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