Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, indicate what is wrong in each set.
(a) n = 3, ℓ = 2, mℓ = 2
allowed
not allowed, n is not valid
not allowed, ℓ is not valid
not allowed, mℓ is not valid

(b) n = 4, ℓ = 3, mℓ = 4
allowed
not allowed, n is not valid
not allowed, ℓ is not valid
not allowed, mℓ is not valid

(c) n = 0, ℓ = 0, mℓ = 0
allowed
not allowed, n is not valid
not allowed, ℓ is not valid
not allowed, mℓ is not valid

(d) n = 2, ℓ = -1, mℓ = 1
allowed
not allowed, n is not valid
not allowed, ℓ is not valid
not allowed, mℓ is not valid