A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron. These atoms are isoelectronic with hydrogen.

In the hydrogen atom, in which the nucleus is just a proton, the ratio M / m is about 1836, so that μ = 0.99946m. For heavier hydrogen-like atoms it is closer to m. Notice that the radius depends on n2, so that, for example, the radius of the n = 2 orbit is four times that of the n = 1 orbit.

2017年7月22日 · Hydrogen-like ions are ions that possess only one electron, just like a hydrogen atom. The fact that these ions have only one ion in the outermost shell makes it simpler to analyze their radii and energies, as a simple electrostatic model can be used to describe them.

A hydrogen-like atom is an atom with one electron. Except for the hydrogen atom itself (which is neutral) these atoms carry the positive charge e (Z-1), where Z is the atomic number of the atom.

In the special case of $ Z = 1 $, when the nucleus is a proton, the hydrogen-like atom is an ordinary hydrogen atom. Meso-atoms (a $ \mu $- meson in the Coulomb field of a nucleus) and positronia (a system consisting of an electron and a positron) may also be considered as hydrogen-like atoms.

Schrödinger’s equation can be solved exactly for hydrogen-like atoms, using the reduced mass concept to simplify the two-body problem to an effective one-body problem. This greatly expands the number of chemical systems that can be treated analytically by …

In physics and chemistry, a hydrogen-like atom (or hydrogenic atom) is an atom with one electron. Except for the hydrogen atom itself (which is neutral) these atoms carry positive charge e(Z-1) , where Z is the atomic number of the atom and e is the elementary charge .

In physics and chemistry, a hydrogen-like atom (or hydrogenic atom) is an atom with one electron. Except for the hydrogen atom itself (which is neutral) these atoms carry positive charge e(Z-1) , where Z is the atomic number of the atom and e is the elementary charge .

A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron. These atoms are isoelectronic with hydrogen. Examples of hydrogen-like atoms include, but are not limited to, hydrogen itself, all alkali metals such as Rb and Cs, singly ionized alkaline earth metals such as Ca+ and Sr+ and other ions such as He+, Li2 ...

2023年12月19日 · Hydrogen-like atoms (or hydrogenic atoms) are atoms with one single electron. Note: The above text is excerpted from the Wikipedia article "Hydrogen-like atom", which has been released...

hydrogen atom or a hydrogen like atom (He+, Li2+, Be+3, etc.) consists of an atomic nucleus of charge Ze and an electron of charge e. Their mutual interaction is given by the Coulomb potential. where r1 = r1(x1; y1; z1) and r2 = r2(x2; y2; z2) are the …

A hydrogen-like atom/ion (usually called a "hydrogenic atom") is any atomic nucleus bound to one electron and thus is isoelectronic with hydrogen. These atoms or ions can carry the positive charge e ( Z − 1), where Z is the atomic number of the atom.

2023年5月11日 · Here we focus on single-electron (hydrogen-like) atoms. The dominance of the Coulomb central potential between the electron and nucleus, translates into a simple Schrödinger equation for their relative position distribution.

2014年7月24日 · A hydrogen-like or hydrogenic atom is a two-body system where the particles are bound by an electrostatic interaction. Examples of such systems include the hydrogen atom, singly ionized helium, and positronium.

Hydrogen-like atom-II Study Goal of This Lecture Energy levels Atomic orbitals 14.1 Recall Recall for hydrogen-like atoms, the Hamiltonian is H^ = ~2 2m e (@2 @x2 + @2 @y2 + @2 @z2) Ze2 4ˇ p x2 + y2 + z2: (14.1) The Schr odinger equation: H ^ = E ; (14.2) can be solved in the spherical coordinates to yield Make sure you under-stand why R(r ...

Such a system is called a hydrogenic or hydrogen-like atom, with atomic number Z. One may view the nucleus as consisting of Ζ protons. For Ζ = 1 we obtain the hydrogen atom. For Ζ = 2, for example, the system is singly ionized helium He +; this is helium with its two protons as usual, but stripped of one of its two electrons.

Hydrogen (1 H) has three naturally occurring isotopes: 1 H, 2 H, and 3 H. 1 H and 2 H are stable, while 3 H has a half-life of 12.32(2) years. [3] [nb 1] Heavier isotopes also exist; all are synthetic and have a half-life of less than 1 zeptosecond (10 −21 s).[4] [5] Of these, 5 H is the least stable, while 7 H is the most.Hydrogen is the only element whose isotopes have different names that ...

2023年1月24日 · Niels Bohr suggested a new atom model in \(1913\) that described some of these phenomena as well as the hydrogen emission spectrum. Bohr’s hypothesis was founded on certain postulates and was based on Planck’s quantum theory. Bohr was able to determine the energy of electrons for hydrogen and hydrogen-like ions.

2011年1月1日 · The hydrogen-like atom consists of an electron of mass m e in position r e, which exhibits the elementary negative charge −e, moving around the positively charged nucleus +Ze of mass M n in position R n. It represents one of the very few prototype systems, the stationary states of which can be determined analytically by solving the associated ...

2023年10月4日 · In a hydrogen atom, an electron is moving in a spherically-symmetric Coulomb potential field produced by a proton. This topic provides us with a good opportunity to study various special functions. The related Schrödinger equation can be separated into an angular part and a radial part.

The hydrogen atom consists of a proton and an electron bound together by the Coulomb force. This system is particularly important because: It is the simplest atomic system and can be solved analytically; More complex atoms can be understood as perturbations of the hydrogen atom; It demonstrates key quantum mechanical concepts like quantization ...

2022年6月9日 · A long-distance effective theory of hydrogen-like atoms, dubbed the relativistic Ritz approach was recently introduced and some its theoretical consequences were explored. In this article, the...

1 天前 · Direct enantioselective decarboxylative transformations of carboxylic acids have become powerful tools for constructing structurally and functionally diverse molecules. Herein, an unprecedented organocatalyzed protocol for enantioconvergent decarboxylative reduction was established by leveraging dual catalysis of photoredox-mediated radical generation and a thiol …

According to the above DFT calculations, we try to simulate the Raman peaks of the G5-7 ring with a hydrogen atom adsorbed on the #1 site (shorted as H-G5-7). The simulated peaks match well with the experimental peaks (SI Appendix, Fig. S24 and Table S1). These results further confirm the formation of G5-7 rings with the #1 site as the accurate ...