Chapter7and8Lecture

# This means that the electron cannot collapse into a

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This means that the electron cannot collapse into a point. This is good. If it could, the negative electron would annihilate with the positive nucleus. Quantum theory is the only thing that explains why the solid world exists and does not blow up in a huge explosion of opposite charges annihilating. To work with this theory, we proceed in two steps. First we figure out all the possible different clouds we could have for different . We call these things orbitals. So we imagine that there are orbitals in space around any nucleus that are possible places to put electrons. Second, we imagine that we put electrons into the orbitals. Each orbital can only have only two electrons. Even these two must be different in some way.

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6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms So there must be many orbitals. There are an infinite number possible, even for hydrogen, although we don’t worry about more than we need. The orbitals have different sizes and shapes. Each electron is tagged with 4 numbers, three of which describe its spatial orbital. The last one describes what we call spin. Spin has two choices for a single electron, which we can call up and down. This is how the two electrons in one orbital space differ. This is the s value. The orbitals are described by values for the overall size, the shape, and how they are affected by a magnetic field. We call these three the values for n, l, and m l . The level is n. This is the same n we saw in the equation for the energy of an electron in hydrogen and in the Rydberg formula. An orbital with a bigger n is bigger in space, and it has a higher (less negative!!!) energy. All energies are negative for bound electrons.
6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms So n describes the overall size. It assumes integer values from 1 to infinity, but mostly 1 or 2 or 3 or maybe 4 or 5. It is the principal quantum number. It is most important in determining the energy. The next quantum number is l. It has to do with angular momentum and shape. It can have a range of values from 0 to n-1. If n is 1, there is only one possible value for l and it is 0. If n is 2, there are 2 values of l, and they are 0 and 1. If n is 3, then l can have three values, namely, 0, 1, and 2. The complication is that the values of l are given letter names. They are, in order, 0=s, 1=p, 2=d, 3=f, 4=g, 5=h, etc. Note that this s is different from the s that refers to spin.

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6 Copyright: 2010 Prof. Magde Chapter 7: Electrons in Atoms So the orbitals with just size and shape are 1 st level: 1s 2 nd level: 2s 2p 3 rd level: 3s 3p 3d 4 th level: 4s 4p 4d 4f Each n level has n sublevels, shown above. But each of the sublevels has sub-sub-levels. They are identified by the m l quantum numbers. They are numerical again. For any value of l, m l can take integer values from –l up to +l. So you have to translate those s, p, d, f things back into numbers.
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