What do you understand by the term quantum number?,

Quantum Number and Atomic Orbital’s :-

Each electron in an atom is described by four different Quantum Number, three of which (n, l, m,) Specify the wave function that gives the probability of finding the electron at various point in space. The fourth quantum number gives idea about the spinning motion of an electron . A wave function for an electron in an atomic in called an Atomic Orbital. Quantum number are defined as a set of four number with the help of which one can get complete information about all the electrons in an atom like the type of location , energy the kids of orbital occupied, shape and orientation of that orbital etc.

1.Principal Quantum Number (n):-

  

It tell us about the shell in which the electron resides and is denoted by the letter ‘n’. It can have any positive value 1,2,3 and so on . So, n=1 signifies that electron in the first orbit. The principal quantum number gives the following information;

1.      It gives the average distance of the electron from the nucleus.

2.     It determines the energy of the electron in hydrogen atom and hydrogen like species.

3.     The maximum number of electron present in any principal shell in gives by 2n^2,   here n is the orbit number or principal quantum number.

Shell                                                         K   L   M   N

Principal quantum number(n)        1   2     3    4 

Maximum number of electrons     2   8   18   32

Apart from this, the angular momentum of an electric in an orbit can be calculated using the formula, mvr= nh/2π , here too n the principal quantum number.

2. Azimuthal or Angular Momentum Quantum Number (I) :-

Azimuthal  Quantum Number mainly deal with the shape of a subshell unlike the principal quantum  number which deal with size of an orbit. It represents the number of subshell present in the main shell and in denoted by ‘l’. It can have any value ranging from 0 to -1. So, it quit obvious that value of l are n dependent. It means that if the value of n is 3 then l=0,1,2. This quantum number gives the following information;

1.      The number of subshells present in the main shell.

2.     The shape of the subshells.

3.     The orbital angular momentum of the electrons in any subshell, L = (l (l+1) )^1/2h/2π  (For a particular value of n)

If the value of l = 0. It refer to s-subshell, l = 1, it refer to p-subshell. Similarly, l = 2 refer to d-subshell and l = 3 refer to f-subshell etc.

3. Magnetic Quantum Number (m) :-   

Magnetic Quantum Number primarily deal with orientation of an orbit in three dimensional space. Orientation refer to the position of lobes of the orbital’s along different axes.

For example, in case of p-subshell or sub orbit, the three orbital’s are designated as p_x p_y and p_z  depending upon the orientation of lobes or the maximum density of electron along the x, y, z, axis, respectively. 

4.Spin Quantum Number (s) :- 

An electron in an atom not only revolves around the nucleus but also spin about its own axis. It is very similar to earth which not only revolves around the Sun but also spin about its own axis. Since an electron can spin either in clockwise direction or in anticlockwise direction, Spin Quantum Number can acquire two values +1/2 and -1/2 and these are represent by two arrow pointing in the opposite directions i.e , # and $.

When an electron occupies a vacant orbital, it can have a clockwise or anticlockwise spin i.e +1/2 or -1/2.

The following table gives the various permissible values of different quantum numbers.