Hydrogen atom electronic state

It has been shown that, under appropriate conditions, the momentum distribution uj py for an individtial electronic state is directly meastired by electron-momentum spectroscopy (ref. 29). Figure 3.8 compares the experimental momentum distribution for the hydrogen atom ground state with the function calculated by the Fourier transform of the hydrogen Is orbital. In general, the electron-momentum spectroscopy results serve to evaluate wavefunctions at various levels of theory for a variety of atomic (and molecular) systems. 

The idea of electrons existing in definite energy states was fine, but another way had to be devised to describe the location of the electron about the nucleus. The solution to this problem produced the modern model of the atom, often called the quantum mechanical model. In this new model of the hydrogen atom, electrons do not travel in circular orbits but exist in orbitals with three-dimensional shapes that are inconsistent with circular paths. The modern model of the atom treats the electron not as a particle with a definite mass and velocity, but as a wave with the properties of waves. The mathematics of the quantum mechanical model are much more complex, but the results are a great improvement over the Bohr model and are in better agreement with what we know about nature. In the quantum mechanical model of the atom, the location of an electron about the nucleus is described in terms of probability, not paths, and these volumes where the probability of finding the electron is high are called orbitals. 

In 1913, Niels Bohr combined elements of quantum theory and classical physics in a treatment of the hydrogen atom. He stated two postulates for an electron in an atom ... 

For the hydrogen-atom ground state, find the probability of finding the electron farther than 2a from the nucleus. 

J0 For the hydrogen-atom ground state (a) find (V ) (b) use the results of (a) and Problem 6.29 to find (T) then find (j )/ V) (c) use (T) to calculate the root-mean-square speed of the electron then find the numerical value of where c is the speed of light... 

EXAMPLE Suppose that we measure of the electron in a hydrogen atom whose state at the time the measurement begins is the 2p state. Give the possible outcomes of the measurement and give the probability of each outcome. 

A FIGURE 6.12 Energy states in the hydrogen atom. Only states for / = 1 through / = 4 and n = oo are shown. Energy is released or absorbed when an electron moves from one energy state to another. 

Postulate 5. For the hydrogen atom Bohr assumed that the electron moved in circular orbits about, the nucleus under the influence of the Coulomb attraction. The allowed circular orbits were then determined simply by the requirement that the cingular momentum of the electron should be an integral multiple of fi. This restricts the energies of the hydrogen atom, in states of angular momentum nh, to the quantized values ... 

Two ground-state hydrogen atoms, for example, interact via the and f> 5 electronic states of H2. The... 

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