How many subshells are possible with (n+1) equal to 6?

1 Answer
Jul 4, 2018

Well, there are five subshells POSSIBLE, but only the first two are ACCESSIBLE.


Well... apparently, you want the principal quantum number PLUS ONE to be:

#n+1 = 6#

so the energy level specified, is #n = 5#. For a given #n#, a certain maximum angular momentum #l# exists:

#l = 0, 1, 2, 3, 4, 5, 6, 7, . . . , overbrace(n - 1)^(l_max)#

and each of these values of #l# correspond to a unique subshell #s,p,d,f,g,h,i,k, . . . #.

Since #n = 5# and #n - 1 -= l_max = 4#,

#color(blue)(l = 0, 1, 2, 3, 4)#

are allowed. Clearly, it means there are FIVE subshells possible (five values of #l# are allowed), and they are:

#s, p, d, f, g#

i.e. there are one #5s#, three #5p#, five #5d#, and seven #5g# orbitals theoretically possible for any given atom among #Z = 37 - 54#.

However, only the #5s# and #5p# are accessible for these atoms.