What quantum number defines a subshell? How do we label each subshell? How many orbitals in each subshell?

1 Answer
Truong-Son N.
Jan 26, 2018

The angular momentum quantum number.

#l = 0, 1, 2, 3, . . . , n-1#

where #n# is the principal quantum number, the energy level. This maximum to #l# is why #1p#, #2d#, #3f#, #4g#, . . . etc. orbitals don't exist.

Each value of #l# designates a subshell, of a certain shape, labeled #s,p,d,f,g,h,i,k, . . . #, corresponding to #l = 0, 1, 2, 3, 4, 5, 6, 7, . . . #.

The #z#-projection of #l# is the magnetic quantum number #m_l#, which corresponds to EACH orbital in a given subshell designated by #l#.

#m_l = {-l, -l+1, . . . , 0, . . . , l-1, l}#

i.e. there are #2l+1# values of #m_l#, so there are #bb(2l+1)# orbitals in one subshell.

CHALLENGE: How many #d# orbitals are there in any given subshell?

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