Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (ℓ), the magnetic quantum number (mℓ), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply.

Question

n = 3, ℓ= –1, mℓ= 0, ms= –1/2
n = 4, ℓ= 0, mℓ= 1, ms= 1/2
n = 5, ℓ= 5, mℓ= –1, ms= –1/2
n = 5, ℓ= 4, mℓ= 0, ms= 1/2
n = 3, ℓ= 0, mℓ= 0, ms= 1/2
n = 2, ℓ= 0, mℓ= 0, ms= 1

I really just don't understand this at all, anything helps! Thank you.

Answer 1

You need to know the rules. Here is how you do it. The rules are:
n = 1,2,3 etc in steps of whole numbers.
ell (I can't write the script l) is 0, 1, 2, etc in steps of whole numbers but never more than n-1.
or less than 0
m_ell = -ell to + ell in steps of whole numbers (including 0)
m_s can be +1/2 or -1/2

So look at +1 in the question.
n = 3. that's permissible.
ell = -1---can be since ell can be 0, 1, 2 etc but no larger than n-1 and no less than 0.

Look at 2 in this problem.
n = 4. That's ok
ell = 0. That's ok
m_ell = 1--can't be. m_ell may be from -ell to + ell so it may be anything but not less than 0

You do each of these one by one. Post if you have questions. There is more than one answer that is correct.