# 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?

## 1 Answer

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.

• Damn, you are right.. It was a trick question then! :( – Thomas Bonini Aug 19 '13 at 1:53
• @AndreasBonini, yeah, it probably was, since the value of $l$ is completely extraneous. – Greg E. Aug 19 '13 at 1:55
• This is the type of question that isn't designed to assess student learning of Chemistry, but rather if the student pays enough attention to get in to med school. – bobthechemist Aug 19 '13 at 2:22
• @bobthechemist, yes, I agree. I'm generally of the opinion that multiple-choice questions of this type are mostly useless in evaluating student understanding. The best questions are conceptual ones that require thoughtful application of learned material in novel ways, or that ask the student to explain particular observations/phenomena based on certain axioms or principles. – Greg E. Aug 19 '13 at 2:31
• @bobthechemist, as it happens, I had no intention of pursuing a career in chemistry until I had the immense good fortune of encountering a pair of excellent general and organic chemistry professors when I started college who were able to consistently formulate such questions. That ended up illuminating many aspects of the natural world in which we live for me and radically changed the direction of my career plans. Sadly, developing that type of coursework takes a lot more effort than many, if not most, instructors are willing to apply. – Greg E. Aug 19 '13 at 2:34