n → any positive integer

ℓ → 0 up to (n-1)

m_{ℓ} →range of values from -ℓ to +ℓ

a) n = 3, ℓ = -2, m_{ℓ}= 0, m_{s} = -1/2

ℓ → cannot be negative → not allowable

b) n = 4, ℓ = 0, m_{ℓ}= 1, m_{s} = +1/2

m_{ℓ}= 1 → not allowable

c) n = 5, ℓ = 1, m_{ℓ}= 0, m_{s} = -1/2

allowable

d) n = 2, ℓ = 1, m_{ℓ}= 1, m_{s} = 0

m_{s} = 0 → cannot be zero → not allowable

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (ℓ), the magnetic quantum number (m_{ℓ}), and the spin quantum number (m_{s}) have strict rules which govern the possible values.

Identify allowable combinations of quantum numbers for an electron.

Select all that apply.

a) n = 3, ℓ = -2, m_{ℓ }= 0, m_{s} = -1/2

b) n = 4, ℓ = 0, m_{ℓ }= 1, m_{s} = +1/2

c) n = 5, ℓ = 1, m_{ℓ }= 0, m_{s} = -1/2

d) n = 2, ℓ = 1, m_{ℓ }= 1, m_{s} = 0

e) n = 6, ℓ = 6, m_{ℓ }= 1, m_{s} = -1/2

f) n = 3, ℓ = 2, m_{ℓ }= 0, m_{s} = -1/2

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