states of the Helium atom using 3 bases have been carried out. It was also found in this study that increasing the number of bases in our numerical calculations has significantly reduced the errors obtained from the analytical calculations.

Penentuan Tingkat-Tingkat Energi Vibrasi Molekul Hidrogen Pada Keadaan Elektronik Dasar Menggunakan Potensial Morse Pingak, Redi Kristian; Johannes, Albert Zicko
Wahana Fisika Vol 5, No 1 (2020): June
Publisher : Universitas Pendidikan Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17509/wafi.v5i1.18614

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 (0â‰¤nâ‰¤4), dengan kesalahan kurang dari 0,7%, dan untuk 5â‰¤nâ‰¤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.Â 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 (0â‰¤nâ‰¤4), with errors being less than 0.7% and for 5â‰¤nâ‰¤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.Â Â Â Â Â Â Â Â Â Â Keywords: Hydrogen Molecule; Morse Potential; Born-Oppenheimer Approximation; Simpson Method; False Position Method

A Simple Matrix Approach to Determination of the Helium Atom Energies Redi Kristian Pingak; Rosara Kolmate; Bernandus Bernandus
Jurnal Penelitian Fisika dan Aplikasinya (JPFA) Vol. 9 No. 1 (2019)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jpfa.v9n1.p10-21

Calculation of He atomic energy levels using the first order perturbation theory taught in the Basic Quantum Mechanics course has led to relatively large errors. To improve its accuracy, several methods have been developed but most of them are too complicated to be understood by undergraduate students. The purposes of this study are to apply a simple matrix method in calculating some of the lowest energy levels of He atom (1s2, triplet 1s2s, and singlet 1s2s states) and to reduce errors obtained from calculations using the standard perturbation theory. The convergence of solutions as a function of the number of bases is also examined. The calculation is done analytically for 3 bases and computationally with the number of bases using MATHEMATICA. First, the 2-electron wave function of the Helium atom is written as the multiplication of two He+ ion wave functions, which are then expanded into finite dimension bases. These bases are used to calculate the elements of the Hamiltonian matrix, which are then substituted back to the energy eigenvalue equation to determine the energy values of the system. Based on the calculation results, the error obtained for the He ground state energy using 3 bases is 2.51 %, smaller than the errors of the standard perturbation theory (5.28 %). Despite the fact that the error is still relatively large from the analytical calculations for singlet-triplet 1s2s energy splitting of He atom, this error is successfully reduced significantly as more bases were used in the numerical calculations. In particular, for n = 25, the current calculation error for all states is much smaller than the errors obtained from calculations using standard perturbation theory. In conclusion, the analytical calculations for the energy eigenvalue equation for the 3 lowest states of the Helium atom using 3 bases have been carried out. It was also found in this study that increasing the number of bases in our numerical calculations has significantly reduced the errors obtained from the analytical calculations.

Kajian Sifat Radial Ion Hidrogenik Menggunakan Polinomial Laguerre Gerda Pandu; Redi Kristian Pingak; Albert Zicko Johannes; Zakarias Seba Ngara
BULETIN FISIKA Vol 23 No 2 (2022): BULETIN FISIKA August Edition
Publisher : Departement of Physics Faculty of Mathematics and Natural Sciences, and Institute of Research and Community Services Udayana University, Kampus Bukit Jimbaran Badung Bali

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/BF.2022.v23.i02.p01

A preliminary study has been carried out on the radial properties of the hydrogenic systems using the Laguerre polynomial. The aims of this study were to investigate radial properties of hydrogenic ions by evaluating the radial probability density, the most probable radial distance and the average distance of electron from the nuclei of hydrogenic ions. Based on the research results for Z=1 to Z=10 with the principal quantum number (n)=1 to 5, 150 radial function forms, 150 radial probability density, 150 most probable radial distance values and 150 electron average distance values were obtained. The most probable radial distance from the nucleus was compared with the Bohr model and showed the same results as the Bohr model.

