Quantum number, azimuthal magnetic

Which of the following is NOT a possible set of quantum number values for the nitrogen atom, in the order of principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number ... 

The bound states (where < 0) are characterized by the three quantum numbers n (the principal quantum number), I (the azimuthal quantum number) and mi (the magnetic quantum number). 

Figure 10.5 Energy levels of atomic orbitals, n is the principal quantum number, and the 5, p, d notation indicates the azimuthal quantum number (/). For / = 1 and above the orbital is split into multiple suborbitals (indicated by the number of lines), corresponding to the values of the magnetic quantum number m Each of these lines can hold two electrons (corresponding to spin up and spin down ), giving rise to the rules for filling up the orbitals.

Three quantum numbers had been proposed, based on spectral lines and inferences about electron energy levels a principal quantum number to specify energy level of the atom an azimuthal quantum number to specify the angular momentum of electrons moving elliptically and an inner or magnetic quantum number to express the orientation of the plane of the electron s orbit in a magnetic field. 20... 

According to quantum mechanics, electrons in atoms occupy the allowed energy levels of atomic orbitals that are described by four quantum numbers the principal, the azimuthal, the magnetic, and the spin quantum numbers. The orbitals are usually expressed by the principal quantum numbers 1, 2, 3, —increasing from the lowest level, and the azimuthal quantum numbers conventionally eiqiressed by s (sharp), p (principal), d (diffuse), f (fundamental), — in order. For instance, the atom of oxygen with 8 electrons is described by (Is) (2s) (2p), where the superscript indicates the munber of electrons occupying the orbitals, as shown in Fig. 2-1. 

The wave functions for a state of a hydrogenlike atom described by the quantum numbers n (total quantum number), l (azimuthal quantum number), and m (magnetic quantum number) are usually expressed in terms of the polar coordinates r, 8, and . The orbital wave function is a product of three functions, each depending on one of the coordinates ... 

The only quantum number that flows naturally from the Bohr approach is the principal quantum number, n the azimuthal quantum number Z (a modified k), the spin quantum number ms and the magnetic quantum number mm are all ad hoc, improvised to meet an experimental reality. Why should electrons move in elliptical orbits that depend on the principal quantum number n Why should electrons spin, with only two values for this spin Why should the orbital plane of the electron take up with respect to an external magnetic field only certain orientations, which depend on the azimuthal quantum number All four quantum numbers should follow naturally from a satisfying theory of the behaviour of electrons in atoms. 

The integers l and mi are called azimuthal (or angular momentum) and magnetic quantum numbers, respectively. 

The principal quantum number is restricted to be a positive integer, n = 1,2,3,. The azimuthal quantum number l is restricted to the integer values l < n. The magnetic quantum number has 21 + 1 allowed values for each l, such that These numbers quantify the eigenvalues of the... 

The principal and azimuthal quantum numbers are directly defined as n and l respectively. The 21+1 multiplicity of sub-levels defines the allowed values of the magnetic quantum number mi, on assuming the Bohr condition ... 

Solution of these equations leads naturally to the principal quantum number n and to two more quantum numbers, / and m The total energy of the electron is determined by n, and its orbital angular momentum by the azimuthal quantum number l. The value of the total angular momentum is /(/ + ) 2h. The angular momentum vector can be oriented in space in only certain allowed directions with respect to that of an applied magnetic field, such that the components along the field direction are multiples of fi the multiplying factors are the mi quantum... 

The spectral term is a symbol which combines the azimuthal quantum number I and magnetic quantum number m to describe the energy level relationship between electronic configurations. 

It is very relevant at this point to note the important work of Bender et al. [25] on the H atom in a uniform magnetic field. These authors derived a semiclassical expansion for the ground-state energy in powers of (21 m -i- 2)", where m is the azimuthal quantum number. 

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. 

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