Gen Chem_Ch 6_12th_d Orbitals
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Overview
Dr. Reza Latifi explains how the angular momentum quantum number l identifies d subshells: l = 2 gives five orbitals, with magnetic quantum numbers from -2 to +2, and a capacity of 10 electrons. He illustrates the five d-orbital shapes and their orientations, then relates their two angular nodes to the 3d subshell, which has no radial nodes.
Key takeaways
- Setting l = 2 produces five d orbitals because the allowed magnetic quantum numbers run from -2 through +2.
- A complete d subshell holds 10 electrons, with a maximum of two electrons in each of its five orbitals.
- The dxy, dxz, and dyz lobes lie between coordinate axes, while dx²−y² lobes align with the x and y axes.
- The dz² orbital differs from the other four d orbitals by combining two z-aligned lobes with a torus around the center.
- Every d orbital has two angular nodes; for 3d, n = 3 and l = 2 also give zero radial nodes.
Chapters
- The allowed angular momentum quantum numbers range from l = 0 to n - 1, while magnetic quantum numbers range from -l to +l.
- For d orbitals, l = 2 yields five possible magnetic quantum numbers: -2, -1, 0, +1, and +2.
- Five d orbitals hold up to 10 electrons, compared with six in three p orbitals and two in one s orbital.
- The dxy, dxz, and dyz orbitals have four lobes positioned between pairs of axes in their respective planes.
- The dx²−y² orbital has four lobes aligned with the x and y axes, unlike dxy, whose lobes sit between them.
- The dz² orbital has two lobes along the z axis and a ring-shaped region around the center in the xy plane.
- Different signs on orbital regions indicate wavefunction phases; they do not change the five-orbital count.
- A d orbital requires a principal quantum number n of at least 3 because l = 2 must be less than n.
- For a 3d orbital, the total node count is n - 1 = 2, and both are angular nodes.
- The radial-node formula n - l - 1 gives zero radial nodes for 3d orbitals.
Transcript excerpt
0:11 [music] >> Hello and welcome back and thank you very much for watching another lecture from general chemistry. In last lecture, we practiced how to find the S and P orbitals in each layer and also we practiced their shapes and we went after L and ML for each one. Now I want to talk about the D orbitals. So again, S orbital we said when come to L, if L is equal to zero we call it S orbital there is only one answer for ML it will be zero and reminder that L is equal to zero to N minus one and ML is equal to minus L to zero to plus L. If you know L, plug in it inside the ML formula that's going to give you idea how many answers or directions you have for ML. If L is equal to zero which is S orbital, there is only one answer for ML
0:58 it will be zero and we said so S orbital must be spherical. Okay, and that's the reason we show the S orbital as a circle. And for a P orbital, L it will be equal to one. If L equal one, then you have three answers for ML and we show them as Px, Py and Pz. And again, we said if you are dealing with only one direction, you show it by one box. If you have three of them, in that case you show them by three boxes. That means the P orbital has the three houses that uh that they can totally accommodate six electrons. So you put two here or there, you put six electrons. Now, I'm going to switch to D orbital. If L is equal to two, then you have five answers five possibilities for ML. That
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Related notes
Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Dr. Reza Latifi at Oklahoma State University, OSU.