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Allowed values for the quantum numbers of electrons are as follows:

Allowed values for the quantum numbers of electrons are as follows:

Allowed values for the quantum numbers of electrons are as follows:

n = 1, 2, 3, . . .

l = 0, 1, 2, 3, . . . , n − 1

ml = 0, ±1, ±2, ±3, . . . ,±l

ms = ±12

The relationships between n and the shell designations are noted in Table .

The Number of Available Electron States in Some of the Electron Shells and Subshells

Principal      

Number of Electrons

Quantum Shell   Number of    
Number n Designation Subshells States Per Subshell Per Shell
1 K s 1 2 2
2 S s 1 2 8
    p 3 6  
    s 1 2  
3 M p 3 6 18
    d 5 10  
    s 1 2  
4 N p 3 6 32
    d 5 10  
    f 7 14  

Relative to the subshells,

l = 0 corresponds to an s subshell

l = 1 corresponds to a p subshell

l = 2 corresponds to a d subshell

l = 3 corresponds to an f subshell

For the K shell, the four quantum numbers for each of the two electrons in the 1s state, in the order of nlmlms , are 100 (½) and 100 (-½). Write the four quantum numbers for all of the electrons in the L and M shells, and note which correspond to the s, p, and d subshells.

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