The principal quantum number, n, describes the energy level of a particular orbital as a function of the distance from the center of the nucleus. Additional quantum numbers exist to quantify the other characteristics of the electron. 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 =1, ms = +1/2

b. n= 5, ℓ=4 , mℓ = 1, ms = -1/2

c. n= 4, ℓ=1 , mℓ = 2, ms = +1/2

d. n= 3, ℓ=2 , mℓ = 1, ms = -1/2

e. n=2 , ℓ=1 , mℓ =-1 , ms = -1

f. n= 3, ℓ= 3, mℓ = -1, ms = -1/2

Rule 1.

n can be 1,2,3,4,… etc.

So a, b, c, d, e and f, are all fine.

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Rule 2.

ℓ can be 0,1 ,2 up to n-1

For example if n=5, ℓ could be 0, 1, 2, 3 or 4.

So:

‘a’ is wrong (ℓ can’t be negative)

‘f’ is wrong (ℓ can’t equal n)

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Rule 3.

mℓ must be an integer in the range -ℓ to ℓ.

E.g. if ℓ =3, mℓ could be -3, -2, -1, 0, 1,2, or 3

So c is wrong because mℓ can’t be bigger than ℓ

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Rule 4.

ms can only be -1/2 or 1/2.

So e is wrong (ms can’t be 1)

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So a, f, c, e are wrong. The only correct ones are b and d.