# 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

n any positive integer

ℓ  0 up to (n-1)

m range of values from -ℓ to +ℓ

a) n = 3, ℓ = -2, m= 0, ms = -1/2

ℓ  cannot be negative  not allowable

b) n = 4, ℓ = 0, m= 1, ms = +1/2

m= 1 not allowable

c) n = 5, ℓ = 1, m= 0, ms = -1/2

allowable

d) n = 2, ℓ = 1, m= 1, ms = 0

ms = 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), 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 = -1/2

b) n = 4, ℓ = 0, mℓ = 1, ms = +1/2

c) n = 5, ℓ = 1, mℓ = 0, ms = -1/2

d) n = 2, ℓ = 1, mℓ = 1, ms = 0

e) n = 6, ℓ = 6, mℓ = 1, ms = -1/2

f) n = 3, ℓ = 2, mℓ = 0, ms = -1/2

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 Introduction to Quantum Mechanics concept. You can view video lessons to learn Introduction to Quantum Mechanics. Or if you need more Introduction to Quantum Mechanics practice, you can also practice Introduction to Quantum Mechanics practice problems.