Absolutely Small - Michael D. Fayer [66]
Rule 2—Lowest Energy First but Don’t Violate the Pauli Principle
Rule 2 is the orbitals are filled with electrons in order of increasing energy. Electrons are placed in the lowest possible energy level first, but the Pauli Principle cannot be violated. So for the helium atom (He), both electrons can go in the 1s energy level, one with spin up (s = +1/2) and one with spin down (s = -1/2). Three of the quantum numbers are the same, but s is different, so the Pauli Principle is not violated. Li is the next largest atom with three electrons. The third electron cannot go in the 1s level because it would have all four quantum numbers, n, l, m, and s, the same as one of the other two electrons. So, the third electron must go into a higher energy level, the 2s orbital. The 2s is the lowest possible level for the third electron. Therefore, rule 2 dictates it will go there.
FIGURE 11.2. Left-hand side: an electron represented by an arrow in an orbital. Right-hand side: two electrons in the same orbital. The s quantum numbers must be +1/2 and -1/2, represented by an up arrow and a down arrow, to obey the Pauli Exclusion principle. The spins are said to be paired.
Rule 3—Hund’s Rule: Don’t Pair Spins If Possible Without Violating Rules 1 and 2
Rule 3 is called Hund’s Rule. Hund’s Rule states that electrons remain unpaired if possible when filling orbitals of identical energy. Figure 11.3 illustrates Hund’s Rule using the 2p orbitals as an example. The first electron, labeled 1 in the figure, is placed in the 2px orbital. This choice is arbitrary since all three 2p orbitals have the same energy. According to Hund’s Rule, the second electron will go into one of the other two 2p orbitals, which have the same energy, so that the spins are not paired. Here it is placed in the 2py orbital. The third electron must go in the 2pz orbital, which is the only choice that obeys Hund’s Rule as well as Rules 1 and 2. Finally, the fourth electron pairs with one of the other electrons. As shown, it is in the 2px. It must be spin down to obey the Pauli Principle, Rule 1.
FIGURE 11.3. Illustration of Hund’s Rule. When filling the 2p orbitals, electron 1 is placed in 2px, electron 2 in 2py, and electron 3 in 2pz. These are all spin up. Electron 4 will have to have its spin down, that is, pair, to avoid violating the Pauli Principle.
Hund’s Rule comes about because it gives electron configurations with the lowest possible energy. Putting two electrons in two different 2p orbitals keeps them further apart on average than putting them in the same orbital. The energy is lowered because keeping the electrons further apart reduces electron-electron repulsion. So what Hund’s Rule says in effect is to put electrons in different orbitals if possible. While the energy reduction associated with keeping the electrons unpaired is significant, the amount the energy is lowered is not large. Therefore, it is better to pair electron 4 in the 2px than to put it unpaired in the next higher energy orbital, the 3s.
THE PERIODIC TABLE OF ELEMENTS
We have laid down the rules for putting electrons in the energy levels shown in Figure 11.1. Now we will use these rules to understand many properties of atoms and the Periodic Table of Elements. In addition, these same rules will be very important in our discussion of molecules presented in subsequent chapters. But first we need to introduce the Periodic Table shown on the next page.
The Periodic Table has one box for each element. The box has the symbol for the element, as well as its atomic number. The atomic number is the number of positively charged protons in the nucleus. For a neutral atom (not a positively or negatively charged ion),