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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