# quantum numbers arise naturally. select all that apply?

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.

The rules for allowable states give the principle number n is: l = 0, 1, 2, … n-1 ml = -l, -l+1, -l2+2,…,0, 1, 2, …,l-1, l ms = -1/2, 1/2 for each ml So if n = 2 then l = 0, ml = 0 and ms = -1/2, 1/2 Apply the rules to each line of your problem first line is not allowed n = 4 is ok n = 5 is ok fourth line is not allowed fifth line is ok sixth line is not allowed

The first three quantum numbers (n,ℓ,mℓ) are all related to one another
n can be any number grater than zero
ℓ can be 0 to n-1
mℓ can be -ℓ to ℓ
ms can only be 1/2 or -1/2

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A set of legitimate quantum numbers satisfies all those criteria

a) doesn t work because mℓ is not between ℓ and -ℓ
b) doesn t work because ℓ is not between n and n-1
c) works
d) doesn t work because ℓ is not between n and n-1
e) works
f) doesn t work because ms is not 1/2 or -1/2

hope this helped!

Source(s): https://en.wikipedia.org/wiki/Quantum_number
Second year nuclear chemistry student