Number of orbitals

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Petrina Kan 2I
Posts: 102
Joined: Fri Aug 30, 2019 12:17 am

Number of orbitals

Postby Petrina Kan 2I » Tue Oct 29, 2019 2:41 am

Can someone explain why s has 1 orbital, p has 3 orbitals, d has 5 orbitals, and f has 7? Is there a conceptual understanding behind this or is it something that we must memorize? Thank you!

Ariel Davydov 1C
Posts: 110
Joined: Thu Jul 11, 2019 12:16 am
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Re: Number of orbitals

Postby Ariel Davydov 1C » Tue Oct 29, 2019 8:29 am

The number of orbitals per angular momentum quantum number can be obtained by looking at the total number of potential m(l)-numbers for an l-number. For example, for l=3 (the f block), m(l) can be anything from 3 to -3 (3, 2, 1, 0, -1, -2, -3) meaning the total number of potential quantum numbers is 7. Since each of these m(l) numbers represents a orbital of the f-block, we can assume that there are 7 total f-orbitals. You can use this same method for s-, p-, and d-orbitals.

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