Which of the following sets of quantum numbers are allowed and which are not allowed? For each incorrect set, select why it is incorrect.
(a) n = 3, ℓ = 3, mℓ = 0, ms = -½
For n = 3, ℓ = 3 is not possible
ms can never be a negative value
mℓ cannot equal -1
All of these quantum numbers are allowed
(b) n = 4, ℓ = 3, mℓ = 2, ms = -½
When n = 4, ℓ = 3 is not possible
ms can never be a negative value
mℓ cannot equal 2 when ℓ = 3
All of these quantum numbers are allowed
(c) n = 4, ℓ = 1, mℓ = 1, ms = +½
When ℓ = 1, mℓ = 1 is not possible
ms can not be positive
mℓ cannot equal 1 when n = 4
All of these quantum numbers are allowed
(d) n = 2, ℓ = 1, mℓ = -1, ms = -1
When n = 2, ℓ = 1 is not possible
ms can never be a negative value
ms cannot equal -1
All of these quantum numbers are allowed
(e) n = 5, ℓ = -4, mℓ = 2, ms = +½
mℓ cannot equal 2
ℓ cannot be a negative number
n has a maximum of four
All of these quantum numbers are allowed
(f) n = 3, ℓ = 1, mℓ = 2, ms = -½
When ℓ = 1, mℓ = 2 is not possible
ms can never be a negative value
ℓ cannot be 1 when n = 3
All of these quantum numbers are allowed