Which of the following are invalid sets of quantum numbers?

#3, 4, 0, 1/2#
#2, 1, 3, 1/2#
#-2, 1, 0, -1/2#
#3, 2, 2, -1/2#
#3, 2, 0, -1/2#

1 Answer
Nov 9, 2016

Several rules apply here:

  1. #n >= 1# in integer increments.
  2. #l >= 0# in integer increments.
  3. #l_max = n-1#.
  4. #m_l = {-l, -l+1, . . . , -1, 0, +1, . . . , l - 1, l}#
  5. #m_s = pm"1/2"#

For the format #(n,l,m_l,m_s)#:

  • #(3, 4, 0, 1/2)# is invalid because #l > n#.
  • #(2, 1, 3, 1/2)# is invalid because #m_l# is outside the range of #l#.
  • #(-2, 1, 0, -1/2)# is invalid because #n < 1#.
  • #(3, 2, 2, -1/2)# is valid because #n > 1#, #l < n#, #m_l# is within the range of #l#, and #m_s# is correctly either #+"1/2"# or #-"1/2"#.
  • #(3, 2, 0, -1/2)# is valid for the same reason as the fourth choice.