Answer:
The valid set of quantum numbers are:
a. 3,1,1,-1/2
b. 4,3,1,-1/2
c. 2,0,0,-1/2
e. 3,2,-1,-1/2
j. 3,0,0,1/2
Explanation:
Quantum numbers (n, l, mℓ, ms) are the set of numbers that describe the state of an electron in an atom.
<u>The four quantum numbers and their rules are</u>:
- Principal: n ≥ 1
- Azimuthal: ℓ ≤ (n-1)
- Magnetic: mℓ = (- ℓ) to (+ ℓ)
- Spin: ms = (- s), (+ s)
Therefore,
a. 3,1,1,-1/2: <em>Valid</em>
b. 4,3,1,-1/2: <em>Valid</em>
c. 2,0,0,-1/2: <em>Valid</em>
d. 1,3,0,1/2: <u>NOT</u> <em>Valid</em>
<u>Reason</u>: ℓ ≤ (n-1). Therefore, ℓ can not be greater than n, .
e. 3,2,-1,-1/2: <em>Valid</em>
f. 3,3,-1,1/2: <u>NOT</u><em> Valid</em>
<u>Reason:</u> ℓ ≤ (n-1). Therefore, ℓ can not be equal to n. (ℓ ≠n)
g. 3,2,1,-1: <u>NOT</u> <em>Valid</em>
Reason: the only allowed values of ms = (- s), (+ s) = (- 1/2), (+ 1/2)
h. 1,-1,-1,-1/2: <u>NOT </u><em>Valid</em>
<u>Reason</u>: ℓ ≤ (n-1) and n ≥ 1. Therefore, ℓ can not be equal to n and also ℓ can't be negative.
i. 3,3,1,1/2: <u>NOT </u><em>Valid</em>
<u>Reason:</u> ℓ ≤ (n-1). Therefore, ℓ can not be equal to n. (ℓ ≠n)
j. 3,0,0,1/2: <em>Valid</em>
k. 4,3,4,-1/2: <u>NOT </u><em>Valid</em>
<u>Reason</u>: mℓ = (- ℓ) to (+ ℓ). Therefore, mℓ can't be greater than ℓ.
l. 0,2,1,1/2: <u>NOT </u><em>Valid</em>
<u>Reason:</u> n ≥ 1. Therefore, value of n can't be 0 (n≠0)
