Lithium ions (3) is a particle that has a single electron and is formed because lithium metal loses 2 of its 3 valence electrons. Probability is the square modulus of a wave function. Electron probability is a description of the discovery of electrons in space. This study aims to determine the probability value of electron momentum of Lithium ion (3). This type of research is non-experimental research in the form of developing existing theories with theoretical research methods. When viewed from the main orbital quantum value, the greater the probability value or the easier the electron is found at a larger quantum number. When viewed from the level of the probability interval, the greater the probability interval, the greater the main quantum value. In accordance with the theory which states that the large main quantum number n and orbital quantum l result in the probability value of Lithium ions getting bigger.
Lithium ions (3) is a particle that has a single electron and is formed because lithium metal loses 2 of its 3 valence electrons. Probability is the square modulus of a wave function. Electron probability is a description of the discovery of electrons in space. This study aims to determine the probability value of electron momentum of Lithium ion (3). This type of research is non-experimental research in the form of developing existing theories with theoretical research methods. When viewed from the main orbital quantum value, the greater the probability value or the easier the electron is found at a larger quantum number. When viewed from the level of the probability interval, the greater the probability interval, the greater the main quantum value. In accordance with the theory which states that the large main quantum number n and orbital quantum l result in the probability value of Lithium ions getting bigger.
Information on electron behavior in a hydrogen atom, such as electron expectation, electron probability, electron position, electron energy spectrum, etc. can be obtained through Schrodinger equation.ions are atoms that lose so that they become hydrogenic atoms. This research aims to determine the expectation value of electron momentum of ion in momentum space at the main quantum number using Schrodinger equation approach. The method used in this research is literature study with non-experimental research type. The results obtained expectation value depends on the interval and the value of the quantum number. The larger the interval, the expectation value of electron momentum increases. While the greater the value of quantum numbers, the expectation value of electron momentum is getting smaller. Based on the analysis, the expectation value of electron momentum is quite varied from to . From this research, it is found that the expectation value of electron momentum is the same as the expectation value of electron position.
Ions resulting from the ionization of helium atoms are known as helium ions. Atom of Helium The probability distribution of the particle locations and velocities inside a helium atom is referred to as probability. Using theoretical study methods, the goal of this research is to find the probability of an electron's position in a helium atom at the quantum number 3 ≤ n ≤ 4. This type of research is non-experimental research by developing previously existing theories. This type of research is non-experimental research by transforming the radial wave function of hydrogenic atoms in position space into a radial wave function in momentum space using the Fourier transformation, then including a number of Gegenbauer functions and using the probability equation of finding an electron in a Helium ion in momentum space. The results of this research provide information regarding the position and probability of the existence of electrons in the helium atom. The probability value for the Helium ion is obtained using the equation P(p) = which is used to indicate the probability of finding an electron in a helium atom is directly proportional to the principal quantum number (n) and the value of the electron's momentum. The larger the electron momentum interval, the greater the probability.
Lithium ion (3Li2+) is a light alkali metal which is reactive and flammable when exposed to water or air. Lithium becomes ionic when lithium metal loses two of its three valence electrons. The wave function is a complex quantity that shows the characteristics of the de Broglie wave. The wave function in question is the radial wave function in the particle, because to find the probability that the electron is in the particle, only the radial part of the wave function is needed. However, there is no literature that discusses the wave function in the momentum space in the case of hydrogenic ions. Therefore, this research will examine the wave function of Lithium ion (3Li2+) in the momentum space. This type of research in the preparation of this article uses non-experimental research. Based on the results of the research that has been done, the wave function of Lithium ion (3 Li2+) in the momentum space at n 3 is obtained. The wave function consists of a radial, angular (polar and azimuth) wave function, as well as the wave function of Lithium ion (3Li2+) as a whole. The fundamental difference between the wave function of Lithium ion (3Li2+) in the momentum space and the wave function of hydrogenic atoms in the other momentum space is the value of the radial function caused by the difference in the value of (z) or atomic number.
The purpose of this study is to determine the electron’s position expectation values and energy spectrum on the Li2+ ion on the principal quantum number n≤3. This research using literature study methods on quantum mechanics. The expectation values of the electron position and the energy spectrum of the Li2+ ion uses numerical calculations using the Matlab 2019a program. The steps in this research method include: preparation; theory development; simulation; validation of the results of theory development; results of theory development; discussion and conclusion. The results obtained in this study are the electron’s position expectation values and energy of the Lithium ion. The electron’s position expectation values indicates the presence of electrons that often appear around the x-axis by relying on the interval used. The larger the interval, the more constant the electron’s position expectation values will be and towards an almost constant value. From the analysis results, the expectation value varies in positions from 0,0001a0 to 0,1637a0. The electron energy spectrum of the Li2+ ion is inversely proportional to the square of the principal quantum number (n),E1= -122,4 eV ; E2= -30,6 eV ; E3= -13,6 eV
This study aims to find the uncertainty value of Helium Ion Momentum (𝐻𝑒+) by using the Heisenberg Uncertainty Approach to Quantum Numbers 𝑛 ≤ 3. This type of research uses non-experimental research. The research was conducted by developing previously existing theories. This research is to calculate the expectation value of the position to find out how often electrons can appear, and determine the uncertainty of the momentum of Helium Ion (𝐻𝑒+) by using the Heisenberg uncertainty approach at number 𝑛 ≤ 3. Based on the results and discussion, it can be concluded that the uncertainty of helium ion momentum (𝐻𝑒+) by using the Heisenberg uncertainty approach to quantum numbers 𝑛 ≤ 3. The uncertainty of helium ion momentum is influenced by the main quantum number (n) and the azimuthal quantum number (l). By entering the values of n and l, the results can be obtained at quantum numbers 𝑛 = 1 with 𝑙 = 0 obtained ∆𝑃𝑟 = 2,977504663 × 10−24. At the quantum number 𝑛 = 2 with 𝑙 = 0 obtained ∆𝑃𝑟 = 8,06312759 × 10−24 and 𝑙 = 1 obtained ∆𝑃𝑟 = 2,03048 × 10−23. At the quantum number 𝑛 = 3 with 𝑙 = 0 obtained ∆𝑃𝑟 = 1,50366086 × 10−23, and 𝑙 = 1 obtained ∆𝑃𝑟 = 3,481407588 × 10−23 and 𝑙 = 2 obtained ∆𝑃𝑟 = 4,47363642 × 10−22. Based on these results, it can be concluded that the uncertainty value of momentum is getting bigger as the two values of n and l increase. This is also proven by using simulation and the results of momentum uncertainty are not much different and only a difference of a few decimal places.
The positive helium ion consists of two protons and one orbital electron to be viewed as a hydrogenic atom. The use of ions has very potential, especially in the development of spintronic devices and plasma-based sterilization. This study aims to determine the expected value and position uncertainty of He^+ ion electrons. Determination of the expected value and position uncertainty is done by analytical calculation through the Schrodinger method approach, especially the radial part at quantum number n≤4, and numerical calculation with the help of a simulation program. The results showed that the main quantum number and orbital n, l influence the expectation value and position uncertainty. The greater the main quantum number n, the expectation value of electron position decreases and the uncertainty of electron position increases. At the same time, the increase in the orbital quantum number l has an impact on the value, which tends to go down. This research is in accordance with de Broglie's hypothesis about the nature of dualism and the principle of uncertainty in the review of position space.