Atomic orbits hydrogen atom quantum numbers

6 Atomic orbits hydrogen atom quantum numbers 

Now it is desirable to generalize the information that we have obtained following the analyses of the Schrodinger equation for the hydrogen atom and introducing the electron spin. We mean the systematization of the values characterizing an atom s state. Herewith 

A typical qnantnm mechanical object such as an atom possesses some classic characteristics that are unexplainable within the framework of generally accepted presentations (refer to Section 6.7) (no orbital motion, yet the existence of angular momentum no rotation of an electron around its own axis, yet intrinsic angular and magnetic moments, i.e., spin, etc.). As a result, these terms are used irrespective of their classical sense. 

Moreover, the Bohr model is a transition from the purely classical presentations to the quantum mechanical ones the motion of electrons along the orbits is accepted, but not all orbits are permitted the angular momentum is accepted though its values, and orientations are the subject of strict limitation. It is possible to consider the Bohr model as a transition from the classical mechanics to quantum, with the preservation of many of its attributes. As a result, many of Bohr model notions will often be met in order to simplify the students understanding. 

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The relationship between orbital size and quantum number for the hydrogen atom. 

The state of a spinless hydrogen atom is completely specified by the principal quantum number n, the orbital angular momentum quantum number and the magnetic (projection) quantum number m. The Schrodinger equation is... 

It turns out that there is not one specific solution to the Schrodinger equation but many. This is good news because the electron in a hydrogen atom can indeed have a number of different energies. It turns out that each wave function can be defined by three quantum numbers (there is also a fourth quantum number but this is not needed to define the wave function). We have already met the principal quantum number, n. The other two are called the orbital angular momentum quantum number (sometimes called the azimuthal quantum number), , and the magnetic quantum number, mi. 

As you have seen, the Schrodinger equation may be written in spherical polar coordinates using the usual transformation. As a result, we can write a radial part and an angular part for the wavefunction ik. As an example, let s look at the wavefunction for the Is and 2pz orbitals in the hydrogen atom. These orbitals have the quantum numbers n = 1, l = 0, mg = 0 and n = 2, = 1, mg = 0, respectively. 

The atom of hydrogen, of atomic number Z = i, in its ground state has a single electron in the K shell of principal quantum number n — i the atom of helium (Z = z) has two electrons in this orbit. This, however, is the maximum number of electrons that can be accommodated in the first shell, for it is an essential feature of the Bohr theory that an orbit of principal quantum number n can accept not more than 2tz2 electrons. Thus the maximum permissible number of electrons in each shell is as follows ... 

A wavefunction, ip, is a solution to the Schrodinger equation. For atoms, wavefunctions describe the energy and probabihty of location of the electrons in any region around the proton nucleus. The simplest wavefunctions are found for the hydrogen atom. Each of the solutions contains three integer terms called quantum numbers. They are n, the principal quantum number, I, the orbital angular momentum quantum number and mi, the magnetic quantum number. These simplest wavefunctions do not include the electron spin quantum number, m, which is introduced in more complete descriptions of atoms. Quantum numbers define the state of a system. More complex wavefunctions arise when many-electron atoms or molecules are considered. 

Four quantum numbers characterize the electron wave-function (atomic orbital) in a hydrogen atom The principal quantum number n identifies the main energy level, or shell, of the orbital the angular momentum quantum number I indicates the shape of the orbital the magnetic quantum number OT specifies the orientation of the orbital in space and the electron spin quantum... 

When an electron makes a transition between energy levels of a hydrogen atom by absorbing or emitting a photon, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum quantum number Z. 

The allowed wave functions of tiie hydrogen atom are called orbitals. An orbital is described by a combination of an integer and a letter, corresponding to values of three quantum numbers for the orbital. The principal quantum number, n, is indicated by tiie integers 1,2,3, This quan-... 

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... 

Quantitative analysis, infrared, 250 Quantitative presentation of data, 14 Quantum mechanics, 259, 260 and the hydrogen atom, 259 Quantum number, 260 and hydrogen atom, 260 and orbitals, 261 principal, 260... 

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