#n# is the principal quantum number, the energy level. #n = 1, 2, 3, . . . ##l# is the angular momentum quantum number, corresponding to the shape of the orbitals of the kind. #l = 0, 1, 2, 3, . . . , n-1#. That is, #l_max = n-1#.#m_l# is the magnetic quantum number, matching to each orbital of the shape. #m_l = -l, -l+1, . . . , 0, . . . , l-1, l+1#. That is, #|m_l| .#m_s# is the spin quantum number for electrons. #m_s = pm1/2#.

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For #n = 4#, the preferably #l# is as such #4-1 = 3#. That course, over there is more 보다 one worth of #l# because that one worth of #n#.

That means:

#bbul(n = 4)#

#l = 0#:#m_l = 0#

#l = 1#:#m_l = -1, 0, +1#

#l = 2##m_l = -2, -1, 0, +1, +2#

#l = 3 -= l_max#:#m_l = -3, -2, -1, 0, +1, +2, +3#

and each #m_l# value synchronizes to one orbital. We have actually #bbul4# subshells in this case; #s,p,d,f# #harr# #0,1,2,3# because that the worth of #l#.

We have actually an odd variety of orbitals every subshell (#2l+1#), and also so:

#overbrace(2(0) + 1)^(s) + overbrace(2(1) + 1)^(p) + overbrace(2(2) + 1)^(d) + overbrace(2(3) + 1)^(f)#

#= 1 + 3 + 5 + 7#

#= bbul16# orbitals in the #bb(n = ul4)# energy level.

If girlfriend repeat the procedure for #n = 3#, you would uncover #l_max = 2# and there room #bbul9# orbitals in #n = bbul3#.

#bbul(n = 3)#

#l = 0#:#m_l = 0#

#l = 1#:#m_l = -1, 0, +1#

#l = 2 -= l_max##m_l = -2, -1, 0, +1, +2#

and each #m_l# value synchronizes to one orbital. We have #bbul3# subshells in this case; #s,p,d# #harr# #0,1,2# for the value of #l#.

If you repeat the process for #n = 2#, friend would find #l_max = 1# and also there space #bbul4# orbitals in #n = bbul2#.

#bbul(n = 2)#

#l = 0#:#m_l = 0#

#l = 1 -= l_max#:#m_l = -1, 0, +1#

and every #m_l# value corresponds to one orbital. We have actually #bbul2# subshells in this case; #s,p# #harr# #0,1# for the value of #l#.

If friend repeat the procedure for #n = 1#, friend would uncover #l_max = 0# and there is #bbul1# orbital in #n = bbul1#.

#bbul(n = 1)#

#l = 0 -= l_max#:#m_l = 0#

and each #m_l# value coincides to one orbital. We have #bbul1# subshell in this case; #s# #harr# #0# because that the value of #l#.

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Thus, we have actually #bb(n^2)# orbitals in one power level, and also #bbn# subshells in one energy level.