Design of Sound Level Meter Using Sound Sensor Based on Arduino Uno Laura Anastasi Seseragi Lapono; Redi Kristian Pingak
Jurnal ILMU DASAR Vol 19 No 2 (2018)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Sound Level Meter (SLM) is a tool used to measure the noise level for a moment. For improved performance, hence required a measure of noise level capable of displaying result automatically on the computer so that simplify user to observe and measure the noise. In this study, the design system of data acquisition consists of a MAX4466 sound sensor, Arduino UNO microcontroller, and computer to display the measurement result. The measurement results are displayed in the form of data and graphs. The display of software designed using the Delphi 7.0. The process of taking data in the room with a sound intensity of 44.6 dB. The value is the measurement result using the SLM tool, while the measurement results using the sound sensor performed every second during an interval of 30 seconds obtained an average of 44.19 dB. It can be seen that between the two results shows a relatively small difference, so it can be concluded that the design of this system is running well. Keywords: Noise, SLM, Sound sensor, Arduino Uno

Analisa Respon Steady dan Transient pada Sistem Mekanik Pegas Ganda serta Terapan Metode PID Memanfaatkan Transformasi Laplace dan Simulink Matlab Sriwiana Laalobang; Ali Warsito; Redi K. Pingak
Magnetic: Research Journal of Physics and It’s Application Vol. 1 No. 1 (2021): Magnetic: Research Journal of Physics and It’s Application
Publisher : Program Studi Fisika - Universitas San Pedro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59632/magnetic.v1i1.67

Telah dilakukan simulasi sistem mekanik pegas ganda menggunakan simulink Matlab dengan tujuan menganalisa respon steady dan transisent pada sistem mekanik pegas ganda dengan menerapkan metode PID memanfaatkan transformasi laplace dan simulink matlab untuk menghasilkan suatu sistem yang stabil. Ketidakstabilan sistem diketahui melalui analisa respon sistem terhadap waktu yaitu respon steady dan respon transient, dimana steady-state error cukup rendah yaitu 2% tetapi respon transient menunjukkan rise time = 5.27 sekon, settling time = 6.27 sekon dan banyak terjadi overshoot. Untuk mendapatkan sistem mekanik pegas ganda yang stabil, fungsi transfer dari persamaan gerak sistem yang telah ditransformasikan dengan transformasi Laplace ke dalam persamaan berdomain s, perlu diformulasikan sebagai representasi sistem kontrol close loop yang memuat variasi metode PID (Proporsional, Integral dan Derivatif). Variasi ini kemudian disimulasikan dengan memberikan input pada konstanta Kp, Ki dan Kd. Hasil simulasi menunjukkan bahwa proses kontrol pada sistem mekanik menghasilkan sistem yang cukup stabil dan terjaga ketika menggunakan metode PD dan PID. Dengan metode PID sistem mencapai kestabilan pada t = 0.01 sekon, dimana nilai Kp = , Ki = dan Kd = , dengan rise time 0.004 sekon, settling time 0.005 sekon dan tidak ada error keadaan tunak.

Kajian Sifat Fisis dan Kimia Bio-Briket Campuran Tempurung Kelapa dan Sekam Padi Kristina Siu; Redi K. Pingak; Albert Zicko Johannes
Magnetic: Research Journal of Physics and It’s Application Vol. 1 No. 1 (2021): Magnetic: Research Journal of Physics and It’s Application
Publisher : Program Studi Fisika - Universitas San Pedro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59632/magnetic.v1i1.70

