# Which of the following sets of 3 quantum numbers is/are possible?

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#a)# #2,1,1#

#b)# #3,2,-2#

#c)# #2,0,0#

#d)# #2,0,-1#

#e)# #1,1,-1#

##### 1 Answer

This is a situation where you'll just have to remember the rules... The following rules are relevant:

- The principal quantum number
#n# is always**one more**than the maximum angular momentum#l# . That is,#l_(max) = n-1# . - The set of valid
#m_l# must be**in the range**#{0, pm1, pm2, . . . , pm l}# . Thus, if for example,#l = 2# ,#m_l# cannot be#-3# because#|-3| > 2# .

These are all that are necessary to determine the impossible combinations. I will identify the possible quantum number combinations, and I will leave you to determine why the remaining combinations are incorrect.

Possible:

#a)# :#(n,l,m_l) = (2,1,1)# . This designates one of the#2p# orbitals.#b)# #(n,l,m_l) = (3,2,-2)# . This designates one of the#3d# orbitals.#c)# #(n,l,m_l) = (2,0,0)# . This designates the one#2s# orbital.

Impossible: the rest, because they violate the above rules. Which one violates which rule? What is a valid correction to the combination?

Here is one example;