Quantum numbers: explain all four quantum numbers of an electron

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 energy of an electron in an atom principally depends; it can have ant positive value :1,2,3 and so on. The energy of an electron in an atom depends on n.The smaller the n is,lower the energy.

        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 (ms) : 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, ml=0 ,ms = +1/2  

(b)  n= 3 , l=1, ml= -2  , ms = -1/2   

(c) n= 2, l= 1, ml=0 ,ms = +1/2  

(d) n = 2,l=o , ml=0 ,ms = 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 ml even if we ignore its sign must not be greater than l as ml = -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  ml=0 which is also correct and  ms = +1/2  correct as well.

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

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