Quantum Mechanics needs of three quantum numbers to describe the distribution of electrons and another atoms. This numbers are the result of the solution of the Schrodingers equations for the hydrogen atom. There are:
The Principal Quantum Number (n):
Can takes entires values such as 1, 2, 3, etc.. It is an integer that determines the overall size and energy of an orbital. As the value of n increases, the number of allowed orbitals increases and the size of those orbitals becomes larger. Thereby, the electron can be farther from de nucleus.
The angular-momentum quantum number (l):
This quantum number expresses the three-dimensional shape of the orbital. The values of l depends of the value of n. It can have any integral value from 0 to n - 1. For example:
If n = 1, then l = 0 If n = 2, then l = 0 or 1 If n = 3, l can have 3 values: 0, 1 and 2 . . . and so forth.
The value of l designed to an orbital is represented by letters such as: s, p, d and f. (Historically, the letters s, p, d, and f arose from the use of the wordssharp, principal, diffuse, and fundamental to describe various lines in atomic spectra.) After f, successive subshells are designated alphabetically: g, h, and so on. So:
Quantum number l: 0 1 2 3 4 … Subshell notation: s p d f g …
The set of orbitals with the same value of n and l are known as subshells. For example, the level with n = 2 is formed of two subshells, l = 0 or 1. So, the correspond to the subshells 2s and 2p, where 2 press the value of n, y s y p related with the values of l.
The magnetic quantum number (ml):
This quantum number describes the spatial orientation of the orbital with respect to a stander set of coordinate axes. Inside the subshell, the value of ml depends of the value of the angular-momentum quantum number. Thus, it can have any integral value from -l to +l. A summary of the allowed combinations of quantum numbers for the first four shells is given in Table 5.2.
Spin Quantum Number (ms):
Different experiments done about the emissions of the spectrum of sodium and hydrogen said that the emission spectrum can be separated when applying a magnetic extreme field. Physicists could only explain the results supposing electrons have a behaviour such as littles magnets. If we imagine that some electrons are spinning in its own axis, as the Earth, is easier to explain its magnetic properties. According to the electromagnetic theory, when a charge is spinning it generates a magnetic field, and this movement is the responsable for the electron behaves like a magnet. The spin quantum number specifies the orientation of the spin of the electron. All electrons have the same amount of spin. A spin can have a value of + 1/2, it is usually represented by an up arrow, and a spin of -1/2 is represented by a down arrow. Note that the value of ms is independent of the other three quantum numbers, unlike the values of n, l, and ml, which are interrelated.
In general...
Notice the following:
The number of sublevels in any level is equal to n, the principal quantum number. Therefore, then n = 1 level has one sublevel, the n = 2 has two sublevels, etc.
The number of orbitals in any sublevel is equal to 2l+1. Therefore, the s sublevel (l = 0) has one orbital, the p sublevel (l = 1) has three orbitals, the d sublevel (l = 2) has five orbitals, etc.
The number of orbitals in a level is equal to n2. Therefore, the n = 1 level has one orbital, the n = 2 level has four orbitals, the n = 3 has nine orbitals, etc.