Quantum numbers: explain all four quantum numbers of an electron


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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