Question

# Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron...

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 = 4, ℓ= 0, mℓ= 1, ms= 1/2

n = 3, ℓ= –2, mℓ= –1, ms= –1/2

n = 5, ℓ= 3, mℓ= 1, ms= 1/2

n = 3, ℓ= 3, mℓ= 0, ms= 1/2

n = 2, ℓ= 1, mℓ= 0, ms= 0

n = 3, ℓ= 2, mℓ= –1, ms= 1/2

for option 1:

Value of l is 0

So, valid values of ml are [0]

so, ml can't be 1

Hence, this is not allowed

for option 2:

l can't be negative

l can't be -2

Hence, this is not allowed

for option 3:

This is allowed

for option 4:

l must be less than n

Here value of n is 3

But value of l is 3

so, l can't be 3

Hence, this is not allowed

for option 5:

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

It can’t be 0

Hence, this is not allowed

for option 6:

This is allowed