Question

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.
n = 3, ℓ= –1, mℓ= 0, ms= –1/2 n = 4, ℓ= 0, mℓ= 1, ms= 1/2 n = 5, ℓ= 5, mℓ= –1, ms= –1/2 n = 5, ℓ= 4, mℓ= 0, ms= 1/2 n = 3, ℓ= 0, mℓ= 0, ms= 1/2 n = 2, ℓ= 0, mℓ= 0, ms= 1 I really just don't understand this at all, anything helps! Thank you.

Answer 1

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 

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