Telah dilakukan penelitian tentang kajian sifat fisis dan kimia biobriket tempurung kelapa dan sekam padi. Penelitian ini bertujuan untuk menentukan pengaruh variasi komposisi sekam padi terhadap sifat fisis dan kimia briket tempurung kelapa juga pengaruh variasi komposisi sekam padi terhadap kualitas briket. Briket bioarang merupakan salah satu jenis bahan bakar yang dibuat dari aneka macam bahan hayati atau biomassa. Biomassa yang digunakan dalam penelitian ini adalah tempurung kelapa dan sekam padi. Persentase tempurung kelapa dan sekam padi yang digunakan adalah 100:0, 85:15, 70:30, 65:35 dan 40:60 dengan ukuran partikel arang yang lolos mesh 60 atau 0,250 mm dan perekat kanji 10%. Hasil penelitian ini menunjukkan bahwa nilai densitas, nilai porositas, nilai kadar air, nilai kadar abu, nilai zat kadar menguap dan kadar karbon terikat secara berturut-turut berkisar antara 0,786 gram/cm3 - 1,263 gram/cm3, 15,22 - 45,39, 4,04 - 4,90, 20,34 - 21,24 , 17,354 - 21,032 dan 59,36 - 61,86. Hasil analisis menunjukkan bahwa penambahan sekam padi pada pembuatan briket tempurung kelapa memberikan pengaruh yang berbeda untuk sifat-sifat fisis dan kimia briket. Dari hasil peneltitian ini secara umum dapat disimpulkan bahwa semua sampel telah memenuhi syarat standar kualitas briket.

Kajian Awal Potensi Ekstrak Kulit Buah Lontar (Borassus Flabellifer L) sebagai Dye Alami untuk Dye Sensitized Solar Cell (Dssc) Alexia Lemau; Redi K.Pingak; Albert Z. Johannes
Magnetic: Research Journal of Physics and It’s Application Vol. 1 No. 2 (2021): Magnetic: Research Journal of Physics and It’s Application
Publisher : Program Studi Fisika - Universitas San Pedro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59632/magnetic.v1i2.112

Telah dilakukan penelitian tentang kajian awal potensi ekstrak kulit buah lontar (Borassus Flabellifer L) sebagai dye alami untuk Dye Sensitized Solar Cell ( DSSC). Tujuan penelitian ini adalah menentukan nilai jangkauan serapan, koefisien serapan, nilai celah energi dan potensi ekstrak kulit lontar sebagai dye alami untuk Dye Sensitized Solar Cell (DSSC). Kulit lontar yang diambil dari Ileape, Kabupaten Lembata dikeringkan dan dihaluskan menggunakan blender, kemudian serbuk kulit lontar diekstraksi secara maserasi, setelah itu dievaporasi menggunakan evaporator. Langkah berikutnya hasil evaporasi diencerkan ulang dengan etanol sehingga dapat dikarakterisasi menggunakan spektrofotometer UV-Vis untuk mendapatkan spektrum serapan. Berdasarkan data hasil spektrum serapannya, jangkauan serapan senyawa ekstrak kulit lontar dengan konsentrasi 100 ppm, 200 ppm, 300 ppm, adalah 200 nm sampai 393 nm. Hasil analisis spektrum serapan menggunakan metode Tauc Plot memberikan nilai celah energi rata- rata sebesar 3.43 eV. Berdasarkan nilai celah energi tersebut senyawa ekstrak kulit buah lontar berpotensi untuk digunakan sebagai dye alami untuk Dye Sensitized Solar Cell ( DSSC).

Studi Potensi Tinta Printer Berbahan Dasar Pigmen Organik Dari Daun Jambu Biji Minsyahril Bukit; Redi K. Pingak; Yovilia Medi
Magnetic: Research Journal of Physics and It’s Application Vol. 2 No. 1 (2022): Magnetic: Research Journal of Physics and It’s Application
Publisher : Program Studi Fisika - Universitas San Pedro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59632/magnetic.v2i1.145

