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# Zirconium $(Z=40)$ has two electrons in an incomplete $d$ subshell. (a) What are the values of $n$ and $\ell$ for each electron? (b) What are all possible values of $m_{\ell}$ and $m_{s}^{7}(\mathrm{c})$ What is the electron configuration in the ground state of zirconium?

## a) $n = 4$, $l = 2$b) \begin{aligned} m_{l} &=-2,-1,0,+1,+2 \\ m_{s} &=\pm \frac{1}{2} \end{aligned}

Atomic Physics

Nuclear Physics

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in this exercise. They have the zirconium that has an atomic number of 40. And we have the information that there are two electrons off the zirconium that are in an incomplete D sexual question. They we have find and the principal can't quantum number and the orbits open toe number l for these two elections s. So what I'm gonna do is to, uh, find what is the electronic configuration off the zirconium. Ah, And from that I can infer. And l of these two electrons. Uh, so let's do it. So I have the first of shallots one as to I feel it completely. Then the next said show is to s to and then comes to be six. Up until now, we have 10 elections. The next one is three s to and then three b six. Okay. Ah, and the next step show. And up until now we have 18. Ah, I'm sorry. We have 2028 elections. The next up shell is four s to remember that the order is this one. Okay, so the next one is for us to And then comes three de 10. So up until now we have 10 plus 18 plus two. So we have 30 electrons. The necks of show is four p six. So have 36. That except so shell is five s to which is completely which is completed entirely. And the next of shell and the final oneness four d and there are only two electrons left. So the the final sexual is for D two. So notice that the the two electrons in the incomplete dese of shell are in the four decent show. Okay, this one here. So they are in the four D and from that we can read the principal quantum number. That's just four. And we can read l ah, and notice that D here in the in the sexual name refers to l being equal to three. That's just another way of saying that l equals street. So for both I'm sorry, Alecos, to, uh, it's not three to Ah, because yes refers to l equals zero p refers to al equals one and d refers to al equals two. So this here is our answer for both elections and for question be we have to find all possible values off an L and M s for these two elections. So we know that l equals two. And we know that ML can range from minus l to l. So this is this gonna be minus two minus one 01 to an M s can be either plus or minus 1/2. Okay, that's just that's being quantum number. That's true for every election. And finally question. So you have to find the Elektronik configuration of the zirconium, and we've write it down. That in question eight. Okay, so I'm gonna copy what we did down here so that this is one s two to us, too. To be sick. B six three s to three b six four. I'm sorry. Four s to then three. Did 10 feel P six? Five s, two. And finally four. Indeed to Okay, this is the electronic configuration off the zirconium.