Hydrogen quantum numbers

Schrodinger equation for many-electron atoms is not possible, the four hydrogen quantum numbers, and the basic orbital shapes they represent, retain their usefulness in describing the quantum state of the electrons in those atoms. Most importantly, the mathematical properties of these four quantum numbers form the basis for the buildup of the elements in the periodic table. 

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... 

It is interesting to note that this is the first time that in the present framework the quantization is formed by two quantum numbers a number n to be termed the principal quantum number and a number , to be termed the secondary quantum number. This case is reminiscent of the two quantum numbers that characterize the hydrogen atom. 

The hydrogen atom is a three-dimensional problem in which the attractive force of the nucleus has spherical symmetr7. Therefore, it is advantageous to set up and solve the problem in spherical polar coordinates r, 0, and three parts, one a function of r only, one a function of 0 only, and one a function of [Pg.171]

The period (or row) of the periodic table m which an element appears corresponds to the principal quantum number of the highest numbered occupied orbital (n = 1 m the case of hydrogen and helium) Hydrogen and helium are first row elements lithium in = 2) IS a second row element... 

Question. Calculate, to three significant figures, the wavelength of the first member of each of the series in the spectrum of atomic hydrogen with the quantum number (see Section f.2) n" = 90 and 166. In which region of the electromagnetic spectrum do these transitions appear ... 

Bohr s treatment gave spectacularly good agreement with the observed fact that a hydrogen atom is stable, and also with the values of the spectral lines. This theory gave a single quantum number, n. Bohr s treatment failed miserably when it came to predictions of the intensities of the observed spectral lines, and more to the point, the stability (or otherwise) of a many-electron system such as He. 

For reasons we will discuss later, a fourth quantum number is required to completely describe a specific electron in a multielectron atom. The fourth quantum number is given the symbol ms. Each electron in an atom has a set of four quantum numbers n, l, mi, and ms. We will now discuss the quantum numbers of electrons as they are used in atoms beyond hydrogen. 

The quantum number ms was introduced to make theory consistent with experiment. In that sense, it differs from the first three quantum numbers, which came from the solution to the Schrodinger wave equation for the hydrogen atom. This quantum number is not related to n, , or mi. It can have either of two possible values ... 

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... 

Soon after Bohr developed his initial configuration Arnold Sommerfeld in Munich realized the need to characterize the stationary states of the electron in the hydrogen atom by. means of a second quantum number—the so-called angular-momentum quantum number, Bohr immediately applied this discovery to many-electron atoms and in 1922 produced a set of more detailed electronic configurations. In turn, Sommerfeld went on to discover the third or inner, quantum number, thus enabling the British physicist Edmund Stoner to come up with an even more refined set of electronic configurations in 1924. 

Suppose we get a little more sophisticated about our question. The more advanced student might respond that the periodic table can be explained in terms of the relationship between the quantum numbers which themselves emerge from the solutions to the Schrodinger equation for the hydrogen atom.5... 

As many textbooks correctly report, the number of electrons that can be accommodated into any electron shell coincides with the range of values for the three quantum numbers that characterize the solutions to the Schrodinger equation for the hydrogen atom and the fourth quantum number as first postulated by Pauli. 

Secondly, due to the smallness of the rotational temperature for the majority of molecules (only hydrogen and some of its derivatives being out of consideration), under temperatures higher than, say, 100 K, we replace further on the corresponding summation over rotational quantum numbers by an integration. We also exploit the asymptotic expansion for the Clebsch-Gordan coefficients and 6j symbol [23] (JJ1J2, L > v,<0... 

FIGURE 1.28 The permitted energy levels of a hydrogen atom as calculated from Eq. 14. The levels are labeled with the quantum number n, which ranges from 1 (for the lowest state) to infinity (for the separated proton and electron). 

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