For any sublevel s the sublevel has l 0 and the sub

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For any sublevel s, the sublevel has l = 0, and the sub-sub-levels must be 0. For this course, all that matters is that there is only one sub- sub-level for any l = s sublevel. For any sublevel p, the sublevel has l = 1, so the m l values can be -1, 0, or +1. What is important for us is that there are 3 sub-sub- levels for each p type sublevel.
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6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms For any sublevel d, the sublevel has l = 2, so the m l values can be -2, -1, 0, +1, or +2. What is important for us is that there are 5 sub-sub- levels for each d type sublevel. To review what we have so far: For the various levels, the total number of possible orbitals is the sum of the possible different m for each of the possible l: 1 st level: 1s 1 2 nd level: 2s 2p 1+3=4 3 rd level: 3s 3p 3d 1+3+5=9 4 th level: 4s 4p 4d 4f =16 But each of these various sublevels of orbitals can have two electrons, one with spin up and one with spin down. So the total electrons are 1 st level: 1s 2 2 nd level: 2s 2p 1+3=8 3 rd level: 3s 3p 3d 1+3+5=18 4 th level: 4s 4p 4d 4f =32
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We will want to learn more about the shapes and their possible orientations, but one of the most important things is just counting how many orbitals there are altogether. This is the main point of the m l quantum numbers for us.
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Shape of s orbitals of different n size
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Shape of smallest p orbitals. (The bigger ones look similar overall, but have two lumps along each axis, with a node between.)
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Shape of smallest d orbitals
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6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms With this array of possible sizes, shapes, and orientations of orbitals, and with two spins for any electron, we explain two different things. We can consider an electron in an atom, say H, and note the many transitions that are possible. Like a 2p electron can lose energy and become a 1s electron in a new orbital. Or that 2p electron could “go” to 3s or 3d. Or 3s could “go” to 2p. The transitions from all higher p states down to 2s would illustrate the Balmer series. Or higher s could go down to 2p. The electron can only “go” someplace where there is no electron. For neutral H, we only have one electron, so that is not a problem. We won’t learn it here, but the only transitions that have much chance to occur are ones that change the l quantum number by 1, like p to s or d, d to p or f, s to p, etc. Not d to s. You don’t need to know that, but you might find it interesting.
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6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms Here we can “see” these transitions better. A 2p electron can lose energy and become a 1s electron in a new orbital. 3p can go to 2s or 1s. 3s or 3d can go to 2p. Or vice versa. If you go higher, the spacings get closer and closer. When there is no gap at all, the electron has been ionized. In the formula, n = . 2 2 18 kZ Energy n where k 2.18 10 J Z is the positive charge "seen" by the electron 
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6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms The second use of our big table of orbitals is to explain the periodic table.
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