Hydrogen atom atomic orbitals

Symmetry Boron atomic orbitals Hydrogen atomic orbitals Molecular orbitals... 

Atomic orbits hydrogen atom quantum numbers... 

So far we have described only the lowest-energy wave function in the hydrogen atom, the Is orbital. Hydrogen has many other orbitals, which are described in the next section. 

So far we have described only the lowest-energy wave function in the hydrogen atom, the li orbital. Hydrogen has many other orbitals, which we will describe in the next section. However, before we proceed, we should summarize what we have said about the meaning of an atomic orbital. An orbital is difficult to define precisely at an introductory level. Technically, an orbital is a wave function. However, it is usually most helpful to picture an orbital as a three-dimensional electron density map. That is, an electron in a particular atomic orbital is assumed to exhibit the electron probability indicated by the orbital map. 

The use of Cartesian Gaussian-type orbitals (GTOs) in ab initio work may come as a surprise to anyone who recalls the functional form of the hydrogen atom orbitals, hydrogen exp( - Ir). Cartesian GTO s have the form ... 

The carbon atom has a share in eight electrons (Ne structure) whilst each hydrogen atom has a share in two electrons (He structure). This is a gross simplification of covalent bonding, since the actual electrons are present in molecular orbitals which occupy the whole space around the five atoms of the molecule. 

Despite its success in reproducing the hydrogen atom spectmm, the Bolir model of the atom rapidly encountered difficulties. Advances in the resolution obtained in spectroscopic experiments had shown that the spectral features of the hydrogen atom are actually composed of several closely spaced lines these are not accounted for by quantum jumps between Bolir s allowed orbits. However, by modifying the Bolir model to... 

The simplest case arises when the electronic motion can be considered in temis of just one electron for example, in hydrogen or alkali metal atoms. That electron will have various values of orbital angular momentum described by a quantum number /. It also has a spin angular momentum described by a spin quantum number s of d, and a total angular momentum which is the vector sum of orbital and spin parts with... 

The simplest system exliibiting a nuclear hyperfme interaction is the hydrogen atom with a coupling constant of 1420 MHz. If different isotopes of the same element exhibit hyperfme couplings, their ratio is detemiined by the ratio of the nuclear g-values. Small deviations from this ratio may occur for the Femii contact interaction, since the electron spin probes the inner stmcture of the nucleus if it is in an s orbital. However, this so-called hyperfme anomaly is usually smaller than 1 %. 

Now we can calculate the ground-state energy of H2. Here, we only use one basis function, the Is atomic orbital of hydrogen. By symmetry consideration, we know that the wave function of the H2 ground state is... 

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