Absolutely Small - Michael D. Fayer [64]
THE ORBITAL SHAPES MATTER FOR ATOMS LARGER THAN HYDROGEN
With more than one electron, the shapes of the orbitals matter. In helium, if its two electrons are placed in the 2s orbital the energy is lower than if they are placed in a 2p orbital. On average, two electrons in the 2s orbital are farther apart than two electrons in a 2p orbital. Electron-electron repulsion increases the energy. Because the two electrons are farther apart in the 2s orbital, the electron-electron repulsion (increase in energy) is not as severe as having the two electrons in a 2p orbital. Therefore, the 2s orbital in many electron atoms (all atoms but hydrogen) is lower in energy than the 2p orbital. For n = 3, two electrons on average are farther apart in a 3s orbital than in a 3p orbital, and two electrons in a 3p orbital are farther apart than if they are in a 3d orbital. So, the 3s orbital is lower in energy than the 3p orbitals, which are lower in energy than the 3d orbitals. However, the 3s orbital is higher in energy than the 2s orbital. On average electrons in a 3s orbital are farther from the nucleus because the 3s orbital is larger than the 2s orbital (see Figures 10.2, 10.5, and 10.6), and therefore have a weaker attractive interaction with the nucleus. Less attractive interaction results in a higher energy. The attraction to the nucleus binds the electron to the nucleus. The sign convention is that the stronger the binding, the lower the energy. The electron falls into the attractive well of the positively charged nucleus. The stronger the attraction, the deeper the electron is in the well. It will take more energy to remove the electron from the well, that is, pull it away from the nucleus.
MANY ELECTRON ATOM ENERGY LEVELS
For a given principal quantum number n, the order of the energy is ns < np < nd < nf. For the same type of orbital, the larger the n the higher the energy. The important feature of many electron atoms is that the energy depends on two quantum numbers, n and l. l is the angular momentum quantum number that determines the shape of the orbital. Figure 11.1 is the energy level diagram for many electron atoms. For n = 1, there is only one type of orbital, l = 0, an s orbital. So the 1s orbital has the lowest energy level. For n = 2, l can be 0 or 1. The l values give rise to the 2s orbital and the three different 2p orbitals. With l = 1, there are three possible values of m, m = 1, 0, -1. This is the same as in hydrogen. The big difference is that for many electron atoms, the 2s orbital is lower in energy than the 2p orbitals, as shown in Figure 11.1. For n = 3, there is the 3s orbital, the 3p orbitals, and the 3d orbitals. As can be seen in Figure 11.1, the 3s orbital is below (lower in energy) the 3p orbitals, which are below the 3d orbitals.
A very important aspect of the ordering of the energy levels is that energy levels with different n quantum numbers are interspersed. Although the 3d orbitals are above the 3p orbitals, the 4s orbital energy is actually below that of the 3d orbitals (see Figure 11.1). The ordering of the orbitals is also shown in Figure 11.1. We see that the energy levels go 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, and so on. As discussed below, switching the order between the 4s and the 3d gives rise to what is called the first transition series, and switching the 5s and the 4d gives rise to the second transition series. The ordering is very important in determining the properties of various atoms. The switches in the order and the meaning of the