# Quantum numbers required to specify the position of an electron

How many quantum numbers are required to specify the position of an electron? $$(A)\ 1 \quad (B)\ 2 \quad (C)\ 3 \quad (D)\ 4$$

The answer key says that the answer is $$(D)$$ but I am feel that the answer should be $$(C)$$ as the spin quantum number describes the angular momentum of the electron.

Please let me know what should be the correct answer keeping in mind that I am a sixteen year old.

Thanks!

P.S. let me know if I should include more or change tags.

Edit: Since it was not clear previously (or so I think), my point is that spin quantum number is not necessary for specifying the position of an electron.

First of all, the question is badly formulated. It asks about "position" but clearly means "orbital", which are two different things. (An orbital is a wave function, which depends on the electrons position: $$\psi(\vec r)$$.) Although the difference may be difficult to explain at high school level, this choice of words is imprecise and often leads to wrong ideas about the basic concepts of quantum mechanics.

The question is obviously about the 4 quantum number ($$n$$, $$l$$, $$m_l$$ and $$m_s$$), thus including spin. Whether spin is really required to describe the spatial part of an orbital is arguable. But if we stick with high school level chemistry and consider what is typically called restricted orbitals, then both electrons ($$\alpha$$ and $$\beta$$) share the same spatial part of the orbital, and the spin quantum number is unrelated to the "position" of the electron. But the spin quantum number is still required to "distinguish" the two electrons, what seams to be what the question has in mind. (I used quotation marks, because the electrons are actually indistinguishable.)

If we go beyond high school level and into actual quantum chemistry, then it depends on what type of orbitals are considered. I already mentioned restricted orbitals. But one may also use unrestricted orbitals, where $$\alpha$$ and $$\beta$$ electrons do not share the same spatial part. Here it is obviously necessary to include the spin quantum number.

One final remark: There are actually 5 quantum numbers that specify an orbital. Analogous to $$l$$ and $$m_l$$ of spatial angular momentum, in spin angular momentum there is $$s$$ and $$m_s$$. However for electrons we always have $$s=\frac{1}{2}$$, therefore explicit specification of $$s$$ is not necessary.

• Well, we don't have what you call the "actual quantum chemistry" in our curriculum, nor do we have the mention of restricted or unrestricted orbitals. So should I consider myself correct and talk to the teacher or what? – AryanSonwatikar May 25 at 9:15
• "we don't have what you call the 'actual quantum chemistry' in our curriculum" that is why I considered high school level first, the other part was just a brief outlook what is beyond. But my main point is, that the question is imprecise and therefore leads to confusion. It should be reformulated, but there are different issue that need to be considered here. Honestly I don't know the best formulation (since I am no teacher). "How many quantum numbers are required to specify an atomic spin orbital?" would be my suggestion, but might be beyond the scope of high school chemistry. – Feodoran May 25 at 9:37
• Yup. Way beyond (probably). Thanks, anyways. – AryanSonwatikar May 25 at 9:40
• "...to specify the 'state' or 'properties' of an electron" maybe – Blaise May 25 at 15:18