Respuesta :
The allowable combination for the atomic orbital is n=3, l=1, [tex]m_{l}[/tex]=-1.
What are the three quantum numbers of an atomic orbital?
Three quantum numbers specify an atomic orbital:
- The principal quantum number, n, which is a positive integer, describes the relative size of the orbital and its distance from the nucleus.
- l is the angular momentum quantum number that is related to the shape of the orbital; l is an integer from 0 to n-1 (so n limits l ),
- [tex]$\boldsymbol{m}_{l}$[/tex] is the magnetic quantum number that prescribes the three-dimensional shape of the orbital around the nucleus; [tex]m_{l}[/tex] values are integers from -l to =l(l limits ml)
For n = 3, l can have three values: 0, 1, and 2. Since [tex]m_{l}[/tex] values are integers from -l to 0 to +l, for l = 0 the value of [tex]m_{l}[/tex] cannot be -1 (l = 0 has [tex]m_{l}[/tex]= 0).
There are two l values that are consistent with n and [tex]m_{l}[/tex] values:
l=1 or 2
Therefore, the allowable condition is n=3, l=1, [tex]m_{l}[/tex]=-1.
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