Video Transcript
If 𝐿 equals zero, how many possible values of 𝑚 sub 𝐿 are there?
𝐿 is the subsidiary quantum number. This quantum number describes the orbital type, that is, whether the orbital is an s-, p-, d-, or f-type orbital. For s-type orbitals, 𝐿 equals zero; for p-type orbitals, 𝐿 equals one; for d-type orbitals, 𝐿 equals two; and three for f. In this question, 𝐿 equals zero. So we know this refers to an s-type orbital, which are spherically shaped.
Now we need to determine the possible values of 𝑚 sub 𝐿 when 𝐿 equals zero. 𝑚 sub 𝐿 is the magnetic quantum number. This quantum number tells us the orbital orientation. 𝑚 sub 𝐿 can be any integer from negative 𝐿 to positive 𝐿. If 𝐿 equals zero, like we have in this question, 𝑚 sub 𝐿 can only equal zero. This corresponds to the single orientation of the spherically shaped s orbital. If 𝐿 equals one, 𝑚 sub 𝐿 can be negative one, zero, or positive one. This corresponds to how each of the three p orbitals are oriented along the 𝑥-, 𝑦-, or 𝑧-axis. But when 𝐿 equals zero, 𝑚 sub 𝐿 can only be zero. So there is only one possible value of 𝑚 sub 𝐿.