Telah dilakukan penelitian mengenai potensi pigmen organik berbahan dasar daun jambu biji (Psidium Guanjava L) dalam pembuatan tinta printer. Parameter fisika yang dikaji yakni taraf intensitas cahaya dari tinta dengan variasi massa karbon yang berbeda, laju serap tinta, juga untuk mengetahui kinerja tinta dengan pigmen organik dari limbah daun jambu biji pada printer komersial. Karbon limbah daun jambu biji yang dibakar dihaluskan sampai menjadi serbuk karbon menggunakan blender, selanjutnya adalah memisahkan tinta menurut variasinya masing-masing kemudian mengukur taraf intensitas cahaya. Berdasarkan hasil analisis dari pengukuran transmitansi cahaya yaitu 0,42, 0,46, 0,58 dan 0,63 dalam satuan lux untuk variasi massa komposisi karbon 8, 16, 24, 32 gram. Laju serap tinta maksimum adalah 1,75 cm/menit pada variasi pelarut karbon menggunakan aquades 30 ml. Uji kinerja tinta dengan pigmen organik dari daun jambu biji memperlihatkan bisa digunakan dengan baik sebagai tinta printer, meskipun secara rata-rata kualitas tinta printer komersil masih lebih baik.

DETEKSI EFEK KONTAMINASI HARMONIK RADIASI SYNCHROTRON PADA DATA SERAPAN SINAR-X STRUKTUR HALUS Redi K. Pingak
Jurnal Fisika : Fisika Sains dan Aplikasinya Vol 1 No 1 (2016): Jurnal Fisika : Fisika Sains dan Aplikasinya
Publisher : Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (790.946 KB)

Abstrak Efek kontaminasi harmonik radiasi synchrotron perlu dideteksi dan dikoreksi karena walaupun telah melalui monokromator, energi sinar-x pada umumnya masih merupakan gabungan energi dasar dan kelipatan bilangan bulatnya. Pada artikel ini, deteksi efek harmonik dilakukan pada data serapan sinar-x struktur halus (XAFS) Ni(II)-bis-(n-isopropylsalicylaldiminato) dengan menggunakan metode X-ray Extended Range Technique (XERT). Dalam metode ini, aluminum foil dengan beberapa variasi ketebalan ditempatkan pada daisy wheel untuk memberikan variasi nilai serapan terukur sampel, yang digunakan untuk menginvestigasi adanya perbedaan gradien plot koefisien serapan vs ketebalan aluminum. Selanjutnya, persamaan Beer-Lambert dimodifikasi dan difit untuk memperoleh nilai fraksi harmonik. Nilai-nilai fraksi harmonik ini kemudian diinterpolasi untuk mencakup nilai-nilai energi lain dimana efek ini dominan. Dari hasil fitting, ditemukan bahwa efek harmonik dominan pada interval energi 8.5 keV - 13.5 keV dengan nilai fraksi harmonik berada pada rentang sekitar 0.02 % sampai 0.04 %. Sementara itu, untuk energi 13.50 keV – 19.00 keV, efek ini tidak ditemukan. Dari hasil ini dapat disimpulkan bahwa kontaminasi harmonik ditemukan dominan pada kawasan energi yang vital pada analisis XAFS Ni(II) kompleks dan oleh karena itu perlu dikoreksi dari data terukur. Kata kunci: kontaminasi harmonik; XERT; radiasi synchrotron; serapan sinar-x struktur halus Abstract Harmonic contamination of synchrotron radiation needs to be detected and corrected because x-ray passing through the monochromator may still have higher order harmonics in addition to its fundamental energy. Here, detection of the harmonic effect on X-ray Absorption Fine Structure Data (XAFS) of Ni(II)-bis-(n-isopropylsalicylaldiminato) was done using the X-ray Extended Range Technique (XERT). The method utilised aluminum foils with various thicknesses mounted in daisy wheels, used to investigate the gradient differences in absorption coefficient vs aluminum thickness plots. The Beer-Lambert equation had to be modified dan fitted to find the harmonic fractions of the beam. These values were then interpolated to account for other energies where the effect was dominant. The results showed that the effect was dominant between 8.5 keV and 13.5 keV, with harmonic fractions being about 0.02 % - 0.04 %. In contrast, there was no such effect found between 13.50 keV and 19.00 keV. To conclude, harmonic contamination was found to be in energy range that was vital for XAFS analysis for Ni(II) complex and thus had to be removed from the measured data. Keywords: harmonic contamination; XERT; synchrotron radiation; X-ray Absorption Fine Structure

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