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.
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.
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.
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.
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.
Deuterium is one of the isotopes of the hydrogen atom, which consists of 1 proton, 1 neutron, and 1 electron, also called a hydrogenic atom. The position of electrons in the atom cannot be determined with certainty because it is probabilistic. The probability of finding a deuterium atom electron in momentum space at quantum number n ≤ 3. This research aims to find the probability value of deuterium atomic electrons in momentum space at n ≤ 3. This research uses the mathematical theory study method through several stages, namely collecting the latest and relevant literature sources, making a simulation program, and then validating the simulation program with existing theory. If it has been validated, continue taking data that will be analyzed and then discussed in the results and discussion stage, and the last step is drawing conclusions. The results of this study show that the probability value for finding atomic electrons in momentum space will be more excellent with increasing integration limit values and the value of the principal quantum number (n).
The aim is the expected value of helium ions to determine its properties as a heat transmitter to reactors and chirogenic science. This research is non-experimental research using quantum mechanics literature study methods because there are many previous studies that are relevant to this research. Data on the expected value of electron momentum in helium ions is determined based on numerical calculations using the Matlab 2015a program to simplify calculations using ion expectation calculations in momentum. The results obtained are that the electron momentum value in the helium ion can provide an overview of the average momentum value of the helium ion electrons in momentum space. This research data also shows that in momentum space the expected value of electron momentum decreases as the principal quantum number (n) increases. This can be seen when n=1,l =0 then 3p0 = 1.3146, and when n=3,l =0 then 3p0 = 0.5098.