Consider the following quantum numbers sets; determine if they can occur together to specify an orbital. If not indicate which rule has been violated?

n=2, l=-1, ml=-1
n=3, l=1, ml=0
n=3, l=3, ml=-3

1 Answer
Truong-Son N.
Jan 26, 2018

Well, recall the ranges of each quantum number.

  • #n > 0#, and must be an integer.
  • #0 <= l <= n-1#, and must be an integer.
  • #|m_l| <= l#

Thus, the first configuration is not possible since #l# must be nonnegative (the orbital shape doesn't exist), and the third configuration is not possible since #l > n-1# (so, #3f# orbitals don't exist).

The second configuration is a #3p_z# orbital.

#n = color(blue)(3) -> color(blue)(3)p_z#

#l = color(blue)(1) -> 3color(blue)(p)_z#

#m_l = color(blue)(0) -> 3p_color(blue)(z)#

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