Question

Which of the following sets of quantum numbers are allowed and which are not allowed? for each incorrect set, select why it is incorrect.

an = 3, ℓ = 3, mℓ = 0, mₛ = −½
b)n = 4, ℓ = 3, mℓ = 2, mₛ = −½
c)n = 4, ℓ = 1, mℓ = 1, mₛ = +½
d) n = 2, ℓ = 1, mℓ = 1, mₛ = −½
e) n = 5, ℓ = -4, mℓ = 2, mₛ = +½
f) n = 3, ℓ = 1, mℓ = 2, mₛ = −½

Answer 1

The set {4, 2, -2, 1} is not allowed because it contains an improper value for the orbital quantum number (l). The set {3, 1, 0, -1/2} is allowed as it satisfies all the requirements for the quantum numbers.

Step-by-step explanation:

a. The set {4, 2, -2, 1} contains an improper value for the orbital quantum number (l). The valid range for l is from 0 to n-1. Since n = 4, the maximum value for l would be 3. Therefore, this set is not allowed.

b. The set {3, 1, 0, -1/2} satisfies all the requirements. The principal quantum number (n) is an integer, the orbital quantum number (l) is less than n, the magnetic quantum number (mê) is between -l and l, and the spin quantum number (ms) is either +1/2 or -1/2. Thus, this set is allowed.