1D.23

[Brandon Valafar]

I am so confused on this problem? Can anyone help?
How many orbitals can have the following quantum numbers in an atom:(a)n=2,l=1; (b)n=4,l=2,ml=-2; (c)n=2;(d)n=3,l=2,ml=1 ?

Solutions manual says the answers are 3,1,4,1 but I have no idea how they got that.

[Matt F]

Basically the question is asking how many possible values of m_l there are for the given set of quantum numbers. Remember, the value of m_l ranges from l to -l. For b) and d), the answer is 1 since they give you m_l already. For a), the answer is 3 since m_l can be 1, 0, or -1 given l=1. For c), the answer is 4 since l could be 1 or 0, meaning that m_l can be 1,0, or -1, or 0 (if l=0).