Why do #2d#, #1d#, and #3f# orbitals not exist?

2 Answers
Sep 12, 2017

Answer:

Each energy level listed does not contain the given sublevels in the ground state.

Explanation:

In the ground state for each energy level:

In the 2nd energy level, electrons are located only in the s and p sublevels, so there are no d orbitals.

In the 1st energy level, electrons occupy only in the s sublevel, so there is no d sublevel.

In the 3rd energy level, electrons occupy only the s, p, and d sublevels, so there is no f sublevel.

Sep 12, 2017

Because those angular momenta are too high for the given quantum levels.


Recall that the first two quantum numbers are:

  • #n = 1, 2, 3, . . . #

  • #l = 0, 1, 2, . . . , n-1# #harr# #s, p, d, f, g, h, i, k, . . . #

where #n# is the principal quantum number indicating the energy level, and #l# is the angular momentum quantum number indicating the shape of the orbital.

Since #l# can be no greater than #n-1# (i.e. #l_(max) = n-1#), it follows that the maximum #l# for each energy level is:

#n = 1 => l_(max) = 0 => s#

#n = 2 => l_(max) = 1 => p#

#n = 3 => l_(max) = 2 => d#

#n = 4 => l_(max) = 3 => f#

#vdots" "" "" "" "" "" "" "vdots#

As a result, the highest angular momentum orbitals we have are #1s#, #2p#, #3d#, #4f#, etc. We cannot have #1p#, #2d#, #3f#, #4g#, etc.

In other words, we have only:

#1s#

#2s, 2p#

#3s, 3p, 3d#

#4s, 4p, 4d, 4f#

#vdots" "" "" "" "ddots#