# Problem: Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect.a. n = 3, ℓ = 3, mℓ = 0, ms = -1/2b. n = 4, ℓ = 3, mℓ = 2, ms = -1/2c. n = 4, ℓ = 1, mℓ = 1, ms = +1/2d. n = 2, ℓ = 1, mℓ = -1, ms = -1e. n = 5, ℓ = -4, mℓ = 2, ms = +1/2f. n = 3, ℓ = 1, mℓ = 2, ms = -1/2

###### FREE Expert Solution

We’re being asked to find which set of quantum numbers is possible

Recall that the quantum numbers that define an electron are:

• Principal Quantum Number (n): deals with the size and energy of the atomic orbital. The possible values for n are 1 to ∞.

• Angular Momentum Quantum Number (l): deals with the shape of the atomic orbital. The possible values for l are 0 to n – 1.

• Magnetic Quantum Number (ml): deals with the orientation of the atomic orbital in 3D space. The possible values for ml are the range of –l to +l.

• Spin Quantum Number (ms): deals with the spin of the electron. The possible values for ms are either –1/2 (spin down) or +1/2 (spin up).

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###### Problem Details

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect.

a. n = 3, ℓ = 3, m = 0, ms = -1/2

b. n = 4, ℓ = 3, m = 2, ms = -1/2

c. n = 4, ℓ = 1, m = 1, ms = +1/2

d. n = 2, ℓ = 1, m = -1, ms = -1

e. n = 5, ℓ = -4, m = 2, ms = +1/2

f. n = 3, ℓ = 1, m = 2, ms = -1/2