The allowed values and general meaning of each of the **four quantum number **of an electron numbers of an electron in an atom are as follows:

__ 1.Principal quantum number (n)__ :

*This quantum number is the one on which the*. The energy of an electron in an atom depends on n.The smaller the n is,lower the energy.

**energy of an electron**in an atom principally depends; it can have ant positive value :1,2,3 and so on **The size of an orbital also depends on n.**The larger the value of n is,the larger the orbital.Orbitals of the same quantum state n are said to belong to the same shell.Shells are sometimes designated by the following letters;

Letter K L M N...........

n 1 2 3 4..............

**2. Angular Momentum quantum number (l ) : ***It is also called Azimuthal quantum number. This quantum number distinguishes orbitals of the given n having different shapes *; ** it can have any integer value from 0 to n-1.**Within each shell of quantum number n,there are n different kinds of orbitals,each with a distinctive shape denoted by an l quantum number. For example: if an electron has a principal quantum number of 3,the possible values for l are 0,1,2.Thus,within the M shell where the electron is most likely to be found.

Although the energy of an orbital is principally determined by the n quantum number,**the enregy also depends somewhat on the l quantum numbers(except for H aotm).For a given n,the energy of an orbital increases with l.**

Orbitals of the same n but different l are said to belong to different subshells of a given shell.The different subshells are usually denoted by letters as follows:

letter s p d f g.......

l 0 1 2 3 4......

To denote a subshell within a perticular shell,we write the value of an quantum number for the shell followed by the letter designation for the subshell.For example,2p denoates a subshell with quantum numbers n = 2 and l=1.

**3.Magnetic quantum number (m _{s}**) :

*This quantum number refers to the two possible orientations of the spin axis of an electron; possible values are +1/2 and -1/2*.

Lets take a look with the help of an example how to use these rules for quantum numbers:

State whether each of the following sets of quantum numbers is permissible for an electron in an atim.If set is not permissible,explain?

(a) n =1 , l=1, m_{l}=0 ,m_{s} = +1/2

(b) n= 3 , l=1, m_{l}= -2 , m_{s} = -1/2

(c) n= 2, l= 1, m_{l}=0 ,m_{s} = +1/2

(d) n = 2,l=o , m_{l}=0 ,m_{s} = 1

**(a) Not permissible**: because the l quantum number is equal to n; it must be less than n , if n = 1 then l= o to n-1 so, 0 to 1-1 or simply 0

**(b)** **Not permissible**; the value of m_{l} even if we ignore its sign must not be greater than l as m_{l} = -l to +l so it must be either - 1 , 0, +1 but it can't be -2

**(c)Permissable: **n=2 , so l = 0 to n-1 which means 0 to 2-1 or 0 , 1 and l =1 which is correct . If l= 1 then m must ne -l to +l which means +1,0,-1 and m_{l}=0 which is also correct and m_{s} = +1/2 correct as well.

**(d) NOt permissable**: The m_{s} = 1 ,the ms quantum number can be only +1/2 or -1/2