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**Problem**: 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 (mℓ), and the spin quantum number (ms) 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, mℓ = 0, ms = -1/2b) n = 4, ℓ = 0, mℓ = 1, ms = +1/2c) n = 5, ℓ = 1, mℓ = 0, ms = -1/2d) n = 2, ℓ = 1, mℓ = 1, ms = 0e) n = 6, ℓ = 6, mℓ = 1, ms = -1/2f) n = 3, ℓ = 2, mℓ = 0, ms = -1/2

###### FREE Expert Solution

###### FREE Expert Solution

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

###### Problem Details

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

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Quantum Numbers: Spin Quantum Number concept. You can view video lessons to learn Quantum Numbers: Spin Quantum Number Or if you need more Quantum Numbers: Spin Quantum Number practice, you can also practice Quantum Numbers: Spin Quantum Number practice problems .

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