What Is a N+L Rule
The principle of construction, first introduced by Niels Bohr in 1920, and its implementation as a rule (n + l), is a very useful abstraction. Coupled with its physical meaning, it can be part of a powerful mental model that students can rely on to build (and explain) their understanding of the structure of the atom. This type of compound demonstrates the true promise of 3D particle representations of atomic and molecular structures and phenomena. Many more of these stories will be told. Consider titanium (Z = 22). Its electronic configuration is 1s2 2s2 2p6 3s2 3p6 4s2 3d2, which correctly predicts the rule (n+l). If the configuration of the electrons depended solely on orbital energies, we would expect: 1s2 2s2 2p6 3s2 3p6 3d4 – without electrons in the 4s orbital. Up to Z = 20 (calcium), the rule (n + l) (and the structure diagram) correctly predicts: What about the l in the rule (n + l)? As mentioned above, l, the angular momentum quantum number, determines the shape of an orbital. In all orbitals for which n > 1, there are regions, called nodes, where it is extremely unlikely to find an electron. There are two types of nodes: radial and planar (or angular).
Figure 4 shows the radial node in a 2s orbital (l = 0) and a planar node in a 2p orbital (l = 1). Note that radial nodes (Figure 4, center) do not pass through the core, but planar nodes (Figure 4, right) do. The S orbitals (which all have l = 0) contain only radial nodes. All other orbitals (p, d, f, etc., for which > 0) contain both radial and planar nodes. Figure 2 is a version of the diagram that shows the dependence on (n + l) for each orbital, where E represents the relative energy of the orbitals. The orbitals are filled according to the values of E for each orbital: E = 1 for 1s, E = 2 for 2s, E = 3 for 2p and 3s, and so on. According to rule (b) above, if two orbitals have the same E, such as E = 3 for 2p and 3s, the orbital is filled with the lower n (2p) first. Figure 2. Structure diagram illustrating the rule (n+l). Why does the (n + l) rule work? This is not magic and now we will discuss the connection between the rule and its physical meaning.
To understand the connection, we need to start with how the quantum numbers n and l relate to the energy of an orbital. We will use 3D models (actually 2D images of 3D models) of atomic orbitals to demonstrate. [I`m sorry to disappoint those who seek to dive deep into quantum mechanical calculations. These models are visual representations of the results of these calculations.] We all know and use what is known as the construction diagram (Figure 1). It is a mnemonic used to recall the order of “filling” atomic orbitals when constructing ground-state electronic configurations of elements. The representation of this diagram is largely separated from any physical meaning. Here`s what we say to our students: “Remember the board, learn how to use it, and you`re sure to get the right answer. A periodic table in which each row corresponds to a value of n + l (where the values of n and l correspond respectively to the principal and azimuthal quantum numbers) was proposed by Charles Janet in 1928, and in 1930 he made explicit the quantum basis of this model, based on the knowledge of atomic fundamental states determined by the analysis of atomic spectra. This table was called the left step table. Janet “adjusted” some of the actual n+l values of the elements because they did not agree with her energy rule, and he felt that the deviations in question must be due to measurement errors. In this case, the actual values were correct and the n+l energy rule turned out to be an approximation rather than a perfect fit. In recent years, it has been found that the order of filling orbitals in neutral atoms does not always correspond to the order of addition or removal of electrons for a particular atom.
For example, Madelung`s rule in the fourth row of the periodic table indicates that the 4s orbital is occupied before the 3d. The neutral atomic ground state configurations are therefore K = (Ar)4s, Ca = (Ar)4s2, Sc = (Ar)4s23d, etc. However, if a scandium atom is ionized by removing (only) electrons, the configurations are Sc = (Ar)4s23d, Sc+ = (Ar)4s3d, Sc2+ = (Ar)3d. Orbital energies and their sequence depend on the nuclear charge; 4s is less than 3d according to the Madelung rule in K with 19 protons, but 3d is less than in Sc2+ with 21 protons. Madelung`s rule should only be used for neutral atoms. The behavior of electrons is elaborated by other principles of atomic physics such as Hund`s rule and Pauli`s exclusion principle. Hund`s rule states that when several orbitals of the same energy are available, the electrons occupy different orbitals individually before being doubly occupied. When a double assignment occurs, the Pauli exclusion principle requires that electrons occupying the same orbital have different spins (+1/2 and -1/2).
In neutral atoms, the approximate order in which the subshells are filled is given by the n+l rule, also known as: An inorganic chemistry textbook describes the Madelung rule essentially as a rough rule of thumb, albeit with some theoretical justification,[5] based on the Thomas-Fermi model of the atom as a quantum mechanical system with many electrons. [6] The third rule, which limits the allowed combinations of quantum numbers n, l and m, has an important consequence. It forces the number of sublayers in a shell to be equal to the principal quantum number of the shell. For example, the shell n = 3 contains three sublayers: the 3s, 3p and 3d orbitals. The diagram in Figure 1 is the result of these rules. Orbitals in ground-state atomic electronic configurations are filled in order of increase. For the same values, the orbital is usually filled with the lowest first. Here is the principal quantum number and is the angular momentum quantum number , denoted by the code , , , for. The “rule”, also called Madelung`s rule or diagonal rule, applies only with some irregularities. The term “diagonal ruler” refers to the pattern of atomic orbitals shown in the graph. The optional configuration diagram also shows the spins of the electrons in the occupied orbitals.
According to the Pauli exclusion principle, each orbital has a maximum capacity of two electrons of opposite spins. Real electronic configurations are derived from spectroscopic and chemical properties. This demonstration deals with natural elements with atomic numbers from 1 to 92. The (n + l) rule is therefore a way of considering the two main factors that affect the relative energies of atomic orbitals: the size of the orbital (as a function of n) and the number of planar nodes (= l). In cases where (n + l) is the same for two orbitals (e.g. 2p and 3s), the rule (n + l) states that the orbital with lower n has a lower energy. In other words, the size of the orbital has a greater impact on orbital energy than the number of planar nodes. How was this diagram constructed in the first place? It turns out to be a representation of a method of predicting the “fill order” called the Madelung rule, also known as the (n + l) rule. The “n” and “l” in the rule (n + l) are the quantum numbers used to specify the state of a particular electron orbital in an atom. n is the principal quantum number and is related to the size of the orbital. L is the angular momentum quantum number and is related to the shape of the orbital.
When we move from one element to another with the next higher atomic number, a proton and an electron are added to the neutral atom each time. The maximum number of electrons in each shell is 2n2, where n is the principal quantum number. The maximum number of electrons in a subshell (s, p, d or f) is equal to 2 (2l + 1), where l = 0, 1, 2, 3. Thus, these subshells can have a maximum of 2, 6, 10 or 14 electrons. In the ground state, the electron configuration can be constructed by placing the electrons in the lowest available orbitals until the total number of electrons added is equal to the atomic number. Thus, orbitals are filled in ascending order of energy, using two general rules to predict electronic configurations: The rule (n+l) is a pattern. And as we tell our students, all models have limitations. The rule (n + l) works quite well up to Z = 20, calcium (Z is the atomic number). What does “work well” mean? He successfully predicts two things: The first point that can be derived from it is that the rule (n + l) is a model and that it works. Until it is no longer like that. If you choose to teach it as a model and relate it to some of the physical meanings discussed above, this is a great example of how models can be both useful and fail.
