AUFBAU PRINCIPLE Mr. Nderitu . The Aufbau principle (from the German Aufbau meaning "building up, construction": also Aufbau rule or building-up principle ) is used to determine the electron configuration of an atom, molecule or ion . The principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons. As they are added, they assume their most stable conditions ( electron orbitals ) with respect to the nucleus and those electrons already there. According to the principle, electrons fill orbitals starting at the lowest available (possible) energy levels before filling higher levels (e.g. 1s before 2s). The number of electrons that can occupy each orbital is 1 limited by the Pauli exclusion principle . If multiple orbitals of the same energy are available, Hund's rule states that unoccupied orbitals will be filled before occupied orbitals are reused (by electrons having different spins ). The Aufbau Principle - Electronic Structure and the Aufbau Principle 2 Stable atoms have as many electrons as they do protons in the nucleus. The electrons gather around the nucleus in quantum orbitals following four basic rules called the aufbau principle . • no two electrons in the atom will share the same four quantum numbers n, l, m, and s. • electrons will first occupy orbitals of the lowest energy level. • electrons will fill an orbital with the same spin number until the orbital is filled before it will begin to fill of the opposite spin number. • electrons will fill orbitals by the sum of the quantum numbers n and l. Orbitals with equal values of ( n+l) will fill with the lower n values first. 3 The second and fourth rules are basically the same. The graphic shows the relative energy levels of the different orbitals. An example of rule four would be the 2p and 3s orbitals. A 2p orbital is n=2 and l=2 and a 3s orbital is n=3 and l=1. ( n+l) = 4 in both cases, but the 2p orbital has the lower energy or lower n value and will get filled before the 3s shell. 4 Probably the worst way to use the aufbau principle to figure the fill order of an atom's orbitals is to try and memorize the order by brute force. 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p 8s Fortunately, there is a much simpler method to get this order. First, write a column of 's' orbitals from 1 to 8. Second, write a second column for the 'p' orbitals starting at n=2. (1p is not an orbital combination allowed by quantum mechanics) Third, write a column for the 'd' orbitals starting at n=3. 5 Fourth, write a final column for 4f and 5f. There are no elements that will need a 6f or 7f shell to fill. Finally, read the chart by running the diagonals starting from 1s. The graphic shows this table and the arrows follow the path to follow. Now that the order of orbitals are known to fill, all that remains is memorizing how large each orbital is. • s orbitals have 1 possible value of m to hold 2 electrons • p orbitals have 3 possible value of m to hold 6 electrons • d orbitals have 5 possible value of m to hold 10 electrons • f orbitals have 7 possible value of m to hold 14 electrons 6 This is all that is needed to determine the electron configuration of a stable atom of an element. For an example, take the element nitrogen. Nitrogen has seven protons and therefore seven electrons. The first orbital to fill is the 1s orbital. An s orbital holds two electrons, so five electrons are left. The next orbital is the 2s orbital and holds the next two. The final three electrons will go to the 2p 7 orbitalwhich can hold up to six electrons . Question: Determine the electron configuration of silicon . Solution: Silicon is element 14. It has 14 protons and 14 electrons. The lowest energy level of an atom is filled first. The arrows in the graphic show the s quantum numbers, spin 'up' and spin 'down'. 8 Step A shows the first two electrons filling the 1s orbital and leaving 12 electrons. Step B shows the next two electrons filling the 2s orbital leaving 10 electrons. The 2p orbital is the next available energy level and can hold six electrons. Step C shows these six electrons and leaves us with four electrons. Step D fills the next lowest energy level, 3s with two electrons. Step E shows the remaining two electrons starting to fill the 3p orbital. Remember one of the rules of the aufbau principle is that the orbitals are filled by one type of spin before the opposite spin starts to appear. In this case, the two spin up electrons are placed in the first two empty slots, but the actual order is arbitrary. It could have been the second and third slot or the first and third. 9 Answer The electron configuration of silicon is 1s 22s 2p63s 23p 2. 10 .