# How many electrons can an orbital of type f hold?

I was taking a chemistry test and I encountered the following question:

How many electrons can an orbital of type f hold?

A. 6
B. 10
C. 2
D. 14
E. 1

Since there can be [-ℓ, ℓ] orientations and since the orbital type f has ℓ = 3, we should have 7 possible orientations with 2 spins, so ${7 \times 2 = 14}$, so I thought the correct answer was D (14).

However, I got it wrong and the correct answer is marked as C (2). Is it an error in the test, or am I missing something?

You're correct that there are seven possible spatial orientations for an f-type orbital, and hence seven possible orbitals in one f-type sub-shell. However, the question specifically asks for the maximum number of electrons in one such orbital, and any single atomic orbital, regardless of the sub-shell type specified by $l$, can only hold two electrons. This is by virtue of the Pauli exclusion principle. Fourteen would be the maximum number of electrons across an entire f-type sub-shell, but the question only asks about one orbital.
• @AndreasBonini, yeah, it probably was, since the value of $l$ is completely extraneous. – Greg E. Aug 19 '13 at 1:55