![]() Where the first term is by the Coulomb force between the nucleus and the electron 1, and the second term is by the force between the two electrons.Ĭonsidering the lithium nuclear mass (nucleus), we use here the reduced mass (rm =1/2 × (2me × nucleus)/(2me + nucleus) = 9.10794 × 10 -31 kg) except when the center of mass is at the origin. So the x component of the acceleration (m/sec 2) of the electron 1 is, Change MM to meter as follows x (m) = xx × 10 -14. When the electron 1 is at (xx, yy, 0), the electron 2 is at (-xx, 0, yy) (in MM). And at intervals of 1 SS we compute the Coulomb force among the two electrons and the nucleus. From the inputted value, we calculate the initial velocity of the electron. In this program, we first input the initial x-coordinate r1 (in MM) of the electron 1, and the absolute value of the total energy E (in eV) of the Li+. The electron 1 initially at (r1, 0, 0) moves one quarter of its orbital to (0, r2, 0), while the electron 2 initially at (-r1, 0, 0) moves to (0, 0, r2). The computer program (class filename: MathMethod) written in the JAVA language (version 1.5.0) to compute the electron orbit of the Li+ is shown in the link below. Here we investigate how the electrons of the Li+ are moving by calculating the Coulomb force among the two electrons and the nucleus (3e+) at short time intervals. In this model, the electron 1 moves on the X-Y plane, the electron 2 moves on the X-Z plane.Įlectron 1 starts at (r1, 0, 0), while electron 2 starts at (-r1, 0, 0). How about this two-electron lithium ion (Li+) ?įig. in which two same-shaped orbital planes are perpendicular to each other.Īs shown in the top page, we have succeeded in computing the two electron atom, helium ground state energy correctly using this model. So here we suppose another model as shown in Fig. 1., the two electrons are just at the opposite positions, so the wave phases of them may interfere with each other and vanish. If the two electrons can be in one small orbit of one de Broglie's wavelength, this means that the ground state electron of the Bohr hydrogen-like model can come closer to the nucleus than the original orbit.Īnd in the orbit of Fig. This value is lower than the experimental value -198.09 eV. Solving the above three equations, the ground state energy (n=1) becomes -205.79 eV. The total energy E of the lithium ion (Li+) is the sum of the kinetic and the Coulomb potential energy of the two electrons, so Where h is Plank's constant (= 6.62606896 x 10 -34 Js), and h/mv is the de Broglie's wavelength. ![]() The circular orbital length is supposed to be an integer times the wavelength of the electron, we have Where r is the circular orbital radius (meter), m is the electron mass (me= 9.1093826 x 10 -31 kg), e is the electron charge (= 1.60217653 × 10 -19 C), and ε is the permittivity of vacuum (= 8.854187817 × 10 -12 C 2/Nm 2). One schematic model of lithum ion (Li+)Įquating the centrifugal force to the Coulomb force, we have 1.) in which two electrons of the lithium ion are on the opposite sides of the nucleus and moving on the same circular orbit.įig. ![]() Lithium ion (Li+) has two electrons and one nucleus (3e+).įirst, suppose we have one model (Fig. So the ground state energy of the lithium ion (Li+) is -75.64 - 122.45 = -198.09 eV. The ionization energies of the lithium is 5.39 eV (1st), 75.64 eV (2nd), and 122.45 eV (3rd), respectively. Naturally occurring lithium is composed of two stable isotopes, Li6 and Li7, the latter being the more abundant (92.5%). because of this, it is a good conductor of both heat and electricity, and used for the lithium (ion) batteries. Lithium has a single valence electron ( its configuration, 1S × 2, 2S × 1 ) that is easily given up to form a cation. It is the lightest metal, and highly reactive and flammable (though more stable than the other alkali metals). ![]() Lithium belongs to the alkali metal group of chemical elements, and has the atomic number 3. So next, we try Lithium atom (Li) and Lithium ion (Li+) by Bohr's theory. Our new Bohr model has suceeded in calculating the Helium ionization energy more correctly than the quantum mechanical variational methods as shown in the Top page. Top page (correct Bohr model including the two-electron atoms). Bohr's Lithium(ion) Li(+) New Bohr model Lithium (Li) ![]()
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