Calculating the density of electronic charge for hydrogen atom and ions like atom

Transcription

1 Vol.8(2)211 Calculating the density of electronic charge for hydrogen atom and ions like atom Ban. Adel* Khalil A. Al-Bayati* Nessrin K. Abd- AL Ameer* Received 3, January, 211 Accepted 7, June, 211 Abstract : The radial wave function and the radial distribution function P(r) as a function of (r), for the ydrogen atom was calculated for several atomic state (1s,2s,2p,3s,3p,3d) The results were compared with ydrogen like atom(e +, +2, +3 ). Key words : ydrogen atom, radial wave function, radial distribution function Introduction : The radial distribution function for e atom and like ions has been calculated by Al-bayati &Ban [1]. The electronic wave function, describes the distribution of the electron positions in terms of the distance of the electron from the nucleus, r, and the orientation of the electron relative to the nucleus. We can separate the wave function into an orientationally dependent part, known as the angular wave function, and an orientationally independent part, which is known as the Radial Wave Function [2]. The angular wave functions for other types of orbital are complicated mathematical expressions, so generally only the shapes of the orbital, are important. Another important function we need to consider is the Radial Distribution Function, P nl (r). This is defined as the probability that an electron in the orbital with quantum numbers n and l will be found at a distance r from the nucleus. It is related to the radial wave function by the following relationship[3]: (1) ;normalized (2) The Radial Wave Function, R nl (r), depends only on the distance of the electron from the nucleus, and is characterized by the values of the principal and orbital angular quantum numbers, whereas the angular wave function, Y, depends on the angles of the electron from the nucleus, and is characterized by the values of the orbital angular and magnetic quantum numbers. The s orbital consist only of a radial part to the wave function. The same procedure, of separation of variables, is possible for other atomic species e.g. e +, +2 and +3, considered to the extent that there is one extra-nuclear electron. Radial Distribution function for the ydrogen atom: Often it is more meaningful physically to make plots of the radial distribution function P(r), of an atomic orbital, since this display emphasizes the spatial reality of the probability * Department of Physics, College of Science for women, University of Baghdad, Baghdad, Iraq 515

2 distribution of the electron density as shell structure about the nucleus.to establish the radial distribution function we need to calculate the probability of an electron, in particular orbital, exhibiting coordinates on a thin shell of width. The calculations and results: Table (1) - The radial components of the hydrogenic atomic orbitals[4] orbital N R 1s 2s ( ) Vol.8(2)211 The radial component of the hydrogenic atomic orbitals with distinct normalization constants for the radial functions[5]. The parameter ρ=(2z/n*a) extents the application of the function in the table (1) entries for non-hydrogen one-electron atomic species. Remark : the maximum P(r) for atom accurse at r=1 Bohr unit 2p ( ) 3s ( ) 3p ( ) 3d ( ) ( ) ( ) r P(r) Atom e Z ρ Fig. (1) The normalized radial wave function and the radial distribution function P(r) for the 1s atomic orbital in the hydrogen atom and hydrogen like 52 e e

3 Vol.8(2)211 r P(r) Atom e Z ρ Fig. (2) The normalized radial wave function and the radial distribution function P(r) for the 2s atomic orbital in the hydrogen atom and hydrogen like e P(r) e 521

4 Vol.8(2)211 r P(r) E-5 Atom e Z ρ Fig. (3) The normalized radial wave function and the radial distribution function P(r) for the 2p atomic orbital in the hydrogen atom and hydrogen like e P(r) e 522

5 Vol.8(2)211 r P(r) (. ) Atom e Z ρ e P(r) e E-5 Fig. (4) The normalized radial wave function and the radial distribution function P(r) for the 3s atomic orbital in the hydrogen atom and hydrogen like 523

6 Vol.8(2)211 r P(r) ( ) E-5 Atom e Z ρ Fig. (5) The normalized radial wave function and the radial distribution function P(r) for the 3p atomic orbital in the hydrogen atom and hydrogen like e e 524

7 Vol.8(2)211 r P(r) E-9 Atom e E-7 Z E- Ρ E E p(r) pe(r) p(r) p(r) Fig. () The normalized radial wave function and the radial distribution function P(r) for the 3d atomic orbital in the hydrogen atom and hydrogen like R ( r) P(r) 525

8 Conclusion: Using equations shown in the table (1), we studied the electronic distribution function and probability density for the different orbits of the hydrogen atom and hydrogen like From present work, we noted the following: 1- In s orbits, the value is not equal to zero at the nucleus, that can be observed in figures (1,2,4), what not observed in other orbits. 2 - The probability of finding an electron in 2s shell within one Bohr radius of the nucleus greater than the probability of finding the electron in 2p shell in the same area, this shows that the electrons 1s more effective in blocking electrons of 2p from the nuclear shipment than in the blocking electrons of 2s. in other words, the orbits 2s, 2p will have the same energy in the atoms that have more than one electron. 3 - Figures (1..), show that the distribution function of the hydrogen atom is greater than the distribution function of ions that hydrogen like Vol.8(2)211 Whenever an atomic number increasing, the function will approach to the nucleus, according to the force of attraction between the nucleus and the electron. References: 1- Adel,.Ban,Al-bayati,K calculate the one expectation to electronic charge of atomic system continue two electron, Baghdad Sci. J. 7(1) : Steiner, E the chemistry maths Book, Oxford Science publications, Oxford. 3- March, N.., 23. Local energy equation for two- electron atoms and relation between kinetic energy and electron densities,j. chem. phys 1(15): Charles, M. 28. Quinn, computational chemistry An interactive Guide to Basis Set Theory, The National University of Ireland, Ireland. 5- حنا هلفن دبليى حسجوت جعفس علي حسين هيكانيك الكن في الكيوياء جاهعت كىلىزادو جاهعت صالح الدين. صالح الدين. حساب كثافت االحتماليت القطزيت والذالت القطزيت لذرة الهيذروجيه وااليىواث المشابهت لذرة الهيذروجيه بان حسه عادل* خليل هادي البياتي * وسزيه خليل عبذ االميز* *جاهعت بغداد / كليت العلىم للبناث / قسن الفيصياء الخالصت : حن حساب الدالت القطسيت ودالت الخىشيع القطسيت P(r) كدالت للوسافت r لودازاث ذزيت لرزة الهيدزوجين و قىزنج النخائج هع االيىناث الوشابهت لرزة الهيدزوجين ( 3+, (. e +, 2+ 52