What are the irrational numbers of the following groups?Why? 1. n=2, l=3, m =0 ； 2. n=2, l=2, m=1 ；

1 Answer
Truong-Son N.
Jun 3, 2018

Both........ of course, all of these numbers are rational, because they are INTEGERS with terminating decimals...

The angular momentum quantum number #l# has a range...

#l = 0, 1, 2, . . . , n-1#

where #n = 1, 2, 3, ... # is the principal quantum number.

And each #l# corresponds to a shape, #s,p,d,f,g,h,...#. For each #l# there may exist magnetic quantum number #m_l# values in the range #{-l, -l+1, . . . , 0, . . . , l-1, l}#, that is, it MUST be that #|m_l| <= l#.

Both sets of quantum numbers presented are IMPOSSIBLE, because #l# must be less than #n#.

That is, we must recognize that #2f# and #2d# orbitals do not exist in atoms. i.e.

#n = 2, l = 3, m_l = 0 -> 2f_(z^3)# orbital, which doesn't exist

#n = 2, l = 2, m_l = 1 -> 2d_(xz)# orbital, which doesn't exist

On the other hand, the #4f_(z^3)# orbital exists, having #n = 4, l = 3, m_l = 0#, and the #3d_(xz)# orbital exists, having #n = 3, l = 2, m_l = 1#.

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