QUANTUM NUMBERS (Principal, Azimuthal, Magnetic and Spin)

                 QUANTUM NUMBERS

 Orbitals represent regions in the space around the nucleus where the probability of finding the electron is maximum. A large number of electron orbitals are possible in atom. These can be distinguished by their size, shape and orientation of the orbitals.

To describe each electron in an atom in different orbitals, we need a set of three numbers known as quantum numbers. These are designated as n, l and m. In addition to these three numbers another quantum number is also needed which specifies the spin of the electron. These four numbers are called quantum numbers. These are discussed below:

1. Principal quantum number (n): This quantum number determines the main energy shell or level in which the electron is present. It is denoted by n. It can have whole number values starting from 1 such as n = 1, 2, 3, 4 ...

This quantum number also identifies as shell. The shell with n 1 is called the first shell. The shell with n 2 is called the second shell and so on. The various shells are also called K, L, M, N as:

The principal quantum number also help determine the average distance of the electron the nucleus. Of n = 1 (first shell), it is closest to the nucleus and has lowest energy. An the value increases, the distance of the electron from the nucleus increases and also the energy of the electron in that shell increases. Thus, principal quantum number given n age distance of the electron from the nucleus average of electron cloud or shell) and energy associated with it. 

2. Azimuthal quantum number (l): This quantum number determines the angular momentum subsidiary of the electron. This quantum number is also on as orbital angular momentum or quantum number.This is denoted by 1. The value of I gives subshell or sublevel in a given principal energy shell to which an electron belongs. It can have positive integer values ranging from zero to (n-1) where the principal quantum number. That is, l = 0, 1, 2, 3, (n -1). For example, for n = 1, I has only one value, 1. For n = 2, 1 has two values :l= 0, 1. For n = 3, 1 has three values :l = 0, 1, 2. Thus, for each value of n, there are n possible values of l. In other words, the number of subshells in a principal shell is equal to the value of n. The various subshells or values of I are also designated by letters s, p, d, f. 

The different subshells or sublevels are represented by first writing the value of n (1, 2, 3.) and then the letter designation for the value of I (s, p. d f). For example, an orbital with n 1 and /=0 in denoted as Is, an orbital with n 3,1=2 is denoted as . The e designations of subshells for n 1 to n = 4 are given below:

Except for hydrogen, the subshells within a given shell differ slightly in energy. The energy of a subshell increases with increasing value of 1. This means that within a given shell, the s-subshell (= 0) has lowest energy, p-subshell (I = 1) has next to lowest, followed by d, then f and so on. For example, in fourth energy shell, the energies of subshell increases as:

                   4s<4p<4d<4f

Thus, angular quantum number determines the subshell in a given principal energy shell. Angular momentum of the electron in an orbital The angular quantum number gives the energy of the electron due to the angular momentum of the electron.

3. Magnetic quantum number (m): This quantum number describes the behaviour of electron in a magnetic field. We know that the movement of electrical charge is always associated with magnetite field. Since the revolving electron possesses angular momentum, it will give rise to a very small magnets field which will interact with the external magnetic field of the earth. Under the influence of external magnetic field, the electrons in a given web shell themselves in certain preferred regions of spice around the nucleus. These are called orbitals. Thu, thin quantum number gives the number of orbitals in s given subshell. It is designated by m The allowed val of m, depends upon the value of For a given value , mean have values -- through Tool. That is m, =-1.0.. In other words, there are (211) valent each value of L. 

For example,If l = 0, m has only one value, L e, m =0 i.e., s subshell has only one orbital called s-orbital. If I = 1, m, may be-1.0, + 1. i.e., p-subshell contains three orbitals called p- orbitals. These are indicated by numerical surge P1 Or P or these are designated by alphabetical subscripts (p P, and p). Thus, there are three 2 orbitals, designated as 2p, 2p, and 2p.

It can be generalised that there are (221 orbitals (or m values) for each value of I(or subshell. By working out different combinations of these quantum numbers, it can be easily calculated that there is one orbital for n = 1 (1s), four for n = 2 (2s and the 2p), nine for = 3 (3s, three 3p, five 3d). Thus, magnetic quantum number determines the number of orbitals present in a given subshell.

4. Spin quantum number(m s): It is observed that the electron in an atom is not only revolving around the nucleus but is also spinning around its own axis. In 1925, George Uh len beck and Samuel Go u d smit proposed fourth quantum number known as electron spin quantum number. This quantum number describes the spin orientation of the electron. It is designated by m. Since the electron can spin in only two ways--clockwise or anti-clockwise and, therefore, the spin quantum number can take only two values: + or - y. This quantum number has a value independent of the values of the other three quantum numbers. Instead of giving number for m = + ½ or - ½ the two orientations are usually designated by arrows pointing up and down : 1 (spin up) or (spin down) respectively.

Thus, an electron momentum commonly called spin. The magnitude of spin angular momentum of an electron is given as : 

  Spin angular momentum = √s(s+1)h/2π 

Thus, the four quantum numbers describe the position of an electron in an atom by specifying its main shell (n), subshell (1), the orientation of the orbital (m,) and direction of its spin (m). In other words, these quantum numbers serve as an address for an electron.